Estimating The Hazard Function for A Mixed Distribution Using the Genetic Algorithm with A Practical Application

Taha Faeq Farhan

doi:10.47134/ppm.v3i1.2081

Authors

Taha Faeq Farhan Ministry of Education, Mathematics Department

DOI:

https://doi.org/10.47134/ppm.v3i1.2081

Keywords:

EKIW Distribution, Kumaraswamy Distribution, Weibull Distribution, Properties, Maximum Likelihood Method, Genetic Algorithm, IMSE, Hazard Function

Abstract

In this research, we presented the EKIW (Exponentiated Kumaraswamy Inverse Weibull) Distribution, which is a flexible distribution used in survival and reliability analysis. This distribution includes parameters (α, β, λ, η, θ). Statistical properties such as the hazard function, the quantile function, and the entropy measure were derived for this distribution. The research aims to estimate the hazard function based on one of the artificial intelligence algorithms, which is the genetic algorithm. It was compared with the maximum likelihood method. To prove the applicability of this distribution and which of the two methods is better, sample sizes (n=5, 15, 30, 80, 150) were generated using the comparison criterion, which is the integral mean square error (IMSE). The research also included a practical application for lung cancer patients obtained from the Medical City Hospital in 2025. The results showed that the hazard function's capabilities increased with increasing time of infection for the group of lung cancer patients under study. This is consistent with the theoretical properties of this function, as it is an increasing monotonic function

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