Exponential Power-Chen Distribution and Its Some Properties
Abstract
In this study, it has been aimed to introduce a new statistical distribution called Exponential Power-Chen by using the method suggested by Alzaatreh et al. (2013). Some statistical properties such as moments, coefficies of skewness and kurtosis, random number generator for Exponential Power Chen (EP-CH) distribution are obtained. Moreover, the maximum likelihood estimators (MLEs) for unknown parameters of EP-CH distribution have been derived and a Monte Carlo simulation study based on mean square errors and biases of this estimators for various sample sizes have been performed. Finally, an application using real data set has been presented for this new distribution.
References
- Akinsete, A., Famoye, F., Lee, C. (2008). The beta-Pareto distribution.Statistics,42(6), 547-563.
- Alzaatreh, A., Famoye, F., Lee, C. (2013). Weibull-Pareto distribution and its applications.Communications in Statistics-Theory and Methods,42(9), 1673-1691.
- Alzaatreh, A., Lee, C., Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71(1), 63-79.
- Alzaghal, A., Famoye, F., Lee, C. (2013). Exponentiated T - X family of distributions with some applications. International Journal of Statistics and Probability, 2(3), 31.
- Bryson, M.C. and Siddiqui, M.M. (1969). Some criteria for aging. Journal of the American Statistical Association 64; 1472-14838
- elik, N., Guloksuz, C. T. (2017). A New Lifetime Distribution, Nowy Rozkad Cyklu yca.Eksploatacja I Nezawodnosc,19(4), 634.
- Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function.Statistics & Probability Letters,49(2), 155-161.
- Cordeiro, G. M., de Castro, M. (2011). A new family of generalized distributions.Journal of statistical computation and simulation,81(7), 883-898.
- Eugene, N., Lee, C., Famoye, F. (2002). Beta-normal distribution and its applications, Communications in Statistics-Theory and methods, 31(4), 497-512.
- Ghitany, M. E., Alqallaf, F., Al-Mutairi, D. K., & Husain, H. A. (2011). A two-parameter weighted Lindley distribution and its applications to survival data.Mathematics and Computers in simulation,81(6), 1190-1201.
- Guess,F., Prosehan.F.(1985). Mean Residual Life: Theory and Applications, The Florida State University ,Department of Statistics , Afosr Technical Report No. 85-178 .
- Hand, D. J. , Daly, F., Lunn, A. D., McConway , K. J. , Ostrowski, E. (1994). A Handbook of Small Data Sets, London: Chapman & Hall, 255.
- Henderson, R. and Milner, A. (1991) Aalenplots under proportional hazards. Applied Statistics, 40, 401-409.
- Murthy D, Xie M, Jiang R. (2004). Weibull models. John Wiley & Sons, Inc.
- Nadarajah, S., Kotz, S. (2004). The beta Gumbel distribution.Mathematical Problems in engineering, (4), 323-332.
- Nadarajah, S., Kotz, S. (2006). The beta exponential distribution.Reliability engineering & system safety,91(6), 689-697.
- Nielsen, F. and Nock, R. (2011). On Renyi and Tsallis entropies and divergences for exponential families, arXiv preprint arXiv:1105.3259 .
- Renyi, A. (1961). On measures of entropy and information, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley (CA):University of California Press, I, 547 - 561.
- Shannon, E.A. (1948). A Mathematical Theory of Communication, The Bell System Technical Journal, 27(10), 623 - 656.
- Smith, R. M., Bain, L. J. (1975). An exponential power life-testing distribution. Communications in Statistics-Theory and Methods, 4(5), 469-481.
- Tahir, M. H., Cordeiro, G. M., Alizadeh, M., Mansoor, M., Zubair, M., Hamedani, G. G. (2015). The odd generalized exponential family of distributions with applications.Journal of Statistical Distributions and Applications,2(1), 1.
- Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., & Zubair, M. (2016a). The Logistic-X family of distributions and its applications. Communications in Statistics-Theory and Methods, 45(24), 7326-7349.
- Tahir, M. H., Zubair, M., Mansoor, M., Cordeiro, G. M., Alizadeh, M., & Hamedani, G. G. (2016b). A new Weibull-G family of distributions. J. Math. Stat, 45, 629-647.
- W. Principles of Mathematical Analysis. McGraw-Hill, New York, 3rd edition, 1976
- Yeh, J. (2006).Real Analysis: Theory of Measure and Integration Second Edition, World Scientific Publishing Company.