The quantile-based skew logistic distribution

Abstract

We show that the quantile-based skew logistic distribution possesses kurtosis measures based on L-moments and on quantiles which are skewness invariant. We furthermore derive closed-form expressions for method of Lmoments estimators for the distribution's parameters together with asymptotic standard errors for these estimators.

Some general results on quantile functions for the generalized beta family

“…the beta QF. Then using the p-transformation rule we obtain a class of distribution having the QF in (33).…”

“…The quantile form of the GBG distribution provides flexibility in generating not only the classical GBG distributions but also quantile based GBG distributions and this provides one of the most important applications of the class of GBGQF. As an example let us consider the quantile based skew logistic distribution (SLD) [33], which is given by…”

“…Thus, valid quantile based distributions can be generated using the generating quantile function in (33) and its various sub cases defined so far.…”

“…Let U be a uniform (U (0, 1)) r.v. and let Q(p), 0 ≤ p ≤ 1 be the quantile function of the beta generated distribution as defined in (33), then by uniform transformation rule, the variable X, where x = Q(u), has a distribution with quantile function Q(p).…”

A generalization of quantile-based skew logistic distribution of van Staden and King

“…In the model provided by van Staden and King [1], the skew form of the standard logistic distribution is obtained by a weighted sum of quantile functions of standard exponential distribution, Q e (p) = − log(1 − p), and of standard reflected exponential distribution, Q re (p) = log(p), namely,…”