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Abstract

Probability distribution has shown its practicality in almost every area of human effort. This paper introduces a novel family of distributions called the [0, 1] Truncated Exponentiated Ailamujia-G family. The [0, 1] Truncated Exponentiated Ailamujia Exponential ([0, 1]TEAE) distribution, which is a sub-model of the recently created family, is completely constructed. The [0, 1]TEAE distribution is created by merging the [0, 1] Truncated and Exponentiated Ailamujia distributions. the mathematical features of the [0, 1]TEAE distribution, including moments, skewness, kurtosis, incomplete moments, renyi entropy, quantile function, and probability-weighted moments, are extensively examined. The quantiles for the chosen parameter values are clearly defined. The techniques used for parameter estimation include maximum likelihood, least squares, weighted least squares, and Anderson-Darling. This study assesses the efficacy of several estimators using a Monte Carlo simulation. In addition, the estimators were used on three actual datasets, and the Kolomogorov-Simirnov statistics were documented for each of them. The [0, 1] Truncated Exponentiated Ailamujia Exponential distribution was used on three real world datasets. Its effectiveness was evaluated by comparing it to other well-known extensions of the Exponential distribution, using criteria such as Hannan-Quinn information criterion, Bayesian information criterion, Akaike information criterion, and consistent AIC and goodness of fit tests such as Anderson-Darling statistic, Cramer-von Mises statistic, and P-value for the KS test.

Keywords

Ailamujia distribution, Estimation methods, Moments, [0, 1] truncated, Renyi entropy

Article Type

Article

First Page

271

Last Page

290

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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