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):
Report Date:
1969-06-15
Pagination or Media Count:
13.0
Abstract:
Consider a random variable X which has median mu. Let X1 or X2 or ... X2 m 1 be an ordered sample of X and let U Xm 1-r, V Xmu 1, W Xmu 1 r. The statistic S V - muW - U is independent of mu and of any scale parameter, hence is distribution-free with regard to any family of probability distributions Fx - ab 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 Students 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:
Subject Categories:
- Statistics and Probability