A Viable Alternative to Resorting to Statistical Tables

Abstract

It is shown in this article that, given the moments of a distribution, any percentage point can be accurately determined from an approximation of the corresponding density function in terms of the product of an appropriate baseline density and a polynomial adjustment. This approach, which is based on a moment-matching technique, is not only conceptually simple but easy to implement. As illustrated by several applications, the percentiles so obtained are in excellent agreement with the tabulated values. Whereas statistical tables, if at all available or accessible, can hardly ever cover all the potentially useful combinations of the parameters associated with a random quantity of interest, the proposed methodology has no such limitation.

The Use of Generalized Gamma-Polynomial Approximation for Hazard Functions

“…A general semi-parametric approach to density approximation is proposed in Ha and Provost (2007). In this section, we review the approximation technique on the use of generalized gamma baseline density function for approximating density and distribution functions, from which the approximated survival and hazard functions are obtained.…”

Polynomially Adjusted Normal Approximation to the Null Distribution of Ansari-Bradley Statistic

“…In this paper, we utilize a special type of general semi parametric approach (the normal-polynomial approximation) proposed in Ha and Provost (2007). Let W be a discrete random variable whose support is the closed interval and let its raw moments E(W h ) be denoted by µW (h), h = 0, 1, .…”

“…Its main concept and computing procedures were proposed in Ha and Provost (2007). While Provost et al (2009) explained that beta-polynomial approximation provides high accuracy for Ansari-Bradley statistic, this paper aims to show that normal-polynomial approximation is also very flexible and fast to adapt the features of the target distributions.…”

Numerical Comparisons for the Null Distribution of the Bagai Statistic

“…In this paper, we present a simple moment-based approximation method, namely the Gaussianpolynomial approximation, which was originally proposed by Ha and Provost (2007). It will be shown that this approach can be successfully utilized to provide accurate percentiles of the Bagai statistic and that is also very flexible and quickly adapt to the features of the target distributions.…”

“…In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009).…”