The Discrete Poisson-Amarendra Distribution

Rama Shanker

doi:doi:10.11648/j.ijsd.20160202.11

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The Discrete Poisson-Amarendra Distribution

Rama Shanker

Published in International Journal of Statistical Distributions and Applications (Volume 2, Issue 2)

Received: 4 June 2016 Accepted: 29 June 2016 Published: 26 August 2016

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Abstract

In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”. The first four raw moments (about the origin) and central moments (about the mean) are obtained. The expression for coefficient of variation, skewness and kurtosis are also given. For the estimation of its parameter, the maximum likelihood estimation and the method of moments are discussed. Moreover, the distribution is fitted using maximum likelihood estimate to certain data sets to test its goodness of fit over Poisson, Poisson-Lindley and Poisson-Sujatha distributions. The corresponding fitting are found to be quite satisfactory in almost all data sets.

Published in	International Journal of Statistical Distributions and Applications (Volume 2, Issue 2)
DOI	10.11648/j.ijsd.20160202.11
Page(s)	14-21
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), 2024. Published by Science Publishing Group

Keywords

Amarendra Distribution, Sujatha Distribution, Poisson-Lindley Distribution, Poisson-Sujatha Distribution, Compounding, Moments, Estimation of Parameter, Goodness of Fit

References

[1]	Beall, G. (1940): The fit and significance of contagious distributions when applied to observations on larval insects, Ecology, 21, 460-474.
[2]	Falls, L. W., Williford, W. O. and Carter, M. C. (1971): Probability distributions for thunderstorm activity at Cape Kennedy, Florida, Journal of Applied Meteorology, 10, 97-104.
[3]	Grandell, J. (1997): Mixed Poisson Processes, Chapman & Hall, London.
[4]	Lindley, D. V. (1958): Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society, 20 (1), 102-107.
[5]	Sankaran, M. (1970): The discrete Poisson-Lindley distribution, Biometrics, 26, 145-149.
[6]	Shanker, R. (2015 a): Akash distribution and Its Applications, International Journal of Probability and Statistics, 4 (3), 65-75.
[7]	Shanker, R. (2015 b): Shanker distribution and Its Applications, International Journal of Statistics and Applications, 5 (6), 338-348.
[8]	Shanker, R. (2016 a): Sujatha distribution and Its Applications, to appear in “Statistics in Transition new Series”, 17 (3).
[9]	Shanker, R. (2016 b): The Discrete Poisson-Sujatha distribution, International Journal of Probability and Statistics, 5 (1), 1-9.
[10]	Shanker, R. (2016 c): Amarendra distribution and Its Applications, American Journal of Mathematics and Statistics, 6 (1), 44-56.
[11]	Shanker, R. and Hagos, F. (2015): On Poisson-Lindley distribution and its Applications to Biological Sciences, Biometrics and Biostatistics International Journal, 2 (4), 1-5.
[12]	Shanker, R. and Hagos, F. (2016 a): On Poisson-Sujatha distribution and Its Applications to model count data from Biological Sciences, Biometrics & Biostatistics International Journal, 3 (4), 1-7.
[13]	Shanker, R. and Hagos, F. (2016 b): Size-biased Poisson-Sujatha distribution with Applications, American Journal of Mathematics and Statistics 6 (4), 145-154.
[14]	Shanker, R. and Hagos, F (2016 c): Zero-truncated Poisson-Sujatha distribution with Applications, Communicated
[15]	Shanker, R. and Hagos, F. (2016 d): On zero-truncation of Poisson, Poisson-Lindley, and Poisson-Sujatha distributions and Their Applications, Biometrics & Biostatistics International Journal, 3 (5), 1-13.

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APA Style

Rama Shanker. (2016). The Discrete Poisson-Amarendra Distribution. International Journal of Statistical Distributions and Applications, 2(2), 14-21. https://doi.org/10.11648/j.ijsd.20160202.11

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ACS Style

Rama Shanker. The Discrete Poisson-Amarendra Distribution. Int. J. Stat. Distrib. Appl. 2016, 2(2), 14-21. doi: 10.11648/j.ijsd.20160202.11

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AMA Style

Rama Shanker. The Discrete Poisson-Amarendra Distribution. Int J Stat Distrib Appl. 2016;2(2):14-21. doi: 10.11648/j.ijsd.20160202.11

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@article{10.11648/j.ijsd.20160202.11,
  author = {Rama Shanker},
  title = {The Discrete Poisson-Amarendra Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {2},
  number = {2},
  pages = {14-21},
  doi = {10.11648/j.ijsd.20160202.11},
  url = {https://doi.org/10.11648/j.ijsd.20160202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20160202.11},
  abstract = {In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”. The first four raw moments (about the origin) and central moments (about the mean) are obtained. The expression for coefficient of variation, skewness and kurtosis are also given. For the estimation of its parameter, the maximum likelihood estimation and the method of moments are discussed. Moreover, the distribution is fitted using maximum likelihood estimate to certain data sets to test its goodness of fit over Poisson, Poisson-Lindley and Poisson-Sujatha distributions. The corresponding fitting are found to be quite satisfactory in almost all data sets.},
 year = {2016}
}

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TY  - JOUR
T1  - The Discrete Poisson-Amarendra Distribution
AU  - Rama Shanker
Y1  - 2016/08/26
PY  - 2016
N1  - https://doi.org/10.11648/j.ijsd.20160202.11
DO  - 10.11648/j.ijsd.20160202.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 14
EP  - 21
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20160202.11
AB  - In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”. The first four raw moments (about the origin) and central moments (about the mean) are obtained. The expression for coefficient of variation, skewness and kurtosis are also given. For the estimation of its parameter, the maximum likelihood estimation and the method of moments are discussed. Moreover, the distribution is fitted using maximum likelihood estimate to certain data sets to test its goodness of fit over Poisson, Poisson-Lindley and Poisson-Sujatha distributions. The corresponding fitting are found to be quite satisfactory in almost all data sets.
VL  - 2
IS  - 2
ER  -

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Author Information

Rama Shanker

Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea

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APA Style

Rama Shanker. (2016). The Discrete Poisson-Amarendra Distribution. International Journal of Statistical Distributions and Applications, 2(2), 14-21. https://doi.org/10.11648/j.ijsd.20160202.11

Copy | Download

ACS Style

Rama Shanker. The Discrete Poisson-Amarendra Distribution. Int. J. Stat. Distrib. Appl. 2016, 2(2), 14-21. doi: 10.11648/j.ijsd.20160202.11

Copy | Download

AMA Style

Rama Shanker. The Discrete Poisson-Amarendra Distribution. Int J Stat Distrib Appl. 2016;2(2):14-21. doi: 10.11648/j.ijsd.20160202.11

Copy | Download

@article{10.11648/j.ijsd.20160202.11,
  author = {Rama Shanker},
  title = {The Discrete Poisson-Amarendra Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {2},
  number = {2},
  pages = {14-21},
  doi = {10.11648/j.ijsd.20160202.11},
  url = {https://doi.org/10.11648/j.ijsd.20160202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20160202.11},
  abstract = {In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”. The first four raw moments (about the origin) and central moments (about the mean) are obtained. The expression for coefficient of variation, skewness and kurtosis are also given. For the estimation of its parameter, the maximum likelihood estimation and the method of moments are discussed. Moreover, the distribution is fitted using maximum likelihood estimate to certain data sets to test its goodness of fit over Poisson, Poisson-Lindley and Poisson-Sujatha distributions. The corresponding fitting are found to be quite satisfactory in almost all data sets.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - The Discrete Poisson-Amarendra Distribution
AU  - Rama Shanker
Y1  - 2016/08/26
PY  - 2016
N1  - https://doi.org/10.11648/j.ijsd.20160202.11
DO  - 10.11648/j.ijsd.20160202.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 14
EP  - 21
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20160202.11
AB  - In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”. The first four raw moments (about the origin) and central moments (about the mean) are obtained. The expression for coefficient of variation, skewness and kurtosis are also given. For the estimation of its parameter, the maximum likelihood estimation and the method of moments are discussed. Moreover, the distribution is fitted using maximum likelihood estimate to certain data sets to test its goodness of fit over Poisson, Poisson-Lindley and Poisson-Sujatha distributions. The corresponding fitting are found to be quite satisfactory in almost all data sets.
VL  - 2
IS  - 2
ER  -

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