Lagrangian coefficients for interpolation between tabled percentage points

Abstract

SUMMARY For a large number of the probability distributions used in statistical practice the percentage points alone are available in published tables. The present paper provides tables making it possible to determine the value of the variable at much finer probability levels, P , lying between these standard levels. Lagrangian coefficients based on a logit transformation are given for seven five-point formulae, each using a different grid, e.g. one grid uses the 10, 5, 2.5, 1 and 0.5 percent points. The accuracy of the resulting interpolation is illustrated by application to several very different distributions.