PROPERTIES OF THE GENERALIZED SPRT BASED ON RANKS.
Abstract
Let (X sub l, Y sub l), (*S sub 2, Y sub 2),...be independently and identically distributed bivariate random variables with a joint distribution H(.,.) which has continuous marginal distribution F(.) and G(.). The authors test the null hypothesis H sub o: X,Y are independent, and G = F against the alternative hypothesis H sub 1: X,Y are independent, and G = F(A) where a > 1 is a known constant. At the n(th) state of experimentation the available information is the ranks of (Y sub 1, . . ., Y sub n) among (X sub 1, . . . , X sub n, Y sub 1, . . . Y sub n). Use is made of a sequential probality-ratio test based on ranks. If the distribution of (X,Y) is H(.,.) with marginals F(.) and G(.) and S(A,H) = S(A,F,G) does not equal o where S(A,F,G) = log 4A-2-integral log(F(x) + AG(x)) (dF(x)) that this sequential test terminates with probability 1 and that the moment generating function of the required sample size is finite.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 10, 1965
- Accession Number
- AD0623832
Entities
People
- I. Richard Savage
- Jayaram Sethuraman
Organizations
- Florida State University