The Geometric-Logistic Distribution: A Versatile New Generalised Logistic Distribution

Abstract The Champernowne distribution is a little-known generalised logistic distribution, useful for modelling data defined on the whole real line, where it can model both leptokurtic and playtkurtic data. We present a similar distribution, the GGL distribution, which also fits data well, but is much more tractable and so has a broad range of uses. The distribution function is simple, and hence so is random number generation and the computation of quantiles and expected shortfall. We describe the properties of the new distribution, and show that it fits long-tailed data comparably to the t-distribution, with the advantage that all moments and the moment generating function exist. It can also fit short-tailed and even bimodal data, enabling a parametric test for bimodality.It also yields a test of goodness of fit for logistic regression, a generalised version of logistic regression, and a generalised growth-model.