Some Structural Properties of the Generalized Kumaraswamy (GKw) $q_T-X$ Class of Distributions
Ampadu [C. B. Ampadu, Quantile-generated family of distributions : a new method for generating continuous distributions, Fundamental Journal of Mathematics and Mathematical Sciences 9(1) (2018), 13-34] introduced quantile generated probability distributions as a new way to generate continuous distributions. Combining this idea with the two-parameter Kumaraswamy (Kw) distribution, for example, see Wikipedia contributors [Wikipedia contributors, Kumaraswamy distribution, In : Wikipedia, The Free Encyclopedia, June 26, 2017. Retrieved 13:38, November 28, 2018, from https://en.wikipedia.org/wiki/Kumaraswamy_distribution], this paper introduces a so-called (GKw) $q_T-X$ class of distributions, and obtains some of their structural properties. Practicality of sub-models of this new class of distributions is shown to be effective in modeling real life data. Practicality to various disciplines is proposed as further investigation. A bivariate extension of this new class of distribution is also proposed, and the reader is asked to investigate its properties and applications.
C. B. Ampadu, Quantile-generated family of distributions : a new method for generating continuous distributions, Fundamental Journal of Mathematics and Mathematical Sciences 9(1) (2018), 13-34.
Z. A. Ahmed, E. Altun, M. Alizadeh, G. Ozel and G. G. Hamedani, The odd exponentiated half-logistic-G family : properties, characterizations and applications, Chilean Journal of Statistics 8(2) (2017), 65-91.
H. Bakouch, F. Jamal, C. Chesneau and A. Nasir, A new transmuted family of distributions : Properties and estimation with applications, 2017. hal-01570370v3
G. M. Cordeiro and M. Castro, A new family of generalized distributions, J. Stat. Comput. Simul. 81 (2011), 883-893.
G. M. Cordeiro, M. Alizadeh, A. Nascimento and M. Rasekhi, The exponentiated Gompertz generated family of distributions : properties and applications, Chilean Journal of Statistics 7(2) (2016), 29-50.
H. A. David and H. N. Nagaraja, Order Statistics, John Wiley and Sons, New Jersey 2003.
N. Eugene, C. Lee and F. Famoye, Beta-normal distribution and its applications, Communications in Statistics - Theory and Methods 31(4) (2002), 497-512. https://doi.org/10.1081/sta-120003130
R. C. Gupta, P. L. Gupta and R. D. Gupta, Modeling failure time data by Lehman alternatives, Communications in Statistics Theory and Methods 27(4) (1998), 887-904. https://doi.org/10.1080/03610929808832134
P. Kumaraswamy, A generalized probability density function for double-bounded random-processes, Journal of Hydrology 462 (1980), 79-88. https://doi.org/10.1016/0022-1694(80)90036-0
D. Kundu and R. D. Gupta, Power-normal distribution, Statistics 47(1) (2013), 110-125.
S. Nasiru, P. N. Mwita and O. Ngesa, Exponentiated generalized transformed-transformer family of distributions, Journal of Statistical and Econometric Methods 6(4) (2017), 1-17.
A. Renyi, On measures entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1 (1961), 547-561.
Wikipedia contributors, Binomial series, In : Wikipedia, The Free Encyclopedia, November 9, 2018. Retrieved 13:35, November 28, 2018, from https://en.wikipedia.org/wiki/Binomial_series
Wikipedia contributors, Exponential function, In : Wikipedia, The Free Encyclopedia, November 22, 2018. Retrieved 13:37, November 28, 2018, from https://en.wikipedia.org/wiki/Exponential_function
Wikipedia contributors, Kumaraswamy distribution, In : Wikipedia, The Free Encyclopedia, June 26, 2017. Retrieved 13:38, November 28, 2018, from https://en.wikipedia.org/wiki/Kumaraswamy_distribution
This work is licensed under a Creative Commons Attribution 4.0 International License.