On Some One Parameter Lifetime Distributions and their Applications

Abstract

The time to the occurrence of event of interest is known as lifetime or survival time or failure time in reliability analysis. The event may be failure of a piece of equipment, death of a person, development (or remission) of symptoms of disease, health code violation (or compliance). The modeling and statistical analysis of lifetime data are crucial for statisticians and research workers in almost all applied sciences including engineering, medical science/ biological science, insurance and finance, amongst others. The classical lifetime distribution namely exponential distribution and Lindley distribution introduced by Lindley (1958) distribution are popular in statistics for modeling lifetime data. But these two classical lifetime distributions are not suitable from theoretical and applied point of view. Shanker et al (2015) have done a critical and comparative study regarding the modeling of lifetime data using both exponential and Lindley distributions and found that there are several lifetime data where these classical lifetime distributions are not suitable due to their shapes, hazard rate functions and mean residual life functions, amongst others. Recently, a number of one parameter lifetime distributions have been introduced by Shanker, namely Shanker, Akash, Rama, Suja, Sujatha, Amarendra, Devya, Shambhu, Aradhana, and Akshya, respectively. The probability density function (pdf), cumulative distribution function (cdf) one parameter lifetime distributions along with their introducer and years are presented in the following Table 1.