Quantile-based generalized logistic distribution

Abstract

This dissertation proposes the development of a new quantile-based generalized logistic distribution GLDQB, by using the quantile function of the generalized logistic distribution (GLO) as the basic building block. This four-parameter distribution is highly flexible with respect to distributional shape in that it explains extensive levels of skewness and kurtosis through the inclusion of two shape parameters. The parameter space as well as the distributional shape properties are discussed at length. The distribution is characterized through its -moments and an estimation algorithm is presented for estimating the distribution’s parameters with method of -moments estimation. This new distribution is then used to fit and approximate the probability of a data set.