Accession Number : AD0698658

Title :   On a Statistic Similar to Student's t.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Birnbaum,Z. W.

Report Date : 15 JUN 1969

Pagination or Media Count : 13

Abstract : Consider a random variable X which has median mu. Let X(1) = or < X(2) = or < ... X(2 m +1) be an ordered sample of X and let U = X(m +1-r), V = X(mu +1), W = X(mu +1 + r). The statistic S = (V - mu)/(W - U) is independent of mu and of any scale parameter, hence is distribution-free with regard to any family of probability distributions F((x - a)/b) where F(.) is a specified distribution function and a any real and b any positive number. A partial answer is given to the problem of a studentized Chebyshev inequality. Properties of S are discussed which, even in the special case of X with normal distribution, make it useful in practical situations in which Student's t is traditionally used, but in which t cannot be applied because of incomplete data, e.g. in case of one-sided or two-sided censoring.

Descriptors :   (*DISTRIBUTION THEORY, INEQUALITIES), STATISTICAL TESTS, PROBABILITY DENSITY FUNCTIONS, SAMPLING

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE