Accession Number : ADA113965
Title : On Subset Selection Procedures for Inverse Gaussian Populations.
Descriptive Note : Technical rept.,
Corporate Author : PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
Personal Author(s) : Gupta,Shanti S ; Yang,Hwa-Ming
PDF Url : ADA113965
Report Date : Mar 1982
Pagination or Media Count : 25
Abstract : The inverse Gaussian or the first passage time probability distribution for Brownian motion with a drift is particularly important for modeling and interpreting observed distributions of time intervals in many different fields of research. In this paper we deal with the problem of selecting a subset of k inverse Gaussian populations which includes the 'best' population, i.e. the (unknown) population which is associated with the largest value of the unknown means. The shape parameters of the inverse Gaussian distributions are assumed to be equal for all the k populations. When the common shape parameter is known, a procedure R1 is defined and studied which selects a subset which is nonempty, small in size and just large enough to guarantee that it includes the best population with a preassigned probability regardless of the true unknown values of the means. For the case when the common shape parameter is unknown a procedure R2 is proposed. For the procedures R1 and R2, we obtain exact results for k=2 concerning the infimum of the probability of a correct selection. For K or = 3 a lower bound on the probability of a correct selection is derived for each case. Formulas for the constants d1 and d2 which are necessary to carry out the procedures R1 and R2, respectively, are obtained. An upper bound on the expected number of populations retained in the selected subset is given.
Descriptors : *Population(Mathematics), *Probability distribution functions, *Inversion, Selection, Gaussian quadrature, Brownian motion, Drift, Time intervals, Value, Parameters, Exponential functions, Shape, Set theory
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE