Further Statistical Properties of Size-Biased Geometric Distribution

Authors

  • Nuri Celik Department of Mathematics/Gebze Technical University, Kocaeli, Turkey
  • Iklim Gedik Balay Department of Business and Finance, Ankara Yildirim Beyazit University, Ankara, Turkey

Keywords:

Discrete random variables, count regression, discrete Gamma, discrete Weibull

Abstract

In this article, size biased geometric distribution is introduced. Some of its statistical and reliability properties are discussed like probability function, cumulative distribution and reliability function, hazard rate function and moments. The unknown distribution parameter is obtained by the moments and the maximum likelihood method in a closed form. Monte Carlo simulation study is performed in order to investigate the performance of maximum likelihood estimators. Additionally, this distribution is evaluated for the new count regression model. Real life data which comes from the statistical literature are considered for the illustration and the results are compared with Poisson, geometric, discrete Weibull, discrete Gamma and discrete Lindley distributions.

References

Baker RD. Application of a new discrete distribution. J Appl Stat. 2000; 27(1): 5-21.

Bakouch HS, Jazi MA, Nadarajah S. A new discrete distribution. Statistics. 2014; 48(1): 200-240.

Chakraborty S, Chakravarty, D. Discrete gamma distribution: Properties and parameter estimation. Commun Stat Theory. 2012; 41(18): 3301-3324.

Damien P, S. Walker S. A Bayesian non-parametric comparison of two treatments. Scand J Stat. 2002; 29: 51-56.

Deniz EG, Sarabia JM, Ojeda EC. A new discrete distribution with actuarial applications. Insur Math Econ. 2006; B48(3): 406-412.

El-Desouky BS, Gomaa RS, Magar AM. New Discrete Lifetime Distribution with Applications to Count Data. J Stat Theory Appl. 2021; 20(2): 304-317.

Gupta RD, Kundu D. A new class of weighted exponential distributions. Statistics. 2009; 43: 621-634.

Jazi MA, Lai CD, Alamatsaz MH. A discrete inverse Weibull distribution and estimation of its parameters. Stat Method. 2009; 7(2): 121-132.

Khan MSA, Khalique A, Abouammoh AM. On estimating parameters in a discrete Weibull distribution. IEEE T Reliab. 1989; 38: 248-250.

Khorashadizadeh M, Rezaei Roknabadi AH, Mohtashami Borzadaran GR. Characterisation of life distributions using log-odds rate in discrete ageing. Commun Stat Theory. 2013; 42(1): 76-87.

Kottas A. Nonparametric Bayesian survival analysis using mixtures of Weibull distributions. J Stat Plan Infer. 2006; 136: 578-596.

Krishna H, Pundir PS. Discrete Burr and discrete Pareto distributions. Stat Method. 2009;6: 177-188.

Kulasekera KB. Approximate mles of the parameters of a discrete Weibull distribution with type-I censored-data. Microelectron Reliab. 1994; 34: 1185-1188.

Lawless JF. Statistical Models and Methods for Lifetime Data, 1st edition: John Wiley and Sons, New York; 1982.

Nakagawa T, Osaki S. Discrete Weibull distribution. IEEE T Reliab. 1975; 24: 300-301.

Roy D. Discrete Rayleigh distribution. IEEE T Reliab. 2004; 53: 255-260.

Roy D. The discrete normal distribution. Commun Stat Theory. 2003; 32(10): 1871-1883.

Stein WE, Dattero R. A new discrete Weibull distribution. IEEE T Reliab. 1984; 33: 196-197.

Zheng Q. A new discrete distribution induced by the LuriaDelbrck mutation model. Statistics. 2010; 44: 529-540.

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Published

2024-12-25

How to Cite

Celik, N. ., & Balay, I. G. . (2024). Further Statistical Properties of Size-Biased Geometric Distribution. Thailand Statistician, 23(1), 64–71. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/257214

Issue

Vol. 23 No. 1 (2025): January

Section

Articles

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.