On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other TeX Export

@article{citeulike:2873803, abstract = {Let x and y be two random variables with continuous cumulative distribution functions f and g. A statistic U depending on the relative ranks of the x's and y's is proposed for testing the hypothesis f = g. Wilcoxon proposed an equivalent test in the Biometrics Bulletin, December, 1945, but gave only a few points of the distribution of his statistic. Under the hypothesis f = g the probability of obtaining a given U in a sample of n x's and m y's is the solution of a certain recurrence relation involving n and m. Using this recurrence relation tables have been computed giving the probability of U for samples up to n = m = 8. At this point the distribution is almost normal. From the recurrence relation explicit expressions for the mean, variance, and fourth moment are obtained. The 2rth moment is shown to have a certain form which enabled us to prove that the limit distribution is normal if m, n go to infinity in any arbitrary manner. The test is shown to be consistent with respect to the class of alternatives \$f(x) > g(x)\$ for every x.}, author = {Mann, H. B. and Whitney, D. R.}, citeulike-article-id = {2873803}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/2236101}, citeulike-linkout-1 = {http://www.jstor.org/stable/2236101}, doi = {10.2307/2236101}, journal = {The Annals of Mathematical Statistics}, number = {1}, pages = {50--60}, posted-at = {2008-07-13 18:25:40}, priority = {2}, publisher = {Institute of Mathematical Statistics}, title = {On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other}, url = {http://dx.doi.org/10.2307/2236101}, volume = {18}, year = {1947} }

TY - JOUR ID - citeulike:2873803 L3 - citeulike-article-id:2873803 N2 - Let x and y be two random variables with continuous cumulative distribution functions f and g. A statistic U depending on the relative ranks of the x's and y's is proposed for testing the hypothesis f = g. Wilcoxon proposed an equivalent test in the Biometrics Bulletin, December, 1945, but gave only a few points of the distribution of his statistic. Under the hypothesis f = g the probability of obtaining a given U in a sample of n x's and m y's is the solution of a certain recurrence relation involving n and m. Using this recurrence relation tables have been computed giving the probability of U for samples up to n = m = 8. At this point the distribution is almost normal. From the recurrence relation explicit expressions for the mean, variance, and fourth moment are obtained. The 2rth moment is shown to have a certain form which enabled us to prove that the limit distribution is normal if m, n go to infinity in any arbitrary manner. The test is shown to be consistent with respect to the class of alternatives $f(x) > g(x)$ for every x. IS - 1 JF - The Annals of Mathematical Statistics EP - 60 TI - On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other PB - Institute of Mathematical Statistics VL - 18 SP - 50 AU - Mann, HB AU - Whitney, DR PY - 1947/// UR - http://dx.doi.org/10.2307/2236101 ER -