Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications

Ramesh Kumar Joshi; Govinda Prasad Dhungana

doi:doi:10.11648/j.ajtas.20200906.13

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Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications

Ramesh Kumar Joshi, Govinda Prasad Dhungana

Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 6)

Received: 6 October 2020 Accepted: 24 October 2020 Published: 4 November 2020

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 9, Issue 6)
DOI	10.11648/j.ajtas.20200906.13
Page(s)	272-282
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Exponentiated G Poisson Model, New Generalization of Rayleigh Distribution, Maximum Likely-hood Estimation (MLE), Probability Weighted Moments (PWM), Order Statistics

References

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APA Style

Ramesh Kumar Joshi, Govinda Prasad Dhungana. (2020). Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications. American Journal of Theoretical and Applied Statistics, 9(6), 272-282. https://doi.org/10.11648/j.ajtas.20200906.13

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ACS Style

Ramesh Kumar Joshi; Govinda Prasad Dhungana. Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications. Am. J. Theor. Appl. Stat. 2020, 9(6), 272-282. doi: 10.11648/j.ajtas.20200906.13

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AMA Style

Ramesh Kumar Joshi, Govinda Prasad Dhungana. Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications. Am J Theor Appl Stat. 2020;9(6):272-282. doi: 10.11648/j.ajtas.20200906.13

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@article{10.11648/j.ajtas.20200906.13,
  author = {Ramesh Kumar Joshi and Govinda Prasad Dhungana},
  title = {Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {6},
  pages = {272-282},
  doi = {10.11648/j.ajtas.20200906.13},
  url = {https://doi.org/10.11648/j.ajtas.20200906.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200906.13},
  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.},
 year = {2020}
}

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TY  - JOUR
T1  - Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications
AU  - Ramesh Kumar Joshi
AU  - Govinda Prasad Dhungana
Y1  - 2020/11/04
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200906.13
DO  - 10.11648/j.ajtas.20200906.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 272
EP  - 282
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200906.13
AB  - 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.
VL  - 9
IS  - 6
ER  -

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Author Information

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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APA Style

Ramesh Kumar Joshi, Govinda Prasad Dhungana. (2020). Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications. American Journal of Theoretical and Applied Statistics, 9(6), 272-282. https://doi.org/10.11648/j.ajtas.20200906.13

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ACS Style

Ramesh Kumar Joshi; Govinda Prasad Dhungana. Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications. Am. J. Theor. Appl. Stat. 2020, 9(6), 272-282. doi: 10.11648/j.ajtas.20200906.13

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AMA Style

Ramesh Kumar Joshi, Govinda Prasad Dhungana. Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications. Am J Theor Appl Stat. 2020;9(6):272-282. doi: 10.11648/j.ajtas.20200906.13

Copy | Download

@article{10.11648/j.ajtas.20200906.13,
  author = {Ramesh Kumar Joshi and Govinda Prasad Dhungana},
  title = {Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {6},
  pages = {272-282},
  doi = {10.11648/j.ajtas.20200906.13},
  url = {https://doi.org/10.11648/j.ajtas.20200906.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200906.13},
  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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications
AU  - Ramesh Kumar Joshi
AU  - Govinda Prasad Dhungana
Y1  - 2020/11/04
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200906.13
DO  - 10.11648/j.ajtas.20200906.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 272
EP  - 282
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200906.13
AB  - 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.
VL  - 9
IS  - 6
ER  -

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