Mises Test Statistic Research Articles

AC++Program for the Cramér-von Mises Two-Sample Test

As larger sets of high-throughput data in genomics and proteomics become more readily available, there is a growing need for fast algorithms designed to compute exact p values of distribution-free statistical tests. We present a program for computing the exact distribution of the two-sample Cramér-von Mises test statistic under the null hypothesis that the two samples are drawn from the same continuous distribution. The program makes it possible to handle substantially larger sample sizes than earlier proposed computational tools. The C++ source code for the program is published with this paper, and an R package is under development.

The -Version of the Cramér-von Mises Test for Two-Sample Comparisons in Microarray Data Analysis

Distribution-free statistical tests offer clear advantages in situations where the exact unadjusted p-values are required as input for multiple testing procedures. Such situations prevail when testing for differential expression of genes in microarray studies. The Cramér-von Mises two-sample test, based on a certain L-distance between two empirical distribution functions, is a distribution-free test that has proven itself as a good choice. A numerical algorithm is available for computing quantiles of the sampling distribution of the Cramér-von Mises test statistic in finite samples. However, the computation is very time- and space-consuming. An L(1) counterpart of the Cramér-von Mises test represents an appealing alternative. In this work, we present an efficient algorithm for computing exact quantiles of the L(1)-distance test statistic. The performance and power of the L(1)-distance test are compared with those of the Cramér-von Mises and two other classical tests, using both simulated data and a large set of microarray data on childhood leukemia. The L(1)-distance test appears to be nearly as powerful as its L(2) counterpart. The lower computational intensity of the L(1)-distance test allows computation of exact quantiles of the null distribution for larger sample sizes than is possible for the Cramér-von Mises test.

A New Modified Goodness of Fit Tests for Type 2 Censored Sample from Normal Population

In this paper a procedure is considered for a new modified goodness of fit test for the normal type2 censored population. Samples of sizes 10(10)60 are chosen and censored at a specified percentage. Cramer von Mises and Anderson Darling test statistics are used with a nonparametric density estimator in place of the empirical distribution function. Tables of critical values for the two tests are generated. The power of the tests for nine alternative distributions is shown. Results show high power of discriminating the alternatives.