The New Generalized 2Kth-Order Equilibrium Model: Estimation and Characterization

Nuzhat  Ahad; S.P.  Ahmad; J.A.  Reshi

Authors

Nuzhat Ahad Department of Statistics,University of Kashmir, Srinagar, Jammu and Kashmir, India
S.P. Ahmad Department of Statistics,University of Kashmir, Srinagar, Jammu and Kashmir, India
J.A. Reshi Department of Statistics,Govt. Degree College, Pulwama, Jammu and Kashmir, India

Keywords:

Generalized equilibrium, Maxwell-Boltzmann distribution, Maximum likelihood estimation, Anderson-Darling test statistic, information criterion tools

Abstract

This manuscript introduces a generalization of familiar probability distributions such as Maxwell, Rayleigh, Half-normal, Chi-square, Gamma, Weibull and some related distributions of Rayleigh andMaxwell-Boltzmann distribution. It utilizes the concept of a weighted probability distribution, applying higher-order weighting to more precisely capture and represent complex real-life scenarios. The introduced model is termed as the Generalized equilibrium Maxwell-Boltzmann distribution (GEMBD). Various structural properties and characterizations of the newly proposed model have been derived. The ordering properties of the proposed model are analyzed and compared with those of the base distribution. Parameters are estimated via the maximum likelihood estimation (MLE)
method. A simulation study is conducted using the Anderson-Darling test statistic to assess the asymptotic normality of the MLEs. Additionally, the behaviors of bias and mean square error are observed with the increase in sample size. The applications of new distribution are illustrated through its fitting to two different real life datasets. Ultimately, a comparison is conducted among GEMBD and its sub-models regarding their fit using Information Criterion tools.

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