Inverse Gaussian random variables with application to price indices

Abstract

Inverse Gaussian distributions have proved to fit economic indices remarkably well in empirical investigations (Aase, 2000). In this note, the exact distribution of the ratio W = X/(X + Y) is derived when X and Y are independent inverse Gaussian random variables. This distribution arises when one is interested in comparing the performances of two economic entities. Several computer programs are given for computing the associated pdf, cdf, percentile points and the random numbers. A detailed application is illustrated for consumer price indices from the six major economics.