B0377
Title: An extension of the quantile splicing technique for piece-wise distributions
Authors: Brenda Otieno Macoduol - University of Pretoria, South Africa (South Africa) [presenting]
Abstract: Quantile splicing was developed as a skewing mechanism for developing two-piece families of distributions with quantile functions of half distributions as the building block. The technique involves splicing quantile functions at the median point and introducing an asymmetry parameter to the half of the distribution whose domain is below the median point, while maintaining the kurtosis level of the parent distribution. This mechanism can be implemented for distributions defined primarily through their CDF, PDF, or quantile function. An extension of quantile splicing is proposed for generating piecewise distributions, where asymmetry is introduced to univariate distributions through splicing the quantile functions at location points other than the median ($0<k<1$). A general formula for the rth order L-moments is derived, which can be expressed in terms of the L-moments of the parent distribution and the expectations of the rth largest observation in a sample of size r from the kth piece distribution. The extension will consider the case where the quantile functions are spliced at the 25th percentile. The closed-form expressions for the families of distributions will be derived, as well as an application to data in which the method of L-moments estimation will be used.
