Kumaraswamy Type I Half Logistic Family of Distributions with Applications

Year 2019, Volume: 32 Issue: 1, 333 - 349, 01.03.2019

El-sayed El-sherpıeny Mahmoud Elsehetry

Abstract

A new
family of distributions called the Kumaraswamy type I half logistic is
introduced and studied. Four new special models are presented. Some
mathematical properties of the Kumaraswamy type I half logistic family are
studied. Explicit expressions for the moments, probability weighted, quantile function,
mean deviation and order statistics are investigated. Parameter estimates of
the family are obtained based on maximum likelihood procedure. One real data
set is employed to show the usefulness of the new family. 

Keywords

Half logistic distribution, Order statistics, Maximum likelihood method

References

• M. Bourguignon, R.B. Silva and G.M. Cordeiro, The Weibull– G family of probability distributions, Journal of Data Science, 12(2014), 53-68.
• G. M. Cordeiro, M. Alizadeh, and P.R. Diniz, (2015). The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, on-line.
• G. M. Cordeiro, M. Alizadeh, and E. M. M. Ortega, (2014). The exponentiated half-logistic family of distributions: properties and applications. Journal of Probability and Statistics, Article ID 864396, 21 pages. http://dx.doi.org/10.1155/2014/864396.
• G.M. Cordeiro and M. de Castro, (2011). A new family of generalized distribution, Journal of Statistical Computations and Simulation, 81, 883-898.
• G.M. Cordeiro, E.M.M. Ortega and D.C.C. da Cunha, (2013). The exponentiated generalized class of distributions, Journal of Data Science, 11, 1-27.
• H. A. David, (1981). Order statistics, Second edition. Wiley, New York.
• M. Elgarhy, A. S. Hassan, and M. Rashed, (2016). Garhy – Generated Family of Distributions with Application. Mathematical Theory and Modeling, 6, 1-15.
• N. Eugene, C. Lee and F. Famoye, (2002). The beta-normal distribution and its applications, Communications in Statistics & Theory and Methods, 31, 497-512.
• J.A. Greenwood, J.M. Landwehr, and N.C. Matalas, (1979). Probability weighted moments: Definitions and relations of parameters of several distributions expressible in inverse form. Water Resources Research, 15, 1049-1054.
• A.S. Hassan, and M. Elgarhy, (2016a). Kumaraswamy Weibull-generated family of distributions with applications. Advances and Applications in Statistics, 48, 205-239.
• A.S. Hassan and M. Elgarhy, (2016b). A New Family of Exponentiated Weibull-Generated Distributions. International Journal of Mathematics and its Applications, 4, 135-148.
• D. Hinkley, (1977). On quick choice of power transformations. Journal of the Royal Statistical Society, Series (c), Applied Statistics,26,67–69.
• C. Lee, F. Famoye, and O. Olumolade, (2007). Beta-Weibull Distribution: Some Properties and Applications to Censored Data. Journal of Modern Applied Statistical Methods, 6, 173-186.
• M. R. Mahmoud, E. A. El-Sherpieny, and M. A. Ahmed, (2015). The new Kumaraswamy Kumaraswamy family of generalized distributions with application. Pakistan Journal of Statistics and Operation Research, 2, 159-180.
• R. R. Pescim, G. M. Cordeiro, C. G. B. Demetrio, E. M. M. Ortega, and S. Nadarajah, (2012). The new class of Kummer beta generalized distributions. Statistics and Operations Research Transactions, 36, 153-180.
• Renyi A.(1961). On measures of entropy and information. In: Proceedings of the 4th Fourth Berkeley Symposium on Mathematical Statistics and Probability, 547-561. University of California Press, Berkeley.
• S. Rama and A. Mishra, (2013). A quasi Lindley distribution, African Journal of Mathematics and Computer Science Research, 6, 64-71.
• M. M. Ristic and N. Balakrishnan (2011). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82, 1191-1206.
• K. Zografos and N. Balakrishnan, (2009). On families of beta and generalized gamma-generated distributions and associated inference, Statistical Methodology, 6, 344- 362.