Keywords and phrases: goodness-of-fit, hazard rate function, maximum likelihood estimation, moments, transmuted distributions, Weibull distribution.
Received: September 15, 2022; Accepted: October 15, 2022; Published: November 12, 2022
How to cite this article: Hatem E. Semary, M. Girish Babu and I. Elbatal, A generalization of Weibull distribution: theory and applications, Advances and Applications in Statistics 83 (2022), 1-25. http://dx.doi.org/10.17654/0972361722083
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References
[1] K. Adamidis, T. Dimitrakopoulou and S. Loukas, On a generalization of the exponential-geometric distribution, Statist. Probab. Lett. 73 (2005), 259-269. [2] A. Z. Afify, M. Alizadeh, H. M. Yousof, G. Aryal and M. Ahmad, The transmuted geometric-G family of distributions: theory and applications, Pakistan J. Statist. 32 (2016a), 139-160. [3] A. Z. Afify, G. M. Cordeiro, H. M. Yousof, A. Alzaatreh and Z. M. Nofal, The Kumaraswamy transmuted-G family of distributions: properties and applications, Journal of Data Science 14 (2016b), 245-270. [4] A. Z. Afify, H. M. Yousof and S. Nadaraj, The beta transmuted-H family for lifetime data, Statistics and its Interface 10 (2017), 505-520. [5] C. Alexander, G. M. Cordeiro, E. M. M. Ortega and J. M. Sarabia, Generalized beta-generated distributions, Comput. Statist. Data Anal. 56 (2012), 1880-1897. [6] M. A. Aljarrah, C. Lee and F. Famoye, On generating T-X family of distributions using quantile functions, Journal of Statistical Distributions and Applications 1 (2014), 1-17. [7] A. Alzaatreh, C. Lee and F. Famoye, A new method for generating families of continuous distributions, Metron 71 (2013), 63-79. [8] A. Alzaghal, F. Famoye and C. Lee, Exponentiated T-X family of distributions with some applications, International Journal of Statistics and Probability 2 (2013), 31-49. [9] G. R. Aryal and C. P. Tsokos, Transmuted Weibull distribution: a generalization of the Weibull probability distribution, European Journal of Pure and Applied Mathematics 4 (2011), 89-102. [10] G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Stat. Comput. Simul. 81 (2011), 883-893. [11] N. Eugene, C. Lee and F. Famoye, Beta-normal distribution and its application, Comm. Statist. Theory Methods 31 (2002), 497-512. [12] K. Jayakumar and M. G. Babu, T-transmuted X family of distributions, Statistica 77 (2017), 251-276. [13] K. Jayakumar and M. G. Babu, A new generalization of Fréchet distribution: properties and application, Statistica 79 (2019), 267-289. [14] M. C. Jones, Families of distributions arising from the distributions of order statistics, Test 13 (2004), 1-43. [15] C. Kundu and A. K. Nanda, Some reliability properties of the inactivity time, Comm. Statist. Theory Methods 39 (2010), 899-911. [16] C. Kus, A new lifetime distribution, Comput. Statist. Data Anal. 51 (2007), 4497-4509. [17] C. D. Lai, M. Xie and D. N. P. Murthy, A modified Weibull distribution, IEEE Transactions on Reliability 52 (2003), 33-37. [18] E. T. Lee and J. Wang, Statistical Methods for Survival Data Analysis, John Wiley and Sons, New York, 2003. [19] A. W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families, Biometrika 84 (1997), 641-652. [20] F. Merovci and I. Elbatal, Transmuted Weibull-geometric distribution and its applications, Sci. Magna 10 (2014), 68-82. [21] G. S. Mudholkar and D. K. Srivastava, Exponentiated Weibull family for analyzing bathtub failure rate data, IEEE Transactions on Reliability 42 (1993), 299-302. [22] D. N. P. Murthy, M. Xie and R. Jiang, Weibull Models, John Wiley and Sons, New Jersey, 2004. [23] A. K. Nanda, H. Singh, N. Misra and P. Paul, Reliability properties of reversed residual lifetime, Comm. Statist. Theory Methods 32 (2003), 2031-2042. [24] Z. M. Nofal, A. Z. Afify, H. M. Yousof and G. M. Cordeiro, The generalized transmuted-G family of distributions, Comm. Statist. Theory Methods 46 (2017), 4119-4136. [25] F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics 5 (1963), 375-383. [26] H. M. Yousof, A. Z. Afify, M. Alizadeh, N. S. Butt, G. G. Hamedani and M. M. Ali, The transmuted exponentiated generalized-G family of distributions, Pakistan Journal of Statistics and Operation Research 11 (2015), 441-464.
|