Kth-order equilibrium Weibull distribution: properties, simulation, and its applications

A generalization of some well-known probability distributions (viz., Weibull, exponential, gamma, Maxwell, and Chi-square) is introduced using the concept of weighted probability distributions. The introduced model is named Kth-order equilibrium Weibull distribution (KEWD). Various properties of the...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2024-12, Vol.53 (12), p.6237-6259
Main Authors: Anas, Mohammad, Dar, Aijaz Ahmad, Ahmed, Aquil, Arshad, Mohd
Format: Article
Language:English
Subjects:
Aging properties
Akaike information criterion
Anderson-Darling test
Asymptotic normality
Equilibrium distribution
Error analysis
Maximum likelihood estimates
Maximum likelihood estimation
Maximum likelihood estimators
Normality
Parameter estimation
Statistical analysis
Weibull distribution
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Summary:A generalization of some well-known probability distributions (viz., Weibull, exponential, gamma, Maxwell, and Chi-square) is introduced using the concept of weighted probability distributions. The introduced model is named Kth-order equilibrium Weibull distribution (KEWD). Various properties of the new distribution are studied in detail. One of the important properties of KEWD is that its hazard rate shows increasing, decreasing, and constant behavior. It is also shown that the new model belongs to the log exponential family. Various ordering relations of the KEWD are studied in comparison with the baseline model, i.e. Weibull distribution. Parameters are estimated using the concept of the maximum likelihood estimation technique. Using the Anderson-Darling test statistic, a simulation study is carried out to analyze the asymptotic normality behavior of maximum likelihood estimators. 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 some incorporated real-life data sets. Finally, a comparison is made between KEWD, its sub-models, and some other introduced extensions of Weibull distribution in terms of fitting using the Akaike information criterion (AIC).
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2023.2230390