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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Vydané v:	Lobachevskii journal of mathematics Ročník 45; číslo 12; s. 6209 - 6223
Hlavní autori:	Ahmad, Aijaz, Rather, Aafaq A., Afful, Raymond B., Volodin, Andrei, Ali, Irfan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Moscow Pleiades Publishing 01.12.2024
Predmet:	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
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Popis
Shrnutí:	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