Parametric Point Estimation of the Geeta Distribution

Betty Korir

doi:doi:10.11648/j.ijsd.20180403.11

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Parametric Point Estimation of the Geeta Distribution

Betty Korir

Published in International Journal of Statistical Distributions and Applications (Volume 4, Issue 3)

Received: 28 September 2018 Accepted: 2 November 2018 Published: 29 November 2018

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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).

Published in	International Journal of Statistical Distributions and Applications (Volume 4, Issue 3)
DOI	10.11648/j.ijsd.20180403.11
Page(s)	51-59
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), 2018. Published by Science Publishing Group

Keywords

Geeta Distribution, Maximum Likelihood Estimators, Methods of Moments

References

[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, 2^nd 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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Betty Korir. (2018). Parametric Point Estimation of the Geeta Distribution. International Journal of Statistical Distributions and Applications, 4(3), 51-59. https://doi.org/10.11648/j.ijsd.20180403.11

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Betty Korir. Parametric Point Estimation of the Geeta Distribution. Int. J. Stat. Distrib. Appl. 2018, 4(3), 51-59. doi: 10.11648/j.ijsd.20180403.11

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Betty Korir. Parametric Point Estimation of the Geeta Distribution. Int J Stat Distrib Appl. 2018;4(3):51-59. doi: 10.11648/j.ijsd.20180403.11

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@article{10.11648/j.ijsd.20180403.11,
  author = {Betty Korir},
  title = {Parametric Point Estimation of the Geeta Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {4},
  number = {3},
  pages = {51-59},
  doi = {10.11648/j.ijsd.20180403.11},
  url = {https://doi.org/10.11648/j.ijsd.20180403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20180403.11},
  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).},
 year = {2018}
}

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TY  - JOUR
T1  - Parametric Point Estimation of the Geeta Distribution
AU  - Betty Korir
Y1  - 2018/11/29
PY  - 2018
N1  - https://doi.org/10.11648/j.ijsd.20180403.11
DO  - 10.11648/j.ijsd.20180403.11
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  - 51
EP  - 59
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20180403.11
AB  - 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).
VL  - 4
IS  - 3
ER  -

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Author Information

Betty Korir

Department of Mathematics & Computer Science, University of Eldoret, Eldoret, Kenya

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Plain Text BibTeX RIS

APA Style

Betty Korir. (2018). Parametric Point Estimation of the Geeta Distribution. International Journal of Statistical Distributions and Applications, 4(3), 51-59. https://doi.org/10.11648/j.ijsd.20180403.11

Copy | Download

ACS Style

Betty Korir. Parametric Point Estimation of the Geeta Distribution. Int. J. Stat. Distrib. Appl. 2018, 4(3), 51-59. doi: 10.11648/j.ijsd.20180403.11

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AMA Style

Betty Korir. Parametric Point Estimation of the Geeta Distribution. Int J Stat Distrib Appl. 2018;4(3):51-59. doi: 10.11648/j.ijsd.20180403.11

Copy | Download

@article{10.11648/j.ijsd.20180403.11,
  author = {Betty Korir},
  title = {Parametric Point Estimation of the Geeta Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {4},
  number = {3},
  pages = {51-59},
  doi = {10.11648/j.ijsd.20180403.11},
  url = {https://doi.org/10.11648/j.ijsd.20180403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20180403.11},
  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).},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Parametric Point Estimation of the Geeta Distribution
AU  - Betty Korir
Y1  - 2018/11/29
PY  - 2018
N1  - https://doi.org/10.11648/j.ijsd.20180403.11
DO  - 10.11648/j.ijsd.20180403.11
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  - 51
EP  - 59
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20180403.11
AB  - 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).
VL  - 4
IS  - 3
ER  -

Copy | Download