The Four-Parameter Weibull-Logistic Distribution : Properties and Application

This study introduced the four-parameter Weibull-Logistic distribution using the T-R{Y} framework based on the standard quantile function of exponential distribution. This was achieved by combining 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 have been presented and simulation study was carried out to study the behaviour of the Four-parameter Weibull-Logistic distribution. It is found that the Logistic distribution is a special case of the Four-parameter Weibull-Logistic distribution is skewed and normal-type for some values of the shape parameter. The distribution is also found to relate with the Weibull distribution through its quantile function, a general feature of the T-R{Y} family. Simulation results show that the shape of the distribution approaches symmetry as the sample size increases. The likelihood estimators of the parameters of the distribution are also presented. The applicability of the distribution has been demonstrated