Transmuted complementary exponential power distribution: properties and applications
Abstract
In this study, we introduce a new lifetime distribution by using quadratic rank transmutation map. The some properties of this new distribution is provided. Furthermore, the parameters of this new distribution are estimated by the maximum likelihood method. The performances of the estimates are examined according to bias and mean squared errors (MSEs) criteria through a Monte Carlo simulation study. Finally, two applications with real data are presented to evaluate the fits of introduced distribution.
Keywords
Maximum Likelihood estimation,Monte Carlo simulation,Transmuted distribution.
References
- [1] Barriga, G. D., Louzada-Neto, F., Cancho, V. G. The complementary exponential power lifetime model. Computational Statistics and Data Analysis, 55 (3) (2011) 1250-1259.
- [2] Smith, R. M., Bain, L. J. An exponential power life-testing distribution. Communications in Statistics-Theory and Methods, 4 (5) (1975) 469-481.
- [3] Shaw, W. T., 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
- [4] Aryal, G. R. Transmuted log-logistic distribution. Journal of Statistics Applications and Probability, (2013), 2-1 11-20.
- [5] Aryal, G. R., Tsokos, C. P. Transmuted Weibull distribution: A generalization of theWeibull probability distribution. European Journal of Pure and Applied Mathematics, 4 (2) (2011) 89-102.
- [6] Khan, M. S., King, R., Hudson, I. L. Transmuted Kumaraswamy Distribution. Statistics in Transition new series, 17 (2) (2016) 183-210.
- [7] Merovci, F. Transmuted exponentiated exponential distribution. Mathematical Sciences and Applications E-Notes, 1-2, (2013) 112-122.
- [8] Gradshteyn, I., Ryzhik, I. M. Table of integrals, series, and products. Academic Press, San Diego, 6th edition, 2000.
- [9] Lemonte, A. J., Barreto-Souza, W., Cordeiro, G. M. The exponentiated Kumaraswamy distribution and its log-transform. Brazilian Journal of Probability and Statistics, 27-1, (2013) 31-53.
- [10] Gupta, R. D., Kundu, D. Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43 (1) (2000) 117-130.