Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications

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.