Abstract
We use the quantile function to define statistical models. In particular, we present a five‐parameter version of the generalized lambda distribution (FPLD). Three alternative methods for estimating its parameters are proposed and their properties are investigated and compared by making use of real and simulated datasets. It will be shown that the proposed model realistically approximates a number of families of probability distributions, has feasible methods for its parameter estimation, and offers an easier way to generate random numbers.
Highlights
Statistical distributions can be used to summarize, in a small number of parameters, the patterns observed in empirical work and to uncover existing features of data, which are not immediately apparent
The aim of this paper is to make a contribution to the use of quantile statistical methods in fitting a probability distribution to data, following the line of thought indicated by Parzen 1 and Gilchrist 2, Section 1.10
Λ1 controls, Journal of Probability and Statistics albeit not exclusively, the location of an Five-Parameter Lambda Distribution (FPLD); the parameter λ2 acts for a multiplier to the translated quantile function X p, λ − λ1 and is, a scale parameter; λ3, λ4, λ5 influence the shape of X p, λ
Summary
Statistical distributions can be used to summarize, in a small number of parameters, the patterns observed in empirical work and to uncover existing features of data, which are not immediately apparent. In the present paper we have used the Tchebycheff metric, that is, the closeness between the theoretical quantile function X p and the FPLD is quantified by the maximum absolute difference Maxd between observed and fitted quantiles: max 1≤i≤500. In this sense, the FPLD is a valid candidate for being fitted to data when the experimenter does not want to be committed to the use of a particular distribution
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