Year: 2015
Type: preprint
Abstract: This paper introduces a polynomial transformation model based on Weibull distribution, whereby the analytical representation of the quantile function for many probability distributions can be obtained. Firstly, the target random variable $x$ with specified distribution is expressed as a polynomial of a Weibull random variable $z$, the coefficients are conveniently determined by the percentile matching method. Then, substituting $z$ with its quantile function $z=λ[-ln(1-u)]^{1/k}$ gives the analytical expression of the quantile function of $x$. Furthermore, using the probability weighted moments matching method, this polynomial transformation model can be used for data fitting. Through numerical experiment, it makes evident that the proposed model is capable of handling some distributions close to binomial which are difficult for the extant approaches, and the quantile functions of various distributions are accurately approximated within the probit range $[10^{-4},1-10^{-4}]$.
Source: arXiv (Cornell University)
Author: Xiao, Qing
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2214850254