Exploring the Fréchet–Power Rayleigh Distribution with Statistical Properties and Medical Data Insights

In this article, we introduce a new form of Power Rayleigh distribution using the Topp–Leone generated family of distributions. The new distribution is called the Fréchet–Power Rayleigh distribution. The different structural properties of the distribution are discussed, including moments, moment-gen...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics Vol. 45; no. 12; pp. 6209 - 6223
Main Authors: Ahmad, Aijaz, Rather, Aafaq A., Afful, Raymond B., Volodin, Andrei, Ali, Irfan
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.12.2024
Subjects:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Fréchet distribution
T-X family
moments
Power Rayleigh distribution
Rényi entropy
2010 Mathematics Subject Classification: Primary 60E05, Secondary 62F10, 62G05
maximum likelihood estimation
ISSN:1995-0802, 1818-9962
Online Access:Get full text
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Summary:In this article, we introduce a new form of Power Rayleigh distribution using the Topp–Leone generated family of distributions. The new distribution is called the Fréchet–Power Rayleigh distribution. The different structural properties of the distribution are discussed, including moments, moment-generating function, incomplete moments, order statistics, Rényi entropy, and mean deviations. The estimation of the parameters is performed by using the classical maximum likelihood method. A simulation analysis is carried out to evaluate and compare the effectiveness of estimators in terms of their bias, variance and mean square error. Finally, the distribution performance and application are investigated using real-life data from medical science.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224607550