# A New K-Product Generalized Transformation: Investigating Weibull Distribution as the Baseline

## Keywords:

G-class of probability distributions, Weibull distribution, hazard function, entropy measure, maximum likelihood estimation## Abstract

This article is about defining and studying an improved technique of parameter induction to a continuous probability distribution through a new G-class of probability models. In particular, the Weibull distribution is used in the defined technique and it is named as KP-W distribution. The importance of this generalization of Weibull distribution comes from its ability to model various kinds of hazard functions such as ascending, descending, first decreasing and then increasing, or constant hazard rate functions. Different properties of this generalized modified model have been deliberated along with raw moments and functions which can generate moments, quantiles, hazard function, Rényi entropy, stress-strength parameter, order statistics, the average time to wait until served and average remaining life. Maximum likelihood (ML) estimation of the proposed G class and its sub-model, the KP-W is also presented. Finally, the KP-W model is judged for its goodness to fit using data sets from different fields to showcase its practical applications.

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*University of Wah Journal of Science and Technology (UWJST)*,

*7*(1), 26–50. Retrieved from https://uwjst.org.pk/index.php/uwjst/article/view/200