WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Maximum Likelihood Estimation for the Parameters of New Mixture
Maxwell–Boltzmann Distribution and Its Applications
Authors: , ,
Abstract: This article introduces a new mixture extension of the Maxwell–Boltzmann distribution (MBD) to
enhance data modeling flexibility. Maximum Likelihood Estimation (MLE) is employed to estimate parameters,
and key statistical properties are analyzed. In addition, simulation studies are conducted to compare the bias,
mean square error, and variance of the estimates over a wide range of sample sizes from n = 5 to 10,000. The
new distribution is applied to a real-world heart attack survival dataset to demonstrate its potential in practical
applications. These findings highlight the potential of the proposed distribution in survival studies and modeling
right-skewed data.
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Keywords: Generalized Maxwell-Boltzmann Distribution, Maximum Likelihood Estimation, Moment
Generating Function, Incomplete Moments, Mixture Distributions, Length-Biased Distributions, Sustainable
Development Goal (SDG) 3
Pages: 551-562
DOI: 10.37394/23206.2025.24.55