Abstract
In this research paper, a new class of life-time distribution is introduced by compounding A new generalization of Rayleigh distribution; properties and applications and The Exponentiated G Poisson model, the so-called Exponentiated Rayleigh Poisson distribution. Main aim of this research article is to enhance the flexibility of Exponentiated G. Poisson distribution by power transformation technique. The probability density function, the survival function and the hazard function of the new proposed model in graphical form are illustrated. We study the properties of this new distribution with special emphasis on its quantile function, mode, skewness, kurtosis and moments. We have discussed residual life function, the probability-weighted moments, order statistics, R'enyi and entropies. We also discussed parameter estimation considering the maximum likelihood estimation approach. We have calculated the value of log-likelihood, Akaike's information criteria, Bayesian information criteria, corrected Akaike's information criteria and Hennan-Quinn information criteria of Generalized Rayleigh distribution, Exponentiated Chen distribution, Exponentiated Exponential distribution, Exponentiated Inverted Weibull distribution, Compound Rayleigh distribution and newly proposed Exponentiated Rayleigh Poisson distribution and found that the newly proposed model has smaller values in comparison to other. We have studied the P-P plot, Q-Q plot Kolmogorov Smirnov test and TTT plot of the proposed distribution for model validation. We compared the empirical distribution CDF and estimated distributed function CDF of the proposed model with five other models. A real dataset is analyzed for illustrative purposes. The importance and flexibility of the new family is illustrated by applying different techniques and tools. A final conclusion concludes the paper.
Highlights
In the last decades, many generalized distributions have been proposed based on different modification methods
The Exponentiated G Poisson family is obtained by compounding the Exponentiated G family and truncated Poisson distribution
It is an alternative of Probability Density Function (PDF) and Cumulative distribution function (CDF), used to obtain statistical measures like median, skewness, and kurtosis
Summary
Many generalized distributions have been proposed based on different modification methods These modification methods require the addition of one or more parameters to the base model which could provide better adaptability in the modeling of real-life data. New family of distributions have been proposed to generalize various distributions by compounding well-known distributions to provide greater flexibility in modeling data from practical viewpoints [12] introduced a general class of distribution generated from the logit of the American Journal of Theoretical and Applied Statistics 2020; 9(6): 272-282 beta random variable. [6] proposed for generating families of continuous distributions proposed a random variable X the "transformer" is used to transform another random variable T, the "transformed ".[25] explored a new three-parameter distribution motivated mainly by lifetime issues.
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