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Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 4

The Weibull-Power Cauchy distribution: model, properties and applications

M. H. TAHİR
Gauss M
CORDEİRO
M. MANSOOR
M. ZUBAİR
Ayman ALZAATREH
Pages
767–789
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The importance of the new distribution is proved empirically bymeans of three real-life data sets.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We propose a new three-parameter distribution with increasing, decreasing, reversed-J and upside-down bathtub shaped hazard rate, called the Weibull-power Cauchy distribution.
📊
Key Findings & Data:We obtain explicit expressions for the mode, ordinary, negative and incomplete moments, mean deviations, mean residual life, quantile and generating functions, order statistics, Shannon entropy and reliability.
💡
Conclusion & Impact:The importance of the new distribution is proved empirically bymeans of three real-life data sets.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Cauchy distribution · half-Cauchy distribution · moments

Abstract

We propose a new three-parameter distribution with increasing, decreasing, reversed-J and upside-down bathtub shaped hazard rate, called the Weibull-power Cauchy distribution. We obtain explicit expressions for the mode, ordinary, negative and incomplete moments, mean deviations, mean residual life, quantile and generating functions, order statistics, Shannon entropy and reliability. We derive a power seriesfor the quantile function using exponential partial Bell polynomials. A useful characterization of the new distribution is also presented. Themethod of maximum likelihood is used to estimate the model parameters. The importance of the new distribution is proved empirically bymeans of three real-life data sets.

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Cite This Article

TAHİR, M. H., M, G., CORDEİRO, C., MANSOOR, M., ZUBAİR, M., ALZAATREH, A. (2022). The Weibull-Power Cauchy distribution: model, properties and applications. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 4, 767–789. https://ajindex.com/articles/529923

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