International Journal of Statistical Distributions and Applications
Volume 2, Issue 2, June 2016, Pages: 14-21
Received: Jun. 4, 2016;
Accepted: Jun. 29, 2016;
Published: Aug. 26, 2016
Views 3616 Downloads 181
Rama Shanker, Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea
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.
The Discrete Poisson-Amarendra Distribution, International Journal of Statistical Distributions and Applications.
Vol. 2, No. 2,
2016, pp. 14-21.
Copyright © 2016 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.
Beall, G. (1940): The fit and significance of contagious distributions when applied to observations on larval insects, Ecology, 21, 460-474.
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.
Grandell, J. (1997): Mixed Poisson Processes, Chapman & Hall, London.
Lindley, D. V. (1958): Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society, 20 (1), 102-107.
Sankaran, M. (1970): The discrete Poisson-Lindley distribution, Biometrics, 26, 145-149.
Shanker, R. (2015 a): Akash distribution and Its Applications, International Journal of Probability and Statistics, 4 (3), 65-75.
Shanker, R. (2015 b): Shanker distribution and Its Applications, International Journal of Statistics and Applications, 5 (6), 338-348.
Shanker, R. (2016 a): Sujatha distribution and Its Applications, to appear in “Statistics in Transition new Series”, 17 (3).
Shanker, R. (2016 b): The Discrete Poisson-Sujatha distribution, International Journal of Probability and Statistics, 5 (1), 1-9.
Shanker, R. (2016 c): Amarendra distribution and Its Applications, American Journal of Mathematics and Statistics, 6 (1), 44-56.
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.
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.
Shanker, R. and Hagos, F. (2016 b): Size-biased Poisson-Sujatha distribution with Applications, American Journal of Mathematics and Statistics 6 (4), 145-154.
Shanker, R. and Hagos, F (2016 c): Zero-truncated Poisson-Sujatha distribution with Applications, Communicated
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.