On the Weibull-X family of distributions

In this paper, the Weibull-X family is proposed and some of its properties are discussed. A member of the Weibull-X family, the Weibull-logistic distribution, is defined and studied. Various properties of the Weibulllogistic distribution are obtained. The distribution is found to be unimodal and the shape can be symmetric, right skewed or left skewed. The structural analysis of the distribution in this paper includes limiting behavior, mode, quantiles, moments, skewness, kurtosis, Shannon’s entropy and order statistics. The method of maximum likelihood estimation is proposed for estimating the model parameters. A real data set is used to illustrate the application of the Weibull-logistic distribution.

[1]  F. Galton.  Inquiries into Human Faculty and Its Development , 1883 .

[2]  M. C. Jones.  Families of distributions arising from distributions of order statistics , 2004 .

[3]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[4]  Ayman Alzaatreh,et al.  On the discrete analogues of continuous distributions , 2012 .

[5]  Ayman Alzaatreh,et al.  A new method for generating families of continuous distributions , 2013 .

[6]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[7]  Ayman Alzaatreh,et al.  Methods for generating families of univariate continuous distributions in the recent decades , 2013 .

[8]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[9]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[10]  Richard A. Johnson,et al.  Testing reliability in a stress-strength model when X and Y are normally distributed , 1992 .

[11]  清水 邦夫.  Continuous Univariate Distributions Volume 1/N.L.Johnson,S.Kotz,N.Balakrishnan(1994) , 1995 .

[12]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[13]  Saralees Nadarajah,et al.  The skew logistic distribution , 2009 .

[14]  Ayman Alzaatreh,et al.  Weibull-Pareto Distribution and Its Applications , 2013 .

[15]  R. Berk,et al.  Continuous Univariate Distributions, Volume 2 , 1995 .

[16]  J. Moors,et al.  A quantile alternative for kurtosis , 1988 .

[17]  I. J. Hall,et al.  Approximate one-sided tolerance limits for the difference or sum of two independent normal variates , 1984 .

[18]  Richard L. Smith,et al.  A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution , 1987 .

[19]  Gauss M. Cordeiro,et al.  A new family of generalized distributions , 2011 .