MARSHALL-OLKIN EXTENDED EXPONENTIAL FAMILY OF DISTRIBUTIONS

Abstract

A three-parameter family of exponential distributions is introduced and investigated
as an alternative to the two-parameter extensions of exponential distribution,. The
Marshall-Olkin exponential distribution is present in this family which is introduced in
Marshall and Olkin (1997). As an alternative to exponential distribution, this family can be
used. This class of distribution’s reliability properties is studied. There are many biomedical applications are noted with these generalized exponential family of distributions.
The odd generalized exponential family and its application is illustrated by means of two
real lifetime data sets by Tahir, et.al.(2015). A New Lifetime Exponential-X Family of
Distributions with Applications to Reliability Data explained by Xiaoyan et.al.,(2020). Also
a Generalization of the Exponential Distributions detailed by García (2020). Hence there are
many real life application based on these family of distribution in Bio-medical, engineering
and insurance research. A Weibull distribution of four parameter is introduced and studied.
The Weibull distribution is found in this family, which has a number of appealing
attributes. A study of this family of distribution’s reliability properties is done. SemiWeibull family of distributions are introduced and studied as a generalization of the four
parameter Weibull family. In order to model the data that exhibit periodic movements, the
generalized semi-Weibull the semi-Weibull family is helpful. Within the context of time
series, the implementation of these distributions is deliberated. The process, first-order
regressive Marshall- Olkin minification is thereby deduced. The discussed methods prove
to be applicable to generate autoregressive models with any marginal Marshall-Olkin
distribution. The study specifically concentrates on the exponential and Weibull families’
time series properties.