WEIBULL-LOGISTIC WITH EXPONENTIAL QUANTILE FUNCTIONDISTRIBUTION

Abstract

The T-R{Y} is a T-X method of using a quantile function to generate probability distributions. It is a generalization of the T-X, Beta-X and many other families. This paper developed a 4-parameter Weibull-Logistic distribution using the T-R{Y} framework. This was achieved by combining the flexibility of the Weibull distribution with the two-parameter logistic distribution that has a location parameter, using the standard quantile function of the exponential distribution. Properties of the resulting distribution are extensively investigated, viz; rth non-central moments, quantiles, mode, survival function and hazard function. Plots of its density and cumulative distribution functions were presented to show its various shapes such as skewness or normal-type for some parameters’ values. The Logistic, Weibull, Weibull-logistic and skew logistic distributions are sub-models of the 4-parameter Weibull-Logistic distribution. The distribution is also found to relate with the Weibull distribution through its quantile function, a general feature of the T-R{Y} family. The maximum likelihood method was used to estimate the parameters of the distribution. Simulation study was carried out to show the consistency of its maximum likelihood parameters estimated, and it showed that the shape of the distribution approaches symmetry as the sample size increases. The applicability of the distribution was demonstrated using real life dataset and the likelihood ratio test showed that the location parameter is significant. The proposed distribution would be very useful in areas where Weibull and Logistic distributions are not good fit. The new generator can also be used to generate many other distributions in this family.