Development and Statistical Analysis of Modified Kies Perks Distribution

Sarwat Rashid

doi:10.64060/JASR2V2i5

Authors

Sarwat Rashid Forman Christian College (A Chartered University) Lahore Professor Author https://orcid.org/0009-0001-4901-4441

DOI:

https://doi.org/10.64060/JASR2V2i5

Keywords:

perk distribution, modified Kies distribution, estimation, reliability measures, simulation

Abstract

This paper introduces a novel development of the Perks Distribution called the Modified Kies Perks distribution (MKPD), a highly adaptable probabilistic model characterized by its versatile probability density function, distribution function (DF) and hazard rate function. The MKPD can take various shapes, such as a single peak (unimodal), leaning to the right (right skewed), leaning to the left (left-skewed), a curve resembling a bathtub, and more, demonstrating its flexibility in statistical modelling and it is one of the most important and well-established ideas in reliability analysis. Several fundamental characteristics of the proposed model have been derived, including its PDF, CDF, quantile function, Hazard rate, survival function, cumulative hazard function, Odds Ratio and Average Failure Rate. Furthermore, a Monte Carlo simulation study is performed to assess the efficiency of different estimation methods across varying sample sizes confirming the MKPD’s flexibility and strong fit for lifetime, epidemiological and actuarial data. To validate its practicality, the proposed distribution is applied to real datasets. The results demonstrate that the MKPD is a valuable contribution to both statistical theory and applied statistical work.

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