Study the properties of Chen-Rayleigh distribution with application
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Abstract
Today's world is characterized by speed and an increasing ability to innovate. Many phenomena have emerged that have data that require distributions that can accurately model their data, which makes it necessary to generate distributions that have the ability to do so. The research aims to expand the Rayleigh distribution by relying on the Chen-G family as one of those statistical distributions, by merging them together, to obtain a new distribution that we call (Chen-Rayleigh distribution (ChR)) with three parameters. The cumulative mass function and probability density have been extended to study their flexibility and suitability for modeling different types of data. Many of its statistical properties have been studied, such as the survival function, risk, moments surrounding the origin, and missing moments. I used the maximum likelihood estimation method to estimate the parameters of the proposed distribution, and to prove that it has good flexibility that enables it to model data with skewness with different tails, I used two sets of actual data programmed in the R program language, and compared their results with the Kumaraswamy Rayleigh (KuR) and Exponential Generalized Rayleigh (EGR) distributions.).), Weibull-Riley (WeR), Gompertz-Riley (GoR), Marshall Olkin-Riley (MoR), Rayleigh (R.) to evaluate the performance of the ChR distribution, and with several statistical parameters, such as (,--2L, AIC, CAIC , HQIC, BIC, W,A,K-S,P-Value), and through the results, the researchers concluded that the distribution (ChR) has an easy probability density function that can be easily managed and inferred and confirms the flexibility of the distribution, which makes it a candidate for use in several fields and for different phenomena.
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