Quantile Based Analysis of Marshall-Olkin Family

In this article, we suggest a way to introduce a new parameter to an existing quantile function to produce a new quantile function. We got an identity connecting the two quantile functions which will be useful for studying the reliability properties of the new quantile function. The hazard functions of some distributions and their extended versions have been discussed. Furthermore, we have applied this to Tukey Lambda distribution and an extended version is obtained which is useful for modeling not only symmetric distributions but also skewed distributions. Some of the reliability properties of the extended Tukey Lambda distribution has also been studied. In addition, a simulation study is conducted to estimate the parameters of the extended Tukey lambda distribution. We have also shown that the extended Tukey Lambda distribution can be used to model Covid-19 data.