The Bivariate Generalized Rayleigh Distribution
| Autor: | Ammar M. Sarhan |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Matematik
Rayleigh distribution Cumulative distribution function Multivariate normal distribution Probability density function Markov chain Monte Carlo Marshal-Olkin multivariate distribution shock models Statistics::Computation symbols.namesake Survival function Joint probability distribution symbols General Earth and Planetary Sciences Applied mathematics Marginal distribution Mathematics General Environmental Science |
| Zdroj: | Volume: 2, Issue: 2 99-111 Journal of Mathematical Sciences and Modelling |
| ISSN: | 2636-8692 |
| DOI: | 10.33187/jmsm.439873 |
| Popis: | This paper introduces a new bivariate distribution named the bivariate generalized Rayleigh distribution (BVGR). The proposed distribution is of type of Marshall-Olkin (MO) distribution. The BVGR distribution has generalized Rayleigh marginal distributions. The joint cumulative distribution function, the joint survival function, the joint probability density function and the joint hazard rate function of the proposed distribution are obtained in closed forms. Statistical properties of the BVGR distribution are investigated. The maximum likelihood and Bayes methods are applied to estimate the unknown parameters. Both maximum likelihood and Bayes estimates are not obtained analytically. Therefore, numerical algorithms are required to report on the model parameters and its reliability characteristics. Markov Chain Monte Carlo (MCMC) algorithm is applied for the Bayesian method. A real data set is analyzed using the proposed distribution and compared it with existing distributions. It is observed that the BVGR model fits this dataset better than the MO and the bivariate generalized exponential (BVGE) distributions. |
| Databáze: | OpenAIRE |
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