Volume 4, Issue 3, September 2018, Page: 51-59
Parametric Point Estimation of the Geeta Distribution
Betty Korir, Department of Mathematics & Computer Science, University of Eldoret, Eldoret, Kenya
Received: Sep. 28, 2018;       Accepted: Nov. 2, 2018;       Published: Nov. 29, 2018
DOI: 10.11648/j.ijsd.20180403.11      View  20      Downloads  12
Abstract
Geeta distribution is a new discrete random variable distribution defined over all the positive integers with two parameters. This distribution belongs to the family of Location-parameter (LDPD) system and is of the form L – shaped model. Pareto and Yule distributions belong to the same family but these distributions have a disadvantage of having a single parameter which makes them not versatile to meet the needs of modern complex data sets. Geeta distribution is found to be very versatile and flexible to fit observed count data sets and can be used efficiently to model different types of sets. This paper investigates the characteristics of Geeta distribution, such as the existence of the mean, variance, moment generating function, probability generating function and that the sum of probabilities for all values of X for Geeta Distribution model is unity. It is well known that the sample mean is the estimator of a population mean from a given population of interest as a point estimator which assume a single number that is obtained by taking a random sample of a specified size from the entire population, depending on whether the population mean and variance is known or unknown These point estimators were obtained by employing the method of Moments, Maximum Likelihood (MLE) and Bayesian estimator. Further the estimators were subjected to the conditions like unbiasedness, efficiency, sufficiency and completeness which are properties of a good estimator. For the first aspect, the results of the mean, variance, moments and generating functions were achieved that proves the distribution is a probability density function (pdf). The methods of moments and the maximum likelihood and their properties were applied and yielded the desired and expected results for any given probability distribution. The best estimator obtained is best linear unbiased estimator (BLUE).
Keywords
Geeta Distribution, Maximum Likelihood Estimators, Methods of Moments
To cite this article
Betty Korir, Parametric Point Estimation of the Geeta Distribution, International Journal of Statistical Distributions and Applications. Vol. 4, No. 3, 2018, pp. 51-59. doi: 10.11648/j.ijsd.20180403.11
Copyright
Copyright © 2018 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.
Reference
[1]
Hogg, R. V. Craig, A. T. (1956): Introduction to mathematical statistics. Pg. 200-227.
[2]
E. L. Lehmann, George Casella (1998), Theory of Point Estimation, 2nd Ed., Springer-Verlag New York, Inc.
[3]
Consul, P. C. (1990a), Geeta distribution and is Properties, Communication in Statistics-Theory and Methods, 19, 3051-3068[7.2.4].
[4]
Consul, P. C (1990b), New Class of Location -Parameter Discrete Probability distribution and their characteristics. Communication in Statistics-Theory and methods, 19, 4653-4666. [2.2.2, 7.2.4].
[5]
Harold J. Larson (1934), Statistics: An introduction to Statistics. Pg. 171-209.
[6]
Robert Bassett, Julio Deride (2016), Maximum a posteriori estimators as a limit of Bayes estimators, Journal of Mathematical Programming.
[7]
Gupta S. P. (2016), Statistical Methods, Sultan Chand & Sons, 43rd Ed.
[8]
H. Cramer (1946), Mathematical Methods of statistics, Princeton University Press.
[9]
Paul Vos and Qiang Wu (2015), Maximum likelihood estimators uniformly minimize distribution variance among distribution unbiased estimators in exponential families, Bernoulli 21(4), Pg. 2120–2138.
[10]
Rohatgi, V. K. (1975), An introduction to probability theory and mathematical statistics. Pg. 337-401.
[11]
Mood, A. N. Gray bill, F. A and Boes, D. C. (1963): Introduction to the theory of statistics. Pg. 271-357. Saxena, H. C. Surendran, P. U. (1967) statistical Inference. Pg. 37-57.
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