The Transmuted Kumaraswamy Pareto Distribution
Abstract
The generalization of probability distributions in view of improving their flexibility in capturing the shape and tail behavior of disparate data sets has become one of the most active aspects of statistical research. We developed a new Pareto distribution by using Kumaraswamy method which gave rise to a new distribution called Kumaraswamy Pareto distribution. This method is called transmutation. The mathematical properties of the new generalized distribution was presented using quartiles, moments, entropy, order statistics mean deviation and maximum likelihood method of parameter estimation. The new generalized distribution was applied to a real life data on the exceedances of flood peaks (in m3/s) where it was observed to be superior to its sub models in terms of some goodness-of-fit test such as log likelihood criterion, Akaike Information Criterion (AIC) and Kolmogorov-Smirnov (K-S) measures.
References
A. Akinsete, F. Famoye and C. Lee, The beta-Pareto distribution, Statistics 42 (2008), 547- 563. https://doi.org/10.1080/02331880801983876
G.R. Aryal and C.P. Tsokos, On the transmuted extreme value distribution with application, Nonlinear Analysis 71 (2009), 1401-1407. https://doi.org/10.1016/j.na.2009.01.168
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.
S.K. Ashour and M.A. Eltehiwy, Transmuted Lomax distribution, American Journal of Applied Mathematics and Statistics 1 (2013a), 121-127. https://doi.org/10.12691/ajams-1-6-3
S.K. Ashour and M.A. Eltehiwy, Transmuted exponentiated Lomax distribution, Australian Journal of Basic and Applied Sciences 7 (2013b), 658-667.
S.K. Ashour and M.A. Eltehiwy, Transmuted exponentiated modified Weibull distribution, International Journal of Basic and Applied Sciences 2 (2013c), 258-269.
A. Azzalini, A class of distributions which includes the normal ones, Candinavian Journal of Statistics 12 (1985), 171-178.
M. Bourguignon, J. Leâo, V. Leiva and M. Santos-Neto, The transmuted Birnbaum-Saunders distribution, REVSTAT – Statistical Journal 15 (2016), 601-628.
M. Bourguignon, R.B. Silva, L.M. Zea and G.M. Cordeiro, The Kumaraswamy Pareto distribution, Journal of Statistical Theory and Applications 12(2) (2012), 129-144. https://doi.org/10.2991/jsta.2013.12.2.1
V. Choulakian and M.A. Stephen, Goodness-of-fit for generalized Pareto distribution Technometrics 43 (2011), 478-484. https://doi.org/10.1198/00401700152672573
I. Elbatal, Transmuted modified inverse Weibull distribution: A generalization of the modified inverse Weibull probability distribution, International Journal of Mathematics Archive 4 (2013a), 117-129.
I. Elbatal, Transmuted generalized inverted exponential distribution, Economics and Quality Control 28 (2013b), 125-133. https://doi.org/10.1515/eqc-2013-0020
I. Elbatal and G. Aryal, On the transmuted additive Weibull distribution, Austrian Journal of Statistics 42 (2013), 117-132. https://doi.org/10.17713/ajs.v42i2.160
I. Elbatal, L.S. Diab and N.A. Abdul Alim, Transmuted generalized linear exponential distribution, International Journal of Computer Applications 83 (2013), 29-37. https://doi.org/10.5120/14671-2681
I. Elbatal and M. Elgarhy, Transmuted quasi-Lindley distribution: a generalization of the quasi-Lindley distribution, International Journal of Pure and Applied Sciences and Technology 18 (2013), 59-70
F. Galton, Colour associations, In F. Galton, Inquiries into human faculty and its development (p. 145-154), MacMillan Co., 1883. https://doi.org/10.1037/14178-018
M.S. Khan and R. King, Transmuted modified Weibull distribution, A generalization of the modified Weibull probability distribution, European Journal of Pure and Applied Mathematics 6 (2013), 66-88.
M.S. Khan, R. King and I.L. Hudson, Transmuted Kumaraswamy distribution, Statistics in Transition New Series 17 (2016), 183-210. https://doi.org/10.21307/stattrans-2016-013
P. Kumaraswamy, A generalized probability density functions for double-bounded random processes, Journal of Hydrology 46 (1980), 79-88. https://doi.org/10.1016/0022-1694(80)90036-0
F. Merovci, Transmuted Rayleigh distribution, Austrian Journal of Statistics 42(2013), 21-31. https://doi.org/10.17713/ajs.v42i1.163
I.J. de Moor and M.N. Bruton, Atlas of alien and translocated indigenous aquatic animals in southern Africa, A Report of the Committee for Nature Conservation Research National Programme for Ecosystem Research, South African Scientific Programmes Report No. 144, 310 p., Port Elizabeth, South Africa, 1988.
P.E. Oguntude, O.S. Babatunde and A.O. Ogumola, Theoretical analysis of the Kumaraswamy-inverse exponential distribution, Journal of Statistics and Applications 4(2) (2014), 113-116.
C.E Shannon, A Mathematical Theory of Communication, The Bell System Technical Journal 27 (1948), 379-423, 623-656. https://doi.org/10.1002/j.1538-7305.1948.tb00917.x
W.T. Shaw and I.R. Buckley, The alchemy of probability distributions: Beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map, 2007. http://library.wolfram.com/infocenter/Articles/6670/alchemy.pdf
K.U. Urama, S.I. Onyeagu and F.C. Eze, Shapes of the transmuted Kumaraswamy Pareto distribution for varying parameter values, Mathlab J. 5 (2020), 102-109.
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
