Uniformity tests under quantile categorization

Abstract

Purpose

In statistical inference, goodness of fit techniques are frequently used to decide if an observed sample X₁=x₁, … ,X_n=x_n can be considered as independent realizations from a proposed cumulative distribution function F₀(x). When goodness of fit tests are based on categorized data, they usually rely on relative frequencies of intervals or on sample quantiles. In this paper, comparisons between frequency‐based and quantile‐based power divergence test statistics are presented to test the hypothesis of uniformity in the interval (0,1) against different families of alternatives and some recommendations are given.

Design/methodology/approach

Divergence test statistics proposed by Cressie and Read are used and Monte Carlo simulation experiments are carried out. Both methods of categorization are applied separately to test the hypothesis of uniformity in the interval (0,1) and power comparisons are done for the families of alternatives proposed by Stephens. Next, a combined analysis is performed with the test statistics which have given the best results in each kind of categorization.

Findings

Results obtained by using quantile categorization are better due to the fact that quantile categorization uses selected exact sample observations. On the other hand, frequency categorization is based on relative frequencies of intervals. For the last type of categorization, there are many samples with the same value at the test statistic, so its discrimination power is reduced.

Research limitations/implications

The recommendation is limited to the power divergence test statistics introduced by Cressie and Read with parameter λ=−2,−1,−1/2,0,2/3,1,2 and several values of m and n.

Practical implications

Among the two types of categorizations, quantile categorization is recommended for testing uniformity.

Originality/value

The paper gives useful recommendations to applied statisticians when testing for uniformity.

Citation

Marhuenda, M.A., Marhuenda, Y. and Morales, D. (2005), "Uniformity tests under quantile categorization", Kybernetes, Vol. 34 No. 6, pp. 888-901. https://doi.org/10.1108/03684920510595553