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2022•Pakistan Journal of Statistics and Operation ResearchOpen access

Pareto-Weibull Distribution with Properties and Applications: A Member of Pareto-X Family

Md. Shohel Rana, Saman Hanif Shahbaz, Muhammad Qaiser Shahbaz, Md. Mahabubur Rahman

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Abstract

In the present study, we propose a new family of distributions namely the Pareto-X family. A sub model of the proposed family called Pareto-Weibull (PW) distribution is discussed. The maximum likelihood estimators of the model parameters are obtained. Different distributional properties of the distribution are described. In order to assess the applicability of the model, two real-life applications from environmental and biological study are considered. The practical applications show that the proposed model provides better fitness than any other models used in this study.

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What this paper is about

In the present study, we propose a new family of distributions namely the Pareto-X family. A sub model of the proposed family called Pareto-Weibull (PW) distribution is discussed. The maximum likelihood estimators of the model parameters are obtained. Different distributional properties of the distribution are described. In order to assess the applicability of the model, two real-life applications from environmental and biological study are considered. The practical applications show that the proposed model provides better fitness than any other models used in this study.

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Available abstract

In the present study, we propose a new family of distributions namely the Pareto-X family. A sub model of the proposed family called Pareto-Weibull (PW) distribution is discussed. The maximum likelihood estimators of the model parameters are obtained. Different distributional properties of the distribution are described. In order to assess the applicability of the model, two real-life applications from environmental and biological study are considered. The practical applications show that the proposed model provides better fitness than any other models used in this study.

Key concepts: Weibull distribution, Pareto principle, Pareto distribution, Generalized Pareto distribution, Lomax distribution, Pareto interpolation, Mathematics, Estimator

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