| Sumario: | As an alternative to the two-parameter extensions of exponential distributions, a three-parameter family of exponential distributions is introduced and investigated. 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 bio-medical 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 Biomedical, 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. Semi-Weibull 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.
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