Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications
American Journal of Theoretical and Applied Statistics
Volume 9, Issue 6, November 2020, Pages: 272-282
Received: Oct. 6, 2020; Accepted: Oct. 24, 2020; Published: Nov. 4, 2020
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Authors
Ramesh Kumar Joshi, Department of Statistics, Trichandra Multiple Campus Saraswoti Sadan, Tribhuvan University, Kathmandu, Nepal
Govinda Prasad Dhungana, Govinda Prasad Dhungana, Birendra Multiple Campus, Tribhuvan University, Chitwan, Nepal
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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.
Keywords
Exponentiated G Poisson Model, New Generalization of Rayleigh Distribution, Maximum Likely-hood Estimation (MLE), Probability Weighted Moments (PWM), Order Statistics
To cite this article
Ramesh Kumar Joshi, Govinda Prasad Dhungana, Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications, American Journal of Theoretical and Applied Statistics. Vol. 9, No. 6, 2020, pp. 272-282. doi: 10.11648/j.ajtas.20200906.13
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Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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