Spline approximation of quantile functions

Abstract

The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.