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This is a Monte Carlo simulation study.

September 10, 2025Statistics Optimization & Information Computing2 citations

The Alpha Power Modified Weibull-Geometric Distribution: A Comprehensive Mathematical Framework with Simulation, Goodness-of-fit Analysis and Informed Decision making using Real Life Data

NMNamsaw Magrisha DBDas Bhanita JPJyoti Hazarika Partha

Key Points

The proposed lifetime distribution improves fitting across real-world datasets.
Maximum likelihood estimation effectively estimates model parameters for the new distribution.
Monte Carlo simulation evaluates the distribution's performance with various sample sizes.
Statistical properties reveal the distribution's advantages over traditional lifetime models.

Abstract

A new lifetime distribution by compounding the Alpha Power Modified Weibull distribution, named Alpha Power Modified Weibull-Geometric distribution is introduced and discussed.The compounding of the distribution is motivated from the failure time of the system with series structure, where only the minimum lifetime value is considered. Various Statistical properties of the proposed distribution are investigated. Maximum likelihoodestimation method is used to estimate the model parameter. To assess the performance of the proposed method, monte carlo simulation study is conducted using various choices of effective sample size and parameter value. Finally, to illustrate the capability and flexibility of the proposed distribution, three real life data sets are considered and showed that the proposed distribution is more compatible by comparing with other competing lifetime distributions.

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