Alpha Power Odd Generalized Exponential Family of Distributions: Model, Properties and Applications

Year 2022, Volume: 35 Issue: 3, 1171 - 1188, 01.09.2022

Ibrahim Elbatal , Selen Çakmakyapan , Gamze Özel

https://doi.org/10.35378/gujs.868555

Cited By: 1

Abstract

In this paper, we exhibit a general family of distributions called alpha power odd generalized exponential family of distributions. The new family is very flexible with increasing, decreasing, J, reversed-J, bathtub shapes. Statistical properties of the family such as quantile, expansion of density function, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves are proposed. The method of maximum likelihood to estimate the model parameters is used. Three applications based on real data sets are the importance and flexibility of the three proposed models.

Keywords

Alpha power transformation, Odd generalized exponential family, Moments, Maximum likelihood estimation

References

• [1] Marshall, A. and Olkin, I., "A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families", Biometrika, 84(3): 641- 652, (1997).
• [2] Eugene, N., Lee, C. and Famoye, F., "Beta-normal distribution and its applications", Communication in Statistics- Theory and Methods, 31(4): 497-512, (2002).
• [3] Gleaton, J. U. and Lynch, J. D., "On the distribution of the breaking strain of a bundle of brittle elastic bers", Advances in Applied Probability, 36: 98-115, (2004).
• [4] Gleaton, J. U. and Lynch, J. D., "Properties of generalized log-logistic families of lifetime distributions", Journal of Probability and Statistics, 4: 51- 64, (2006).
• [5] Shaw W.T. and Buckley I.R., "The Alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map", (2009). arXiv preprint arXiv:0901.0434.
• [6] Zografos, K. and Balakrishnan, N., " On families of beta and generalized gamma-generated distributions and associated inference", Statistical Methodology, 6: 344 – 362, (2009).
• [7] Cordeiro, G. and de Castro, M., "A new family of generalized distributions", Journal of Statistical Computation and Simulation, 81: 883- 898, (2011).
• [8] Torabi, H. and Montazeri, N. H., "The logistic-uniform distribution and its application", Communications in Statistics - Simulation and Computation, 43: 2551- 2569, (2014).
• [9] Cordeiro, G, Ortega, E. and da Cunha, D.C., "The exponentiated generalized class of distributions", Data Science Journal, 11: 127, (2013).
• [10] Alexander, C., Cordeiro, G. M., Ortega, E. M. M. and Sarabia, J. M., "Generalized betagenerated distributions", Computational Statistics & Data Analysis, 56: 1880-1897, (2012).
• [11] Alzaatreh, A., Lee, C. and Famoye, F., "A new method for generating families of continuous distributions", Metron, 71: 63-79, (2013).
• [12] Bourguignon, M., Silva, R. and Cordeiro, G. M., "The Weibull–G family of probability distributions", Journal of Data Science, 12: 53-68, (2014).
• [13] Cakmakyapan, S., and Ozel, G., "Generalized Lindley Family with application on Wind Speed Data", Pakistan Journal of Statistics and Operation Research, 387-397, (2021).
• [14] Tahir, M. Cordeiro, G, Alizadeh, M, Mansoor, M, Zubair, M. and Hamedani, G., "The odd generalized exponential family of distributions with applications", Journal of Statistical Distributions and Applications, 2(1): 1-28, (2015).
• [15] Cordeiro, G. M., Alizadeh, M., Tahir, H., Mansoor, M., Bourguignon, M. and Hamedani, G., "The beta odd log-logistic family of distributions", Hacettepe Journal of Mathematics and Statistics, 45(4): 1175-1202, (2016).
• [16] Nofal, Z. M., Afy, A. Z., Yousof, H. M. and Cordeiro, G. M., The generalized transmuted-G family of distributions, Communication in Statistics- Theory and Methods, 46(8): 4119- 4136, (2017).
• [17] Mahdavi A. and Kundu D., "A new method for generating distributions with an application to exponential distribution," Communication in Statistics- Theory and Methods, 46(13): 6543-6557, (2017).
• [18] Karakaya, K., Kinaci, I., Coskun, K. U. S., and Yunus, A. K. D. O., “A new family of distributions”, Hacettepe Journal of Mathematics and Statistics, 46(2), 303-314, (2017).
• [19] Kenney, J. and Keeping, E., Mathematics of Statistics 1 th ed., D. Van Nostrand Company, Princeton, (1962).
• [20] Moors, J.J.A., "A Quantile Alternative for Kurtosis", Journal of the Royal Statistical Society: Series D, 37(1): 25-32, (1988).
• [21] Shanker R. and Shukla K., "On Modeling Of Lifetime Data Using Three-Parameter Generalized Lindley and Generalized Gamma Distributions", Biometrics & Biostatistics International Journal, 4(7), (2016).
• [22] Shukla K.," A comparative study of one parameter lifetime distributions", Biometrics & Biostatistics International Journal, 8(4): 111-123, (2019).
• [23] Tesfalem E., Shanker R., Shukla K.K. and Leonida T.A., " Weighted quasi Akash distribution: properties and applications", American Journal of Mathematics and Statistics, 9(1): 30-43, (2019).
• [24] Fayomi A., "The odd Frechet inverse Weibull distribution with application", Journal of Nonlinear Sciences and Applications, 12: 165-172, (2019).
• [25] Abdelfattah M., Beih E.D. and Shamsan A.G., "Weibull Generalized Exponential Distribution", (2016). arXiv:1606.07378v1 [math.ST].