A New Family of Discrete Alpha Power Distributions

A. EL-Helbawy, A.; A. Hegazy, M.; R. AL-Dayian, G.

doi:10.21608/jsfc.2022.299825

A New Family of Discrete Alpha Power Distributions

نوع المستند : المقالة الأصلية

المؤلفون

¹ 1Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt

² Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt

³ Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt

10.21608/jsfc.2022.299825

المستخلص

Abstract
In this paper, a new family of discrete alpha power distributions is introduced. Some properties including quantiles, mean residual life, mean time to failure, R nyi entropy, moments and order statistics are obtained. Discrete alpha power Weibull distribution, as a member from this family, is studied in detail. Discrete two-parameter Weibull distribution, discrete alpha power one parameter Weibull distribution, discrete alpha power exponential distribution, discrete one parameter Weibull distribution, discrete Rayleigh distribution, discrete exponential distribution, discrete alpha power Rayleigh distribution are sub models of discrete alpha power Weibull distribution. A simulation study is conducted to investigate the precision of the theoretical results based on simulated and real data through some measurements of accuracy. Three real data sets are analyzed to illustrate the suitability and applicability of the proposed model.

الكلمات الرئيسية

المراجع

References

Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE transactions on reliability, R-36(1), 106-108.

Alzaatreh, A., Lee, C. and Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71(1), 63-79.

Arnold, B., Balakrishnan, N. and Nagaraja, H. N. (2008). A First Course in Order Statistics. John-Wiley and Sons, New York.

Bhaumik, D. K., Kapur, K. and Gibbons, R. D. (2009). Testing parameters of a gamma distribution for small samples. Journal of Taylor & Francis Online. Vol. 51, 326-334.

Bracquemond, C. and Gaudoin, O. (2003). A survey on discrete lifetime distributions. International Journal of Reliability, Quality and Safety Engineering, 10, 69-98.

Chakraborty, S. (2015). Generating discrete analogues of continuous probability distributions – A survey of methods and constructions. Journal of Statistical Distributions and Applications, 2(6):1-30.

Chakraborty, S. and Chakravorty, D. (2016). A new discrete probability distribution with integer support on (−∞, ∞). Communication in Statistics –Theory and Methods, 45(2):492-505.

Cordeiro, G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898.

Dey, S., Alzaatreh, A., Zhang, C. and Kumar, D. (2017). A new extension of generalized exponential distribution with application to ozone data. Ozone: Science & Engineering, 39, 273-285.

Eliwa, M. S., Alhussain, Z. A. and El-Morshedy, M. (2020). Discrete Gompertz-G family of distributions for over- and under-dispersed data with properties, estimation, and applications. Mathematics, 8, 358.

Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics, Theory and Methods, 31, 497-512.

Gomez-Deniz, E. and Calderin-Ojeda, E. (2011). The discrete Lindley distribution: properties and application. Journal of Statistics Computation and Simulation, 81 (11): 1405-1416.

Inusah, S. and Kozubowski, J. T. (2006). A discrete analogue of the Laplace distribution. Journal of Statistics Planning Inference 136, 1090-1102.

Jazi, M. A., Lai, C. D. and Alamatsaz, M. H. (2010). A discrete inverse Weibull distribution and estimation of its parameters. Elsevier Statistical Methodology, 7 (2):121- 132.

Jones, M. C. (2015). On families of distributions with shape parameters. International Statistical Review, 83(2), 175-192.

Kemp, A. (2004). Classes of discrete lifetime distributions, Communications in Statistics Theory and Methods, 33(12): 3069– 3093.

Khan, M. S. A., Khalique, A. and Abouammoh, A. M. (1989). On estimating parameters in a discrete Weibull distribution. IEEE Transactions on Reliability, 383, 348-350.

Krishna, H. and Pundir, P. S. (2009). Discrete Burr and discrete Pareto distributions. Statistical Methodology, 6, 177-188.

Lai, C.D. (2013). Issues concerning constructions of discrete lifetime models. Quality Technology and Quantitative Management, 10(2): 251-262.

Lai, C.D. (2014). Generalized Weibull Distribution. Springer Heidelberg, New York, Dordrecht, London.

Lee, C., Famoye, F. and Alzaatreh, A. Y. (2013). Methods for generating families of univariate continuous distributions in the recent decades. Wiley Interdisciplinary Reviews: Computational Statistics, 5(3), 219-238.

Mahdavi, A. and Kundu, D. (2017). A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Methods, 46(13), 6543-6557.

Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84(3), 641-652.

Murthy, D. N. P., Xie, M. and Jiang, R. (2004). Weibull Models. John Wily & Sons, New York.

Mead, M. E., Cordeiro, G. M., Afify, A. Z. and Al Mofleh, H. (2019). The alpha power transformation family: properties and applications. Pakistan Journal of Statistics and Operation Research, 15(3), 525-545.

Nadarajah, S. and Okorie, I. E. (2018). On the moments of the alpha power transformed generalized exponential distribution. Ozone: Science & Engineering, 40, 330-335.

Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 24 (5): 300-301.

Nassar, M., Alzaatreh, A., Mead, M. and Abo-Kasem, O. (2017). Alpha power Weibull distribution: Properties and applications. Communications in Statistics-Theory and Methods, 46(20), 10236-10252. 23

Nassar, M., Afify, A. Z. and Shakhatreh, M. K. (2020). Estimation methods of alpha power exponential distribution with applications to engineering and medical data. Pakistan Journal of Statistics and Operation Research, 16 (1), 149-166.

Nekoukhou, V., Alamatsaz, M. H., and Bidram, H. (2012). A discrete analog of generalized exponential distribution. Communication in Statistics-Theory and Methods, 41 (11): 2000-2013.

Roy, D. (2003). Discrete normal distribution. Communication in Statistics-Theory and Methods, 32 (10): 1871-1883.

Roy, D. (2004). Discrete Rayleigh distribution. IEEE Transactions on Reliability, 53(2): 255-260.

Roy, D. and Gupta, R. P. (1992). Classifications of discrete lives. Microelectronics and Reliability, R-34(3): 253-255.

Xie, M, Gaudoin, O. and Bracquemond, C. (2002). Redefining failure rate function for discrete distribution. International Journal of Reliability, Quality and Safety Engineering, 9(3): 275-286.