Half Cauchy Generalized Rayleigh Distribution: Bayesian Inferences and Applications to Engineering Data

Laxmi  Prasad Sapkota; Vijay  Kumar

Authors

Laxmi Prasad Sapkota Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, India
Vijay Kumar Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, India

Keywords:

Generalized Rayleigh distribution, Hamiltonian Monte Carlo, moments, Rhat, posterior distribution

Abstract

We introduce a novel distribution termed the half-Cauchy generalized Rayleigh distribution, characterized by three parameters, derived from the half-Cauchy family of distributions. Various statistical properties of this distribution are explored, encompassing explicit expressions for the survival function, median, hazard function, mode, moments, mean deviation, order statistics, cumulative hazard function, quantiles, and measures of dispersion based on quartiles and octiles. Parameter estimation for this model is conducted utilizing three widely employed techniques: maximum likelihood estimation (MLE), Cramer-Von-Mises (CVM), and least-square estimation (LSE) methods. To validate its applicability, we leverage two real datasets, subjecting the proposed model to a rigorous goodness-of-fit test. Results indicate a strong alignment between the proposed distribution and real-world data, showcasing its superior flexibility when compared to established models examined in the study. Additionally, we delve into a Bayesian analysis of the suggested model, employing the Hamiltonian Monte Carlo (HMC) algorithm with the No-U-Turn sampler (NUTS).

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