STUDY ON GENERALIZED EXPONENTIAL DISTRIBUTIONS SUMMARY OF THE PROJECT
One important parametric family among the life distributions is the exponential distribution which play a central role within the class of all life distributions. Exponential distribution has been studied by various researchers. The importance of exponential distribution is partly due to the fact that several of the most commonly used families of life distributions are parametric extension of this distribution. Such a parametric extension of a particular family of distributions will help to capture the skewness and peaked ness inherent in the data sets, which enables a more realistic modeling arising many different life situations. It has applications in various fields such as reliability, random summation, geometric compounding and so on.
Exponentiated family of distributions are one among the Lehman alternative family of distributions. Let T be a nonnegative random variable having distribution function F(t) with F(0)=0 and probability density function f(t). Now let T* be a non negative random variable such that its distribution function G(t) is
G(t)={F(t)}α, t>0,α >0. ...(1)
Here F(t) is base line distribution function and α is a positive real number.
This class of distributions with distribution function (1) have importance in reliability and life time data modelling. This model gives rise to monotonic as well as non monotonic failure rates even though the failure rate of the baseline distribution is monotonic.
Many authors considered the exponentiated family of distributions corresponding to different choice of F(t) in equation (1),studied their flexibility in modelling data and their applications. In a series of papers Gupta and Kundu investigated the exponentiated exponential (Generalized Exponential) distribution and has shown that this distribution is a better alternative to the situations where the Gamma and Weibull models are applied.
The importance of double Exponential Distribution and random sums has been depicted. Originally Generalized Exponential Distribution is defined on the positive real line. In this work symmetric version of the Generalized ExponentialDistribution on the entire real line is presented. Some properties of the distribution are derived. In addition some properties of Geometric Linnik and Generalized Geometric Linnik distribution has been obtained.
Dr.Mariamma Antony
