A New Exponent-Generator Family of Statistical Distribution with Simulation and Analysis to Cancer Data

Nuzhat  Ahad; Ahmad SP SP; Reshi  JA

Authors

Nuzhat Ahad Department of Statistics, University of Kashmir, Srinagar, J&K, India
Ahmad SP SP Department of Statistics, University of Kashmir, Srinagar, J&K, India
Reshi JA Department of Statistics, Govt. Degree College, Pulwama, J&K, India

Keywords:

Exponent-Generator family of distribution, power function distribution, exponent power function distribution, hazard rate function, maximum likelihood estimation

Abstract

A novel family of distribution has been introduced, named as "exponent-Generator family of statistical distribution", designed for optimal univariate modeling. We explored the structural and characterizing properties of a newly proposed distribution, the exponent power function (EPF) distribution. We provide explicit expressions for the probability density function (PDF), cumulative distribution function (CDF), reliability function (RF), and hazard rate function (HRF). Also the r-th moment, moment generating function (MGF), and the order statistics are obtained. The manuscript also includes a detailed discussion on the shapes of PDF and HRF for selected parameter values, providing valuable insights into the behavior of distribution. Moreover, we discussed maximum likelihood estimation (MLE) and Bayesian estimation method. The adaptability of the proposed distribution is evaluated by analyzing the three real data sets related to lifetime of cancer patients as well as a simulated dataset.

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