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Lampiran 1 Tabel Migran Keluar dari Wilayah Jawa Bali menuju Luar Jawa Bali

No Umur Migran Penduduk ASMR Est-ASMR

1 5 9 097 2 579 971 0,003526009 0,003016360 2 6 6 105 2 291 242 0,002664494 0,002977662 3 7 6 491 2 429 198 0,002672075 0,002938992 4 8 5 683 2 450 659 0,002318968 0,002900352 5 9 5 685 2 580 915 0,002202707 0,002861742 6 10 9 290 2 617 751 0,003548848 0,002823161 7 11 5 677 2 418 094 0,002347717 0,002784610 8 12 6 064 2 504 294 0,002421441 0,002746088 9 13 5 831 2 471 306 0,002359481 0,002707596 10 14 6 967 2 409 006 0,002892064 0,002669133 11 15 7 560 2 393 703 0,003158287 0,002630699 12 16 7 220 2 235 056 0,003230344 0,002594333 13 17 7 367 2 334 004 0,003156378 0,002879677 14 18 11 785 2 286 567 0,005154015 0,005161645 15 19 20 094 2 275 315 0,008831305 0,008549214 16 20 23 966 2 508 967 0,009552138 0,010588795 17 21 23 541 2 231 381 0,010549969 0,011113474 18 22 36 275 2 468 406 0,014695719 0,010819981 19 23 24 181 2 393 253 0,010103821 0,010204579 20 24 19 125 2 337 881 0,008180485 0,009502131 21 25 19 852 2 544 259 0,007802665 0,008807181 22 26 14 211 2 154 723 0,006595279 0,008153427 23 27 17 339 2 298 340 0,007544141 0,007550346 24 28 14 314 2 209 360 0,006478799 0,006998264 25 29 17 212 2 219 593 0,007754575 0,006494286 26 30 12 589 2 438 511 0,005162577 0,006034566 27 31 11 924 1 943 451 0,006135478 0,005615154 28 32 10 596 2 299 615 0,004607728 0,005232299 29 33 9 295 2 113 451 0,004398020 0,004882540 30 34 13 014 2 082 062 0,006250534 0,004562720 31 35 9 898 2 479 842 0,003991383 0,004269977 32 36 12 883 2 100 609 0,006132983 0,004001721 33 37 7 100 2 022 862 0,003509879 0,003755613 34 38 5 188 1 820 420 0,002849892 0,003529548 35 39 7 159 1 958 002 0,003656278 0,003321641 36 40 9 088 2 336 852 0,003888993 0,003130220 37 41 5 711 1 823 031 0,003132695 0,002953833 38 42 5 020 1 941 598 0,002585499 0,002791254 39 43 2 552 1 614 237 0,001580933 0,002641499 40 44 3 067 1 612 863 0,001901587 0,002503841 41 45 4 346 2 106 107 0,002063523 0,002377814 42 46 5 387 1 555 540 0,003463106 0,002263199 43 47 4 025 1 628 652 0,002471369 0,002159994 44 48 1 981 1 412 238 0,001402738 0,002068343 45 49 3 194 1 364 491 0,002340800 0,001988452 46 50 2 278 1 601 389 0,001422515 0,001920476 47 51 1 736 1 226 258 0,001415689 0,001864410 48 52 3 564 1 381 899 0,002579060 0,001819983

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No Umur Migran Penduduk ASMR Est-ASMR 49 53 1 289 1 141 460 0,001129256 0,001786583 50 54 1 639 1 180 109 0,001388855 0,001763213 51 55 3 182 1 268 212 0,002509044 0,001748496 52 56 1 263 957 047 0,001319684 0,001740716 53 57 1 221 921 436 0,001325106 0,001737901 54 58 2 175 811 254 0,002681035 0,001737930 55 59 1 858 924 595 0,002009528 0,001738649 56 60 383 893 888 0,000428465 0,001737991 57 61 2 341 616 124 0,003799560 0,001734084 58 62 2 394 881 732 0,002715111 0,001725331 59 63 662 749 523 0,000883228 0,001710471 60 64 542 695 468 0,000779331 0,001688613 61 65 1 500 929 118 0,001614434 0,001659233 62 66 686 510 925 0,001342663 0,001622161 63 67 937 565 186 0,001657861 0,001577542 64 68 586 446 865 0,001311358 0,001525786 65 69 0 459 761 0 0,001467513 66 70 455 661 909 0,000687406 0,001403496 67 71 316 404 776 0,000780679 0,001334607 68 72 784 447 278 0,001752825 0,001261761 69 73 388 330 030 0,001175651 0,001185880 70 74 599 316 642 0,001891726 0,001107852 71 75 1 481 403 074 0,003674263 0,001028510 72 76 703 214 305 0,003280371 0,000948605 73 77 218 201 176 0,001083628 0,000868801 74 78 0 189 643 0 0,000789668 75 79 0 140 191 0 0,000711678 76 80 0 201 702 0 0,000635209 77 81 0 105 056 0 0,000560554 78 82 0 117 430 0 0,000487927 79 83 0 74 283 0 0,000417469 80 84 0 70 154 0 0,000349263 81 85 0 88 507 0 0,000283337 82 86 0 36 315 0 0,000219680 83 87 0 33 808 0 0,000158245 84 88 0 19 818 0 9,89579E-05 85 89 0 19 946 0 4,17252E-05 86 90 0 33 374 0 -1,35603E-05 87 91 0 9 114 0 -6,70156E-05 88 92 0 11 311 0 -0,000118763 89 93 0 7 651 0 -0,000168925 90 94 0 7 439 0 -0,000217625 91 95 0 39 569 0 -0,000264982 510 129 120 644 428 0,25790605 0,257907392

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Lampiran 2 Tabel Migran Keluar dari Wilayah Luar Jawa Bali menuju Jawa Bali:

No Umur Migran Penduduk ASMR Est-ASMR

1 5 10 918 1 952 934 0,005590563 0,005327126 2 6 8 244 1 764 974 0,004670890 0,004968978 3 7 7 910 1 837 577 0,004304582 0,004632519 4 8 7 711 1 798 657 0,004287088 0,004316438 5 9 8 380 1 877 818 0,004462626 0,004019499 6 10 6 816 1 919 751 0,003550460 0,003740544 7 11 5 400 1 677 019 0,003219999 0,003478483 8 12 5 639 1 834 519 0,003073830 0,003232305 9 13 7 034 1 703 297 0,004129638 0,003002224 10 14 4 953 1 751 059 0,002828574 0,002812288 11 15 4 125 1 776 325 0,002322210 0,002829715 12 16 6 188 1 639 852 0,003773511 0,003489961 13 17 9 071 1 686 575 0,005378356 0,005222410 14 18 9 822 1 627 861 0,006033685 0,007961433 15 19 19 016 1 541 663 0,012334732 0,011128255 16 20 26 205 1 749 471 0,014978814 0,014044176 17 21 22 914 1 432 016 0,016001218 0,016267994 18 22 28 743 1 476 833 0,019462593 0,017661132 19 23 22 357 1 437 214 0,015555791 0,018292537 20 24 24 219 1 409 757 0,017179556 0,018322260 21 25 34 493 1 781 108 0,019366035 0,017923144 22 26 21 770 1 334 453 0,016313800 0,017243733 23 27 24 920 1 419 999 0,017549308 0,016397666 24 28 19 725 1 361 560 0,014487059 0,015465842 25 29 19 994 1 356 698 0,014737252 0,014502964 26 30 21 851 1 675 839 0,013038842 0,013544464 27 31 13 658 1 197 737 0,011403171 0,012612299 28 32 15 534 1 356 872 0,011448390 0,011719328 29 33 16 280 1 154 313 0,014103627 0,010872417 30 34 10 240 1 158 178 0,008841473 0,010074576 31 35 19 303 1 623 422 0,011890316 0,009326390 32 36 12 775 1 174 653 0,010875552 0,008626961 33 37 8 352 1 145 716 0,007289765 0,007974535 34 38 8 689 1 051 441 0,008263897 0,007366907 35 39 5 658 1 077 133 0,005252833 0,006801699 36 40 7 944 1 454 154 0,005462970 0,006276569 37 41 5 216 947 247 0,005506484 0,005789366 38 42 5 606 1 043 044 0,005374653 0,005338270 39 43 4 007 878 827 0,004559487 0,004921901 40 44 2 933 838 049 0,003499795 0,004539402 41 45 5 944 1 268 418 0,004686152 0,004190457 42 46 2 826 810 845 0,003485253 0,003875245 43 47 2 716 816 295 0,003327229 0,003594294 44 48 2 239 740 772 0,003022522 0,003348264 45 49 1 668 679 460 0,002454891 0,003137663 46 50 2 072 1 003 555 0,002064660 0,002962529 47 51 1 288 623 761 0,002064893 0,002822151 48 52 1 033 674 822 0,001530774 0,002714851

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No Umur Migran Penduduk ASMR Est-ASMR 49 53 2 480 560 463 0,004424913 0,002637872 50 54 1 844 547 348 0,003368972 0,002587393 51 55 2 398 671 254 0,003572418 0,002558677 52 56 1 275 440 905 0,002891779 0,002546312 53 57 871 431 363 0,002019181 0,002544528 54 58 755 402 973 0,001873575 0,002547547 55 59 1 139 433 140 0,002629635 0,002549914 56 60 2 071 528 627 0,003917696 0,002546785 57 61 939 275 416 0,003409388 0,002534152 58 62 352 370 407 0,000950306 0,002508975 59 63 438 333 517 0,001313276 0,002469238 60 64 601 267 125 0,002249883 0,002413926 61 65 344 439 017 0,000783569 0,002342943 62 66 837 198 796 0,004210346 0,002256983 63 67 602 207 622 0,002899500 0,002157374 64 68 332 180 543 0,001838897 0,002045912 65 69 164 174 332 0,000940734 0,001924701 66 70 797 318 589 0,002501656 0,001796002 67 71 156 129 803 0,001201821 0,001662105 68 72 155 155 492 0,000996836 0,001525223 69 73 81 119 812 0,000676059 0,001387415 70 74 275 105 596 0,002604265 0,001250529 71 75 493 170 694 0,002888209 0,001116168 72 76 146 76 108 0,001918327 0,000985674 73 77 40 65 110 0,000614345 0,000860129 74 78 0 64 100 0 0,000740363 75 79 0 49 340 0 0,000626977 76 80 0 102 419 0 0,000520361 77 81 0 33 455 0 0,000420725 78 82 0 36 574 0 0,000328128 79 83 0 25 429 0 0,000242500 80 84 0 31 114 0 0,000163668 81 85 0 45 264 0 9,13854E-05 82 86 0 13 784 0 2,53447E-05 83 87 0 12 706 0 -3,48001E-05 84 88 0 8 065 0 -8,94199E-05 85 89 0 9 257 0 -0,000138898 86 90 0 17 051 0 -0,000183620 87 91 0 5 158 0 -0,000223965 88 92 0 4 833 0 -0,000260303 89 93 0 5 208 0 -0,000292986 90 94 0 3 056 0 -0,000322348 91 95 0 21 300 0 -0,000348701 563 984 73 635 708 0,441735387 0,441735050

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Lampiran 3 Data Jumlah Penduduk Jawa Bali dan Luar Jawa Bali Menurut Kelompok Umur (SUPAS, 2005)

Kelompok Umur Jawa-Bali Luar Jawa-Bali Jumlah 0 - 4 10 759 353 8 335 798 19 095 151 5 - 9 12 331 985 9 231 960 21 563 945 10 - 14 12 420 451 8 885 645 21 306 096 15 - 19 11 524 645 8 272 276 19 796 921 20 - 24 11 939 888 7 505 291 19 445 179 25 - 29 11 426 275 7 253 818 18 680 093 30 - 34 10 877 090 6 542 939 17 420 029 35 - 39 10 381 735 6 072 365 16 454 100 40 - 44 9 328 581 5 161 321 14 489 902 45 - 49 8 067 028 4 315 790 12 382 818 50 - 54 6 531 115 3 409 949 9 941 064 55 - 59 4 882 544 2 379 635 7 262 179 60 - 64 3 836 735 1 775 092 5 611 827 65 - 69 2 911 855 1 200 310 4 112 165 70 - 74 2 160 635 829 292 2 989 927 75-79 1 148 389 425 352 1 573 741 80-84 568 625 228 991 797 616 85+ 306 852 145 682 452 534 131 403 781 81 971 506 213 375 287

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Lampiran 4. Data Penduduk Wanita Usia Reproduksi Menurut Kelompok Umur (SUPAS, 2005)

Umur Jumlah Wanita Proporsi Wanita

10-14 10 349 448 0,485750557 15-19 9 693 143 0,489628817 20-24 9 911 219 0,509700579 25-29 9 601 769 0,514010771 30-34 8 876 409 0,509551907 35-39 8 268 040 0,502491172 40-44 7 216 349 0,498026074 45-49 6 079 149 0,490934212

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Lampiran 5 Data Angka Harapan Hidup (e0) penduduk Indonesia menurut propinsi dan jenis kelamin (SUPAS 2005)

Kode

Prop Propinsi

Jenis Kelamin Total Laki-laki Wanita 11 NAD 65,1 69,03 67,13 12 Sumatera Utara 64,17 68,06 66,17 13 Sumatera Barat 62,06 65,87 64,02 14 Riau 63,23 67,08 65,21 15 Jambi 62,06 65,87 64,02 16 Sumatera Selatan 62,06 65,87 64,02 17 Bengkulu 62,06 65,87 64,02 18 Lampung 63,23 67,08 65,21

19 Kep. Bangka Belitung 62,06 65,87 64,02 31 DKI Jakarta 69,12 73,03 71,13 32 Jawa Barat 61,13 64,9 63,07 33 Jawa Tengah 64,17 68,06 66,17 34 DI Yogyakarta 69,12 73,03 71,13 35 Jawa Timur 63,23 67,08 65,21 36 Banten 59,14 62,81 61,03 51 Bali 66,04 70,01 68,08

52 Nusa Tenggara Barat 54,41 57,79 56,15 53 Nusa Tenggara Timur 61,13 64,9 63,07 61 Kalimantan Barat 61,13 64,9 63,07 62 Kalimantan Tengah 63,23 67,08 65,21 63 Kalimantan Selatan 58,28 61,91 60,15 64 Kalimantan Timur 65,1 69,03 67,13 71 Sulawesi Utara 68,23 72,17 70,26 72 Sulawesi Tengah 59,14 62,81 61,03 73 Sulawesi Selatan 61,13 64,9 63,07 74 Sulawesi Tenggara 62,06 65,87 64,02 75 Gorontalo 61,13 64,9 63,07 81 Maluku 60,25 63,97 62,16 82 Maluku Utara 57,24 60,8 59,07 94 Papua 61,13 64,9 63,07

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Lampiran 6 Data Angka Kelahiran Menurut Umur Wanita, Daerah, Periode, dan Propinsi (SUPAS, 2005)

Kode

Prop Referensi Waktu

Umur Wanita (Kelahiran per 1000 Wanita) _TFR 15-19 20-24 25-29 30-34 35-39 40-44 45-49 11 NAD 23 99 128 104 58 22 8 2,21 12 Sumatera Utara 21 114 155 123 63 22 8 2,52 13 Sumatera Barat 14 92 155 138 82 30 7 2,59 14 Riau 20 96 147 118 63 25 10 2,39 15 Jambi 31 106 131 102 54 22 9 2,28 16 Sumatera Selatan 28 105 136 113 65 31 18 2,48 17 Bengkulu 26 114 145 113 59 21 8 2,43 18 Lampung 29 108 133 106 61 28 12 2,37 19 Babel 32 111 125 96 48 20 6 2,19 31 DKI Jakarta 20 73 98 78 39 14 5 1,63 32 Jawa Barat 41 109 127 100 57 25 10 2,35 33 Jawa Tengah 25 91 113 88 48 20 7 1,95 34 DI Yogyakarta 10 58 93 75 36 11 3 1,43 35 Jawa Timur 25 81 96 71 35 14 6 1,64 36 Banten 35 107 125 101 57 27 15 2,33 51 Bali 27 95 112 75 30 11 5 1,77 52 NTB 46 123 131 106 64 33 14 2,58 53 NTT 18 94 147 132 81 34 15 2,63 61 Kalimantan Barat 30 106 133 108 64 27 10 2,39 62 Kalimantan Tengah 51 119 121 92 53 23 10 2,34 63 Kalimantan Selatan 39 102 112 87 47 18 7 2,06 64 Kalimantan Timur 36 112 129 99 53 20 8 2,28 71 Sulawesi Utara 36 99 105 80 40 15 6 1,9 72 Sulawesi Tengah 31 101 122 101 53 19 8 2,17 73 Sulawesi Selatan 27 89 119 106 64 27 10 2,21 74 Sulawesi Tenggara 37 125 152 124 69 28 11 2,73 75 Gorontalo 43 120 123 98 51 19 5 2,3 81 Maluku 27 105 131 118 68 31 16 2,48 82 Maluku Utara 33 110 129 110 65 31 14 2,46 94 Papua 40 129 146 117 66 31 18 2,73

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Lampiran 7 Perhitungan Life Table Uniregional

Perhitungan life table di mulai dengan penentuan nilai l(x) berdasarkan Brass logit. Dari tabel l(x) diketahui :

l(x) = jumlah orang yang bertahan hidup dari lahir hingga tepat umur x l(0) = 100 000 (asumsi awal) l(5) = 95002,4286 l(1) = 96278,0714 l(10) = 94620,7143 d(x) = l(x) – l(x+1) d(0) = l(0) – l(5) = 100 000 – 95002,4286 = 4997,5714 q(x) = q(x) = . = 0,0500 L(0) = L(0)+ L(1) = [0,3×l(0) + 0,7×l(1)] + 4 [0,4×l(1) + 0,6×l(5)] = [ 0,3 (100000) + 0,7 ( 96278,0714)] + 4 [ 0,4 (96278,0714) + 0,6 ( 95002,4286)] = 479445,3929 L(5) = 5 [0,5×l(5) + 0,5×l(10)] = 5 [ 0,5 (95002,4286) + 0,5 (94620,7143)] = 474057,8571 T(x) = ∑ = 6772067,3571 e(x) = e(0) = = , = 67,7207 m(x) = m(x) = = , , = 0,0104

Proses perhitungan dilakukan dengan cara yang serupa hingga diperoleh tabel sebagai berikut:

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Life Table untuk wilayah Jawa Bali Umur (x) qx lx dx Lx Tx ex mx 0-4 0,0500 100000,0000 4997,5714 479445,3929 6772067,3571 67,7207 0,0104 5-9 0,0040 95002,4286 381,7143 474057,8571 6292621,9643 66,2364 0,0008 10-14 0,0075 94620,7143 707,0000 471336,0714 5818564,1071 61,4936 0,0015 15-19 0,0071 93913,7143 666,9286 467901,2500 5347228,0357 56,9377 0,0014 20-24 0,0095 93246,7857 886,8571 464016,7857 4879326,7857 52,3270 0,0019 25-29 0,0112 92359,9286 1031,5714 459220,7143 4415310,0000 47,8055 0,0022 30-34 0,0131 91328,3571 1193,4286 453658,2143 3956089,2857 43,3172 0,0026 35-39 0,0154 90134,9286 1387,1429 447206,7857 3502431,0714 38,8576 0,0031 40-44 0,0184 88747,7857 1636,8571 439646,7857 3055224,2857 34,4259 0,0037 45-49 0,0233 87110,9286 2029,5000 430480,8929 2615577,5000 30,0258 0,0047 50-54 0,0332 85081,4286 2822,7143 418350,3571 2185096,6071 25,6824 0,0067 55-59 0,0480 82258,7143 3947,2143 401425,5357 1766746,2500 21,4779 0,0098 60-64 0,0770 78311,5000 6029,8571 376482,8571 1365320,7143 17,4345 0,0160 65-69 0,1245 72281,6429 8996,1429 338917,8571 988837,8571 13,6803 0,0265 70-74 0,2128 63285,5000 13467,6429 282758,3929 649920,0000 10,2697 0,0476 75-79 0,3553 49817,8571 17699,6429 204840,1786 367161,6071 7,3701 0,0864 80-84 0,5469 32118,2143 17566,2143 116675,5357 162321,4286 5,0539 0,1506 85+ 0,7453 14552,0000 10845,6429 45645,8929 45645,8929 3,1367 0,2376

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Life Table untuk wilayah Luar Jawa Bali Umur (x) qx lx dx Lx Tx ex mx 0-4 0,0665 100000,0000 6647,5000 472972,0500 6500193,137 65,0019 0,0141 5-9 0,0059 93352,5000 554,3913 465376,5217 6027221,087 64,5641 0,0012 10-14 0,0092 92798,1087 851,2174 461862,5000 5561844,565 59,9349 0,0018 15-19 0,0091 91946,8913 832,6739 457652,7717 5099982,065 55,4666 0,0018 20-24 0,0120 91114,2174 1097,4565 452827,4457 4642329,293 50,9507 0,0024 25-29 0,0140 90016,7609 1263,4565 446925,1630 4189501,848 46,5414 0,0028 30-34 0,0163 88753,3043 1445,4783 440152,8261 3742576,685 42,1683 0,0033 35-39 0,0190 87307,8261 1660,0217 432389,0761 3302423,859 37,8251 0,0038 40-44 0,0226 85647,8044 1931,9565 423409,1304 2870034,783 33,5097 0,0046 45-49 0,0282 83715,8478 2359,3261 412680,9239 2446625,652 29,2254 0,0057 50-54 0,0396 81356,5217 3219,1739 398734,6739 2033944,728 25,0004 0,0081 55-59 0,0562 78137,3478 4391,7609 379707,3370 1635210,054 20,9274 0,0116 60-64 0,0879 73745,5869 6488,3913 352506,9565 1255502,717 17,0248 0,0184 65-69 0,1376 67257,1956 9252,3696 313155,0543 902995,761 13,4260 0,0295 70-74 0,2253 58004,8261 13069,0435 257351,5217 589840,707 10,1688 0,0508 75-79 0,3589 44935,7826 16131,8478 184349,2935 332489,185 7,3992 0,0875 80-84 0,5351 28803,9348 15412,2391 105489,0761 148139,891 5,1430 0,1461 85+ 0,7261 13391,6956 9723,0652 42650,8152 42650,815 3,1849 0,2279

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Lampiran 8 Hasil perhitungan tingkat migrasi menurut kelompok umur

Tingkat migrasi menurut kelompok umur dari Jawa Bali ke Luar Jawa Bali:

M12(0-4) = , M12(5-9) = , dan seterusnya, dan jumlah tingkat migrasi dari Luar Jawa Bali ke Jawa Bali:

M21(0-4) = , M21(5-9) = , dan seterusnya, Dengan M(x) adalah model skedul migrasi pada masing-masing wilayah.

Proses perhitungan dibantu program mathematica 6.0 sehingga diperoleh hasil sebagai berikut: Umur M12 M21 0-4 0,00311 0,00635 5-9 0,00292 0,00449 10-14 0,00273 0,00315 15-19 0,00514 0,00721 20-24 0,01030 0,01736 25-29 0,00732 0,01588 30-34 0,00509 0,01134 35-39 0,00366 0,00771 40-44 0,00273 0,00516 45-49 0,00212 0,00350 50-54 0,00181 0,00270 55-59 0,00174 0,00255 60-64 0,00171 0,00248 65-69 0,00155 0,00209 70-74 0,00122 0,00146 75-79 0,00083 0,00081 80-84 0,00045 0,00029 85 + 0,00013 0,00006

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Lampiran 9 Perhitungan Matriks Peluang Transisi P(x)

Perhitungan matriks peluang transisi P(x) yang melibatkan data migrasi dan tingkat kematian adalah :

P(x) = [ I + A(x) ]-1 [I + A(x) ] A(0) = = 0,01354_0,00311 _0,020410,00635 M11 (0) = Mortalitas mjb + M12 = 0,01042 + 0,00311 = 0,01354 M22 (0)= Mortalitas mljb + M21 = 0,01405 + 0,00635 = 0,02041 P(0) = [ I + A(0) ]-1 [I - A(0) ] = [ I + 0,01354 0,00635 0,00311 0,02041 ]-1 [I - 0,013540,00311 0,020410,00635 ] = 0,93475 0,02925_{0,01433 0,90312}

Proses perhitungan dilakukan dengan cara yang serupa hingga diperoleh tabel sebagai berikut: Umur M12 M11 M21 M22 p12 p11 p21 p22 0-4 0,00311 0,01354 0,00635 0,02041 0,01433 0,93475 0,02925 0,90312 5-9 0,00292 0,00372 0,00449 0,00568 0,01426 0,98171 0,02195 0,97214 10-14 0,00273 0,00423 0,00315 0,00500 0,01333 0,97919 0,01541 0,97543 15-19 0,00514 0,00656 0,00721 0,00903 0,02473 0,96815 0,03468 0,95629 20-24 0,01030 0,01221 0,01736 0,01978 0,04766 0,94277 0,08034 0,90772 25-29 0,00732 0,00957 0,01588 0,01870 0,03417 0,95461 0,07411 0,91196 30-34 0,00509 0,00772 0,01134 0,01462 0,02408 0,96281 0,05368 0,93012 35-39 0,00366 0,00676 0,00771 0,01155 0,01749 0,96708 0,03685 0,94420 40-44 0,00273 0,00645 0,00516 0,00972 0,01311 0,96842 0,02480 0,95270 45-49 0,00212 0,00684 0,00350 0,00922 0,01021 0,96647 0,01684 0,95502 50-54 0,00181 0,00856 0,00270 0,01078 0,00864 0,95815 0,01288 0,94759 55-59 0,00174 0,01157 0,00255 0,01411 0,00817 0,94381 0,01196 0,93188 60-64 0,00171 0,01773 0,00248 0,02088 0,00779 0,91517 0,01126 0,90082 65-69 0,00155 0,02809 0,00209 0,03164 0,00669 0,86880 0,00906 0,85344 70-74 0,00122 0,04885 0,00146 0,05224 0,00481 0,78234 0,00574 0,76899 75-79 0,00083 0,08724 0,00081 0,08831 0,00779 0,91517 0,01126 0,90082 80-84 0,00045 0,15101 0,00029 0,14639 0,00121 0,45188 0,00077 0,46414 85+ 0,00013 0,23773 0,00006 0,22791 0,00026 0,25444 0,00011 0,27406

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Lampiran 10 Perhitungan Life Table Multiregional Misalkan diketahui : 10l1(0) = 20l2(0) = 100000 10l2(0) = 20l1(0) = 0 Maka diperoleh : 10l1(5) = p11(0) 10l1(0) + p21(0) 10l2(0) = 0,93475 (100000) + 0,02925 (0) = 93475,12366 10l2(5) = p12(0) 10l1(0) + p22(0) 10l2(0) = 0,01433 (100000) + 0,90312 (0) = 1432,74142 10l(5) = 10l1(5) + 10l2(5) = 93475,12366 + 1432,74142 = 94907,86508 20l1(5) = p11(0) 20l1(0) + p21(0) 20l2(0) = 0,93475 (0) + 0,02925 (100000) = 2924,5825 20l2(5) = p12(0) 20l1(0) + p22(0) 20l2(0) = 0,01433 (0) + 0,90312 (100000) = 90312,2322 20l(5) = 20l1(5) + 20l2(5) = 2924,5825 + 90312,2322 = 93236,8148 10L1(0) = [10l1(0) + 10l1(5)] = [ 100000 + 93475,12366] = 483687,8092 10L2(0) = [10l2(0) + 10l2(5)] = [ 0 + 1432,74142] = 3581,8535 20L1(0) = [20l1(0) + 20l1(5)] = [ 0 + 2924,5825] = 7311,4563 20L2(0) = [20l2(0) + 20l2(5)] = [ 100000 + 90312,2322] = 475780,5806 qi(x) = 1-pii(x) –pij(x) q1(0) = 1-p11(0) –p12(0) = 1 – 0,93475 – 0,01433 = 0,05092 q2(0) = 1-p22(0) –p21(0) = 1 – 0,90312 – 0,02925 = 0,06763 ixTj(x) = ∑ 10T1(0) = ∑ 0 = 6067947,2736 10T2(0) = ∑ 0 = 804313,1547 20T1(0) = ∑ 0 = 1436301,7650 20T2(0) = ∑ 0 = 5214570,9523

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ixej(x) =

10e1(0) = = , = 60,6795

10e2(0) = = , = 8,0431

20e1(0) = = , = 14,363

20e2(0) = = , = 52,1457

Proses perhitungan dilakukan dengan cara yang serupa hingga diperoleh tabel sebagai berikut:

(19)

Life Table Multiregional untuk wilayah Jawa Bali Umur p11(x) p12(x) q1(x) 10l1(x) 10l2(x) l1(x) 10L1(x) 10L2(x) 10T1(x) 10T2(x) 10e1(x) 10e2(x) 10e(x) 0‐4 0,93475 0,01433 0,05092 100000 0 100000 483687,8092 3581,85354 6067947,2736 804313,1547 60,6795 8,0431 68,7226 5‐9 0,98171 0,01426 0,00403 93475,12366 1432,74142 94907,86508 463179,1433 10396,83173 5584259,4645 800731,3011 58,8387 8,4369 67,2757 10‐14 0,97919 0,01333 0,00748 91796,53364 2725,99127 94522,52492 454312,1428 16520,70162 5121080,3212 790334,4694 54,1784 8,3613 62,5397 15‐19 0,96815 0,02473 0,00713 89928,32346 3882,28937 93810,61284 442816,9664 24546,50924 4666768,1785 773813,7678 49,7467 8,2487 57,9954 20‐24 0,94277 0,04766 0,00957 87198,46310 5936,31432 93134,77743 424708,0974 38701,97788 4223951,2120 749267,2585 45,3531 8,0450 53,3981 25‐29 0,95461 0,03417 0,01122 82684,77587 9544,47683 92229,25270 405810,0643 52684,86841 3799243,1146 710565,2807 41,1935 7,7043 48,8978 30‐34 0,96281 0,02408 0,01311 79639,24985 11529,47053 91168,72039 392339,9849 60427,20386 3393433,0503 657880,4122 37,2215 7,2161 44,4375 35‐39 0,96708 0,01749 0,01542 77296,74412 12641,41101 89938,15513 381287,7338 64824,17281 3001093,0653 597453,2084 33,3684 6,6429 40,0113 40‐44 0,96842 0,01311 0,01847 75218,34941 13288,25811 88506,60752 370977,7412 67334,21954 2619805,3315 532629,0356 29,6001 6,0180 35,6181 45‐49 0,96647 0,01021 0,02332 73172,74707 13645,42970 86818,17677 360303,6447 68560,69897 2248827,5903 465294,8160 25,9027 5,3594 31,2621 50‐54 0,95815 0,00864 0,03320 70948,71079 13778,84989 84727,56068 347764,8630 68621,75965 1888523,9457 396734,1171 22,2894 4,6825 26,9718 55‐59 0,94381 0,00817 0,04802 68157,23440 13669,85397 81827,08837 331621,3491 67412,74836 1540759,0827 328112,3574 18,8295 4,0098 22,8393 60‐64 0,91517 0,00779 0,07704 64491,30523 13295,24537 77786,55060 309153,4352 64435,52475 1209137,7336 260699,6091 15,5443 3,3515 18,8958 65‐69 0,86880 0,00669 0,12451 59170,06884 12478,96453 71649,03337 276725,4437 58812,29348 899984,2985 196264,0843 12,5610 2,7392 15,3003 70‐74 0,78234 0,00481 0,21284 51520,10862 11045,95286 62566,06149 229724,9517 49470,50701 623258,8548 137451,7908 9,9616 2,1969 12,1585 75‐79 0,91517 0,00779 0,07704 40369,87206 8742,24994 49112,12200 193533,7938 42329,73727 393533,9031 87981,2838 8,0130 1,7914 9,8044 80‐84 0,45188 0,00121 0,54691 37043,64548 8189,64497 45233,29044 134472,9779 30088,95902 200000,1093 45651,5466 4,4215 1,0092 5,4308 85+ 0,25444 0,00026 0,74530 16745,54569 3845,93864 20591,48433 52514,6330 12260,84822 65527,1313 15562,5875 3,1822 0,7558 3,9380

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Life Table Multiregional untuk wilayah Luar Jawa Bali Umur P22(x) P21(x) q2(x) 20l1(x) 20l2(x) l2(x) 20L1(x) 20L2(x) 20T1(x) 20T2(x) 20e1(x) 20e2(x) 20e(x) 0‐4 0,90312 0,02925 0,06763 0 100000,0000 100000,0000 7311,4563 475780,5806 1436301,7650 5214570,9523 14,3630 52,1457 66,5087 5‐9 0,97214 0,02195 0,00592 2924,5825 90312,2322 93236,8148 19444,0674 445374,4568 1428990,3087 4738790,3717 15,3265 50,8253 66,1518 10‐14 0,97543 0,01541 0,00916 4853,0445 87837,5505 92690,5949 27397,0062 433953,7769 1409546,2412 4293415,9149 15,2070 46,3199 61,5269 15‐19 0,95629 0,03468 0,00902 6105,7580 85743,9603 91849,7183 37477,3282 419728,5344 1382149,2350 3859462,1380 15,0479 42,0193 57,0673 20‐24 0,90772 0,08034 0,01194 8885,1732 82147,4535 91032,6267 59653,1091 392844,7812 1344671,9068 3439733,6036 14,7713 37,7857 52,5570 25‐29 0,91196 0,07411 0,01393 14976,0704 74990,4590 89966,5294 87074,8519 359726,4285 1285018,7977 3046888,8224 14,2833 33,8669 48,1502 30‐34 0,93012 0,05368 0,01620 19853,8704 68900,1124 88753,9827 106669,8869 333659,1191 1197943,9458 2687162,3939 13,4974 30,2765 43,7739 35‐39 0,94420 0,03685 0,01895 22814,0844 64563,5353 87377,6197 118141,7500 314808,6981 1091274,0589 2353503,2748 12,4892 26,9349 39,4240 40‐44 0,95270 0,02480 0,02251 24442,6156 61359,9439 85802,5595 124087,5175 300344,2273 973132,3089 2038694,5767 11,3415 23,7603 35,1018 45‐49 0,95502 0,01684 0,02814 25192,3914 58777,7470 83970,1384 126323,8582 287922,7636 849044,7914 1738350,3494 10,1113 20,7020 30,8133 50‐54 0,94759 0,01288 0,03953 25337,1519 56391,3585 81728,5103 125851,1048 275115,7258 722720,9332 1450427,5858 8,8429 17,7469 26,5898 55‐59 0,93188 0,01196 0,05616 25003,2901 53654,9319 78658,2219 123108,7125 259648,2382 596869,8284 1175311,8600 7,5881 14,9420 22,5302 60‐64 0,90082 0,01126 0,08792 24240,1949 50204,3634 74444,5584 117473,8134 239045,3211 473761,1158 915663,6217 6,3639 12,2999 18,6639 65‐69 0,85344 0,00906 0,13750 22749,3304 45413,7650 68163,0954 107313,2276 210809,7403 356287,3024 676618,3007 5,2270 9,9265 15,1534 70‐74 0,76899 0,00574 0,22527 20175,9606 38910,1311 59086,0917 90459,5907 172321,9986 248974,0748 465808,5604 4,2138 7,8836 12,0973 75‐79 0,90082 0,01126 0,08792 16007,8757 30018,6683 46026,5440 77489,7164 142961,7257 158514,4841 293486,5618 3,4440 6,3765 9,8204 80‐84 0,46414 0,00077 0,53508 14988,0109 27166,0220 42154,0329 54454,5249 99482,7425 81024,7676 150524,8361 1,9221 3,5708 5,4929 85+ 0,27406 0,00011 0,72605 6793,7990 12627,0750 19420,8741 21302,4351 40223,6905 26570,2427 51042,0936 1,3681 2,6282 3,9963

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Lampiran 11 Perhitungan Matriks Survivorship S(x)

Perhitungan matriks Survivorship dilakukan berdasarkan data perhitungan Life

Table multiregional. Berikut ini perhitungan matriks S(x):

sij(x)

=

i,j = 1,2 s11 (0) =

= , , , , , , , , = 0,95741 s12 (0) = = , _, , _, _,, _,, = 0,01456

Proses perhitungan dilakukan dengan cara yang serupa hingga diperoleh tabel sebagai berikut: Umur s11 s12 s22 s21 0-4 0,95741 0,01456 0,93587 0,02615 5-9 0,98044 0,01381 0,97375 0,01871 10-14 0,97379 0,01890 0,96603 0,02488 15-19 0,95596 0,03569 0,93276 0,05677 20-24 0,94843 0,04118 0,90944 0,07763 25-29 0,95843 0,02941 0,92042 0,06453 30-34 0,96480 0,02094 0,93681 0,04563 35-39 0,96769 0,01538 0,94828 0,03101 40-44 0,96743 0,01169 0,95381 0,02090 45-49 0,96237 0,00942 0,95139 0,01487 50-54 0,95114 0,00837 0,93995 0,01238 55-59 0,92990 0,00792 0,91690 0,01153 60-64 0,89301 0,00716 0,87836 0,01007 65-69 0,82860 0,00566 0,81455 0,00730 70-74 0,72070 0,00373 0,71218 0,00417 75-79 0,56762 0,00199 0,57045 0,00176 80-84 0,39043 0,00081 0,40389 0,00042 85+ 0,00000 0,00000 0,00000 0,00000

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Lampiran 12 Perhitungan Matriks Kelahiran B(x) : Fi(x)= ) ( ) ( x x i i ρ β , bji(x) = ₂1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + +

∑

= m k k k i k jk j j i j _F _x l L x S x F l L 1 0 0 ₍ ₅₎ ) 0 ( ) 0 ( ) ( ) ( ) 0 ( ) 0 (

Bayi yang lahir di daerah-2 pada waktu t, dan bertahan hidup di daerah-1 pada waktu t+1.

b21 (x) = [ F2(x) + S21(x) F1(x+5) + S22(x) F2 (x+5)]

b21(20) = [(0,07311) F2(20) + (0,07763) (4,83687)F1(25) + (0,90944) (0,07311) F2 (25)]

dengan F2(20) = 0,10593, F1(25) = 0,11170, F2(25) = 0,13528

Dalam menentukan jumlah bayi lahir dari wanita usia reproduksi selama selang interval waktu, maka harus dikalikan dengan proporsi penduduk wanita usia reproduksi.

Proses perhitungan dilakukan dengan cara yang serupa hingga diperoleh tabel sebagai berikut:

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Berdasarkan rumus di atas maka diperoleh Fi (x) dan B(x) seperti pada tabel berikut ini: Umur F1(x) F2(x) b11(x) b12(x) b22(x) b21 (x) 0-4 0 0 0 0 0 0 5-9 0 0 0 0 0 0 10-14 0 0 0,03431 0,00087 0,03146 0,00136 15-19 0,02998 0,02818 0,13998 0,00544 0,14796 0,00847 20-24 0,09223 0,10593 0,24438 0,00856 0,27770 0,01496 25-29 0,11170 0,13528 0,24186 0,00577 0,28988 0,01139 30-34 0,08640 0,11054 0,16131 0,00277 0,20459 0,00574 35-39 0,04610 0,06215 0,07855 0,00105 0,10339 0,00231 40-44 0,01915 0,02567 0,03199 0,00038 0,04224 0,00084 45-49 0,00765 0,01047 0,00909 0,00007 0,01222 0,00019 50-54 0 0 0 0 0 0 55-59 0 0 0 0 0 0 60-64 0 0 0 0 0 0 65-69 0 0 0 0 0 0 70-74 0 0 0 0 0 0 75-79 0 0 0 0 0 0 80-84 0 0 0 0 0 0 85+ 0 0 0 0 0 0

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Lampiran 13 Menentukan formula matriks transisi P(x) Diketahui : m(x) = ) ( ) ( x L x d _{m(x) = A(x)}

Akan ditunjukkan bahwa : p(x) = ( )] 2 5 [I+ A x -1 ₍ _)] 2 5 [I− A x Jawab: m(x) = ) ( ) ( x L x d d(x) = m(x) L(x) = m(x) [( ) ( 1)] 2 1 _l _x _{+ x}_l ₊ = ( )( 1) 2 1 ) ( ) ( 2 1_m _x _l _x ₊ _m _x_l _x₊

Disisi lain d(x) juga didefinisikan sebagai d(x)= l(x)-l(x+1), sehingga:

) 1 ( ) ( 2 1 ) ( ) ( 2 1 ) 1 ( ) (x −l x+ = m x l x + m x l x+ l ) 1 ( ) ( 2 1 ) 1 ( ) ( ) ( 2 1 ) (x − m x l x =l x+ + m xl x+ l ) 1 ( )] ( 2 1 1 [ ) ( )] ( 2 1 1 [ − m x l x = + m x l x+ Sehingga: ) ( . ) ( 2 1 1 ) ( 2 1 1 ) 1 ( l x x m x m x l + − = + Karena l(x+1)= p(x)l(x), maka )] ( 2 1 1 [ )] ( 2 1 1 [ ) ( 2 1 1 ) ( 2 1 1 ) ( _m _x 1 _m _x x m x m x p = + − + − = −

Sehingga untuk sebaran umur kelompok 5 tahunan formula di atas menjadi:

)] ( 2 5 1 [ )] ( 2 5 1 [ ) (_x _m _x 1 _m _x p = + − −

Untuk kasus multiregional berlaku:

)] ( 2 5 [ )] ( 2 5 [ ) (_x _I _A _x 1 _I _A _x p = + − − _■

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Lampiran 14 Bukti Sistem Logit Life Table

Diketahui : λ(l*(x)) = α + βλ(l(x))

Dimana untuk setiap nilai x , maka λ didefinisikan secara spesifik sebagai :

λ(l(x)) = logit (1.0 – l(x)) = 0,5 ln .

Akan dibuktikan : l*(x) = (1.0 + exp(2α + 2βλ(l(x))))-1 Bukti :

Karena λ(l(x)) = 0,5 ln . untuk semua nilai x

Maka berlaku λ(l*(x)) = 0,5 ln . λ(l*(x)) = α + βλ(l(x)) (diketahui) 0,5 ln . = α + βλ(l(x)) ln . = 2α + 2βλ(l(x)) . = exp(2α + 2βλ(l(x))) = 1+exp(2α + 2βλ(l(x))) l*(x) = l*(x) = (1.0 + exp(2α + 2βλ(l(x))))-1 ■

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Lampiran 15 Tabel Nilai α dan β dalam menentukan l(x) dengan sistem Brass logit (United Nation, 1983)

Level Angka harapan hidup (e 0₎ α β Female Male 1 20 18,034 1,3431 1,2829 2 22,5 20,444 1,2112 1,2248 3 25 22,852 1,0922 1,1757 4 27,5 25,26 0,9833 1,1337 5 30 27,667 0,8825 1,0978 6 32,5 30,073 0,7881 1,0671 7 35 32,479 0,6988 1,0408 8 37,5 34,885 0,6137 1,0186 9 40 37,29 0,5318 1,0001 10 42,5 39,695 0,4523 0,9852 11 45 42,1 0,3747 0,9737 12 47,5 44,504 0,2983 0,9658 13 50 47,082 0,2232 0,9631 14 52,5 49,546 0,1532 0,9759 15 55 51,816 0,0783 0,9867 16 57,5 54,122 0,0012 1,0015 17 60 56,46 -0,0787 1,0218 18 62,5 58,828 -0,1622 1,0502 19 65 61,222 -0,2500 1,0911 20 67,5 63,637 -0,3429 1,1531 21 70 66,03 -0,4461 1,2397 22 72,5 68,57 -0,5697 1,3245 23 75 71,204 -0,7133 1,4410 24 77,5 73,905 -0,8866 1,6056 25 80 76,647 -1,0599 1,8867

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Lampiran 16 Contoh perhitungan l(x) menggunakan Brass Logit

Akan ditentukan: l*(5) untuk nilai angka harapan hidup female (e0) = 68,06 Dengan cara interpolasi dapat ditentukan nilai α dan β untuk e0 = 68,06

e0 level α β

67,5 20 -0,3429 1,0911

68,06 20,224 -0,3660 1,1050

70 21 -0,4461 1,1531

l(x) yang digunakan sebagai standar adalah level 16 λ(l(x)) = logit (1.0 – l(x)) = 0,5 ln .

l*(x) =

Misalkan l(5) = 87954 (pada level 16)

Maka berlaku λ(l(5)) = 0,5 ln

= 0,5 ln

= -0,99404 Sehingga l*(5) = = , , ,

x

100000 = 95027

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Lampiran 17 Uji Maksimum Kurva Angkatan Kerja

Akan diuji menggunakan turunan kedua bahwa kurva angkatan kerja mempunyai maksimum lokal di f2(xh)

Kurva angkatan kerja berupa persamaan:

f2(x) = a2 exp{-α2(x - µ2) – exp[-λ2(x-µ2)]} Turunan pertama dari f2(x) adalah :

′ _{= [a}

2 exp{-α2(x - µ2) – exp[-λ2(x-µ2)]}] [ λ2 exp [-λ2(x-µ2)]-α2]

Turunan kedua dari f2(x) adalah :

′′ _{= [a}

2 exp{-α2(x - µ2) – exp[-λ2(x-µ2)]}] [ λ2 exp [-λ2(x-µ2)]-α2]2 + [a2 exp{-α2(x - µ2) – exp[-λ2(x-µ2)]}] [ -(λ2)2exp [-λ2(x-µ2)]]

Dengan mensubstitusikan xh = µ2 - ln[ ] pada ′′ maka diperoleh: ′′ _{= [a} 2 exp{-α2(µ2 - ln[ ] - µ2) – exp[-λ2(µ2 - ln[ ] - µ2)]}] [ λ2 exp [-λ2(µ2 - ln[ ] - µ2)]-α2]2 + [a2 exp{-α2(µ2 - ln[ ] - µ2) – exp[-λ2(µ2 - ln[ ] - µ2)]}] [ - (λ2)2exp [-λ2(µ2 - ln[ ] - µ2)]]

= [a2 exp{ ln[ ] – exp[(ln[ ] )]}] [ λ2 exp [(ln[ ] )] - α2]2 + [a2 exp{ ln[ ] – exp[(ln[ ] )]}] [ -(λ2)2exp [( ln[ ] )]]

= [a2 exp[ ] [ λ2 [ ] - α2]2 + [a2 exp[ ] [ -(λ2)2[ ] ] = 0 + [a2 exp[ ] [ - (λ2) ]

Sehingga ′′ < 0

Menurut teorema uji turunan kedua, karena ′′ < 0 maka f2( ) adalah maksimum lokal pada kurva angkatan kerja ada.

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Lampiran 18 Matriks Pertumbuhan G dan Hasil Proyeksi K(t+1) 0 0 0 0 0.034 0.001 0.140 0.008 0.244 0.015 0.242 0.011 0.161 0.006 0.079 0.002 0.032 0.001 0.009 0.000 0 0 0 0 0.001 0.031 0.005 0.148 0.009 0.278 0.006 0.290 0.003 0.205 0.001 0.103 0.000 0.042 0.000 0.012 0.957 0.026 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.015 0.936 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.980 0.019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.014 0.974 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.974 0.025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.019 0.966 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.956 0.057 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.036 0.933 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.948 0.078 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.041 0.909 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.958 0.065 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.029 0.920 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.965 0.046 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.021 0.937 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.968 0.031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.015 0.948 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.967 0.021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.012 0.954 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.962 0.015 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.009 0.951 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(30)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10759353 10996134 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8335798 8214514 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12331985 10519089 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9231960 7957914 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12420451 12263463 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8885645 9159971 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11524645 12316052 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8272276 8818528 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11939888 11486668 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7505291 8127430 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11426275 11906802 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7253818 7317271 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10877090 11419392 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6542939 7012590 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10381735 10792817 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6072365 6357249 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9328581 10234598 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5161321 = 5917946 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8067028 9132658 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4315790 5031980 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6531115 7827634 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3409949 4181975 0.951 0.012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4882544 6254207 0.008 0.940 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2379635 3259860 0 0 0.930 0.012 0 0 0 0 0 0 0 0 0 0 0 0 3836735 4567741 0 0 0.008 0.917 0 0 0 0 0 0 0 0 0 0 0 0 1775092 2220529 0 0 0 0 0.893 0.010 0 0 0 0 0 0 0 0 0 0 2911855 3444116 0 0 0 0 0.007 0.878 0 0 0 0 0 0 0 0 0 0 1200310 1586657 0 0 0 0 0 0 0.829 0.007 0 0 0 0 0 0 0 0 2160635 2421537 0 0 0 0 0 0 0.006 0.815 0 0 0 0 0 0 0 0 829292 994180 0 0 0 0 0 0 0 0 0.721 0.004 0 0 0 0 0 0 1148389 1560626 0 0 0 0 0 0 0 0 0.004 0.712 0 0 0 0 0 0 425352 598653 0 0 0 0 0 0 0 0 0 0 0.568 0.002 0 0 0 0 568625 652596 0 0 0 0 0 0 0 0 0 0 0.002 0.570 0 0 0 0 228991 244927 0 0 0 0 0 0 0 0 0 0 0 0 0.390 0.000 0 0 306852 222103 0 0 0 0 0 0 0 0 0 0 0 0 0.001 0.404 0 0 145682 92945 225113350

(31)

Program Pendugaan Parameter Model Skedul

Keluar wilayah JB

1> Model Penuh

data= Import@"d:\\dataJB.csv"D; dataêê TableForm; data= data;

fgs= a1 Exp@−α1 xD + a2 Exp@H−α2 Hx − μ2L − Exp@−λ2 Hx − μ2LDLD +

a3 Exp@H−α3 Hx − μ3L − Exp@−λ3 Hx − μ3LDLD + c;

f1= FindFit@data, fgs, 88a1, 0<, 8a2, 0.2<, 8a3, 0<, 8α1, 0.7<, 8α2, 0.2<,

8α3, 0.4<, 8μ2, 18<, 8μ3, 77<, 8λ2, 0.4<, 8λ3, 0.1<, 8c, 0<<, xD

8a1 → 0.050819, a2 → 0.012608, a3 → 0.001438,

α1 → 0.000764716, α2 → 0.100865, α3 → 0.144974, μ2 → 18.5611, μ3 → 77.0189, λ2 → 0.857421, λ3 → 0.0704837, c → −0.0476087<

a= ListPlot@data, PlotRange → 880, 100<, 8−0.002, 0.012<<,

Frame→ True, FrameLabel →8umur@thD, ASMR<D

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR

M1@x_D := a1 Exp@−α1 xD + a2 Exp@H−α2 Hx − μ2L − Exp@−λ2 Hx − μ2LDLD +

a3 Exp@H−α3 Hx − μ3L − Exp@−λ3 Hx − μ3LDLD + c ê. f1

b= Plot@M1@xD, 8x, 5, 95<, PlotLabel → "Model Penuh",

PlotRange→880, 100<, 8−0.002, 0.012<<,

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 ASMR Model Penuh

(32)

Show@a, b, Frame → True, FrameLabel → 8umur@thD, ASMR<D 0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR

dataAsli= data@@All, 2DD;

dataDuga= Table@M1@xD, 8x, 5, 95<D;

atas= ‚

i=1 Length@dataAsliD

Abs@HdataAsli@@iDD − dataDuga@@iDDLD

bawah= ‚ i=1 Length@dataAsliD dataAsli@@iDD 0.05796 0.257906

⁄i=1Length@dataAsliD

dataAsli@@iDD 100 22.4733 FindMinimum@8M1@xD, 5 ≤ x ≤ 95<, 8x, 20<D 80.00259246, 8x → 16.1461<< FindMaximum@8M1@xD, 5 ≤ x ≤ 95<, 8x, 19<D 80.0111135, 8x → 21.0075<< FindMaximum@8M1@xD, 5 ≤ x ≤ 95<, 8x, 65<D 80.00173866, 8x → 59.3893<< NIntegrate@M1@xD, 8x, 0, 5<D 0.0155663

2> Model Tidak Penuh

a3 Exp@α3 xD + c;

f1= FindFit@data, fgs, 88a1, 0.4<, 8a2, 0.5<, 8a3, 0.01<,

8α1, 0.1<, 8α2, 0.1<, 8α3, 0<, 8μ2, 18<, 8λ2, 0.3<, 8c, 0<<, xD

8a1 → −0.0372215, a2 → 0.0136456, a3 → 0.120297, α1 → 0.00627391,

α2 → 0.126957, α3 → −0.0018832, μ2 → 18.7839, λ2 → 0.774194, c → −0.0803137<

(33)

a3 Exp@α3 xD + c ê. f1

c= Plot@M2@xD, 8x, 5, 95<, PlotLabel → "Model tdk Penuh",

PlotRange→880, 100<, 8−0.002, 0.012<<,

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR Model tdk Penuh

Show@a, c, Frame → True, FrameLabel → 8umur@thD, ASMR<D

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR dataAsli= data@@All, 2DD; dataDuga= Table@M2@xD, 8x, 5, 95<D; atas= ‚ i=1 Length@dataAsliD

dataAsli@@iDD

100

22.6255

(34)

3> Model Sederhana

fgs= a1 Exp@−α1 xD + a2 Exp@H−α2 Hx − μ2L − Exp@−λ2 Hx − μ2LDLD + w;

f1= FindFit@data, fgs, 88a1, 0.1<, 8a2, 0.3<,

8α1, 0.1<, 8α2, 0.3<, 8μ2, 18<, 8λ2, 0.2<, 8w, 0<<, xD

8a1 → 0.363698, a2 → 0.0126825, α1 → 0.000089754,

α2 → 0.107801, μ2 → 18.6257, λ2 → 0.851603, w → −0.360453<

M3@x_D := a1 Exp@−α1 xD + a2 Exp@H−α2 Hx − μ2L − Exp@−λ2 Hx − μ2LDLD + w ê. f1

d= Plot@M3@xD, 8x, 5, 95<, PlotLabel → "Model Sederhana",

PlotRange→880, 100<, 8−0.002, 0.012<<,

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR Model Sederhana

Show@a, d, Frame → True, FrameLabel → 8umur@thD, ASMR<D

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR

atas= ‚

bawah= ‚ i=1 Length@dataAsliD dataAsli@@iDD 0.0612448 0.257906 4 data-JB-gab.nb

(35)

dataAsli@@iDD

100

23.7469

4> Model Polinom derajat-7

fgs= a0 + a1 x + a2 x2_{+ a3 x}3_{+ a4 x}4_{+ a5 x}5_{+ a6 x}6_{+ a7 x}7_;

f1= FindFit@data, fgs, 8a0, a1, a2, a3, a4, a5, a6, a7<, xD

9a0 → 0.0216813, a1 → −0.00617557,

a2→ 0.000668425, a3 → −0.0000314898, a4 → 7.57905 × 10−7, a5→ −9.79498 × 10−9, a6→ 6.4793 × 10−11, a7→ −1.72387 × 10−13=

M4@x_D := a0 + a1 x + a2 x2_{+ a3 x}3_{+ a4 x}4_{+ a5 x}5_{+ a6 x}6_{+ a7 x}7ê. f1

e= Plot@M4@xD, 8x, 5, 95<, PlotLabel → "Model Polinom der−7",

PlotRange→880, 100<, 8−0.002, 0.012<<,

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR

Model Polinom der-7

Show@a, e, Frame → True, FrameLabel → 8umur@thD, ASMR<D

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR

(36)

atas= ‚ i=1 Length@dataAsliD

dataAsli@@iDD

100

30.0808

5> Model Polinom derajat-15

fgs= a0 + a1 x + a2 x2+ a3 x3+ a4 x4+ a5 x5+ a6 x6+ a7 x7+

a8 x8_{+ a9 x}9_{+ a10 x}10_{+ a11 x}11_{+ a12 x}12_{+ a13 x}13_{+ a14 x}14_{+ a15 x}15_;

f1= FindFit@data, fgs, 8a0, a1, a2, a3, a4, a5, a6,

a7, a8, a9, a10, a11, a12, a13, a14, a15<, xD

9a0 → 0.502771, a1 → −0.337518, a2 → 0.0960703, a3 → −0.0153314, a4→ 0.00154259, a5 → −0.00010452, a6 → 4.97367 × 10−6,

a7→ −1.70802 × 10−7, a8→ 4.30206 × 10−9, a9→ −8.00172 × 10−11, a10→ 1.09636 × 10−12, a11→ −1.09201 × 10−14, a12→ 7.68557 × 10−17, a13→ −3.62107 × 10−19, a14→ 1.02438 × 10−21, a15→ −1.31519 × 10−24=

M5@x_D := a0 + a1 x + a2 x2_{+ a3 x}3_{+ a4 x}4_{+ a5 x}5_{+ a6 x}6_{+ a7 x}7_{+ a8 x}8₊

a9 x9_{+ a10 x}10_{+ a11 x}11_{+ a12 x}12_{+ a13 x}13_{+ a14 x}14_{+ a15 x}15ê. f1

f= Plot@M5@xD, 8x, 5, 95<, PlotLabel → "Model polinom der−15",

PlotRange→880, 100<, 8−0.002, 0.012<<,

0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR

Model polinom der-15

(37)

Show@a, f, Frame → True, FrameLabel → 8umur@thD, ASMR<D 0 20 40 60 80 100 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 umurHthL ASMR

atas= ‚

dataAsli@@iDD

100

24.3147

(38)

Program Pendugaan Parameter Model Skedul

Keluar wilayah LJB

1> Model Penuh

data= Import@"d:\\dataLJB.csv"D; dataêê TableForm; data= data;

a3 Exp@H−α3 Hx − μ3L − Exp@−λ3 Hx − μ3LDLD + c;

f1= FindFit@data, fgs, 88a1, 0<, 8a2, 0.1<, 8a3, 0<, 8α1, 0.2<, 8α2, 0.15<,

8α3, 0.1<, 8μ2, 18<, 8μ3, 77<, 8λ2, 0.1<, 8λ3, 0.1<, 8c, 0<<, xD

8a1 → 0.008082, a2 → 0.029128, a3 → 0.0031272,

α1 → 0.0624743, α2 → 0.0753041, α3 → 0.154708, μ2 → 19.4569, μ3 → 75.3528, λ2 → 0.365258, λ3 → 0.0729692, c → −0.000586551<

a= ListPlot@data, PlotRange → 880, 100<, 8−0.005, 0.025<<,

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR

a3 Exp@H−α3 Hx − μ3L − Exp@−λ3 Hx − μ3LDLD + c ê. f1

b= Plot@M1@xD, 8x, 5, 95<, PlotLabel → "Model Penuh",

PlotRange→880, 100<, 8−0.005, 0.025<<,

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR Model Penuh

(39)

Show@a, b, Frame → True, FrameLabel → 8umur@thD, ASMR<D 0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR

atas= ‚

dataAsli@@iDD 100 15.4582 FindMinimum@8M1@xD, 5 ≤ x ≤ 95<, 8x, 20<D 80.00277367, 8x → 14.5066<< FindMaximum@8M1@xD, 5 ≤ x ≤ 95<, 8x, 19<D 80.018372, 8x → 23.5438<< FindMaximum@8M1@xD, 60 ≤ x ≤ 70<, 8x, 65<D 80.00254649, 8x → 60.0402<< NIntegrate@M1@xD, 8x, 0, 5<D 0.0317747

2> Model Tidak Penuh

a3 Exp@α3 xD + c;

f1= FindFit@data, fgs, 88a1, 0<, 8a2, 0.3<, 8a3, 0.2<,

8α1, 0.1<, 8α2, 0.1<, 8α3, 0.1<, 8μ2, 18<, 8λ2, 0.3<, 8c, 0<<, xD

8a1 → 0.0070274, a2 → 0.0311134, a3 → −0.0000196107, α1 → 0.131613,

α2 → 0.0945731, α3 → 0.050405, μ2 → 19.9214, λ2 → 0.334908, c → 0.00179919<

(40)

a3 Exp@α3 xD + c ê. f1

c= Plot@M2@xD, 8x, 5, 95<, PlotLabel → "Model tdk Penuh",

PlotRange→880, 100<, 8−0.005, 0.025<<,

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR Model tdk Penuh

Show@a, c, Frame → True, FrameLabel → 8umur@thD, ASMR<D

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR dataAsli= data@@All, 2DD; dataDuga= Table@M2@xD, 8x, 5, 95<D; atas= ‚ i=1 Length@dataAsliD

dataAsli@@iDD

100

16.7348

(41)

3> Model Sederhana

fgs= a1 Exp@−α1 xD + a2 Exp@H−α2 Hx − μ2L − Exp@−λ2 Hx − μ2LDLD + w;

f1= FindFit@data, fgs, 88a1, 0.1<, 8a2, 0.5<,

8α1, 0.2<, 8α2, 0.4<, 8μ2, 18<, 8λ2, 0.2<, 8w, 0<<, xD

8a1 → 0.00704807, a2 → 0.0274997, α1 → 0.0732484,

α2 → 0.0747377, μ2 → 19.3142, λ2 → 0.400639, w → 0.000381101<

M3@x_D := a1 Exp@−α1 xD + a2 Exp@H−α2 Hx − μ2L − Exp@−λ2 Hx − μ2LDLD + w ê. f1

d= Plot@M3@xD, 8x, 5, 95<, PlotLabel → "Model Sederhana",

PlotRange→880, 100<, 8−0.005, 0.025<<,

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR Model Sederhana

Show@a, d, Frame → True, FrameLabel → 8umur@thD, ASMR<D

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR

atas= ‚

bawah= ‚ i=1 Length@dataAsliD dataAsli@@iDD 0.0793097 0.441735 4 data-LJB-gab.nb

(42)

dataAsli@@iDD

100

17.9541

4> Model Polinom derajat-7

fgs= a0 + a1 x + a2 x2_{+ a3 x}3_{+ a4 x}4_{+ a5 x}5_{+ a6 x}6_{+ a7 x}7_;

f1= FindFit@data, fgs, 8a0, a1, a2, a3, a4, a5, a6, a7<, xD

9a0 → 0.0519699, a1 → −0.0145862,

a2→ 0.0014834, a3 → −0.0000668489, a4 → 1.55656 × 10−6, a5→ −1.9606 × 10−8, a6→ 1.2706 × 10−10, a7→ −3.32448 × 10−13=

M4@x_D := a0 + a1 x + a2 x2_{+ a3 x}3_{+ a4 x}4_{+ a5 x}5_{+ a6 x}6_{+ a7 x}7ê. f1

e= Plot@M4@xD, 8x, 5, 95<, PlotLabel → "Model Polinom der−7",

PlotRange→880, 100<, 8−0.005, 0.025<<,

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR

Model Polinom der-7

Show@a, e, Frame → True, FrameLabel → 8umur@thD, ASMR<D

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR

(43)

atas= ‚ i=1 Length@dataAsliD

dataAsli@@iDD

100

23.8598

5> Model Polinom derajat-15

fgs= a0 + a1 x + a2 x2+ a3 x3+ a4 x4+ a5 x5+ a6 x6+ a7 x7+

a8 x8_{+ a9 x}9_{+ a10 x}10_{+ a11 x}11_{+ a12 x}12_{+ a13 x}13_{+ a14 x}14_{+ a15 x}15_;

f1= FindFit@data, fgs, 8a0, a1, a2, a3, a4, a5, a6,

a7, a8, a9, a10, a11, a12, a13, a14, a15<, xD

9a0 → 0.614006, a1 → −0.407755, a2 → 0.11473, a3 → −0.0180439, a4→ 0.00178501, a5 → −0.000118823, a6 → 5.55919 × 10−6, a7→ −1.88017 × 10−7, a8→ 4.67391 × 10−9, a9→ −8.59937 × 10−11, a10→ 1.16805 × 10−12, a11→ −1.15566 × 10−14, a12→ 8.094 × 10−17, a13→ −3.80102 × 10−19, a14→ 1.07327 × 10−21, a15→ −1.37705 × 10−24=

M5@x_D := a0 + a1 x + a2 x2_{+ a3 x}3_{+ a4 x}4_{+ a5 x}5_{+ a6 x}6_{+ a7 x}7_{+ a8 x}8₊

a9 x9_{+ a10 x}10_{+ a11 x}11_{+ a12 x}12_{+ a13 x}13_{+ a14 x}14_{+ a15 x}15ê. f1

f= Plot@M5@xD, 8x, 5, 95<, PlotLabel → "Model polinom der−15",

PlotRange→880, 100<, 8−0.005, 0.025<<,

0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR

Model polinom der-15

(44)

Show@a, f, Frame → True, FrameLabel → 8umur@thD, ASMR<D 0 20 40 60 80 100 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 umurHthL ASMR dataAsli= data@@All, 2DD; dataDuga= Table@M5@xD, 8x, 5, 95<D; atas= ‚ i=1 Length@dataAsliD

dataAsli@@iDD

100

16.6967

(45)