TY  - JOUR
ID  - epos1868
UR  - http://www.jstor.org/stable/2236446
IS  - 2
A1  - Anderson, Theodore Wilbur
A1  - Darling, Donald Allan
N2  - The statistical problem treated is that of testing the hypothesis that n independent, identically distributed random variables have a specified continuous distribution function F(x). If Fn(x) is the empirical cumulative distribution function and ?(t) is some nonnegative weight function (0 ? t ? 1), we consider n^1/2 sup (-?<x<?) {|F(x)-Fn(x)|?^1/2[F(x)]} and n?[F(x)-Fn(x)]^2?[F(x)]dF(x). a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations. For certain weight functions including ?=1 and ?=1/[t(1-t)] we give explicit limiting distributions. A table of the asymptotic distribution of the von Mises ?^2 criterion is given.
VL  - 23
TI  - Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
AV  - none
EP  - 212
Y1  - 1952/06//
PB  - The Institute of Mathematical Statistics
JF  - The Annals of Mathematical Statistics
KW  - Weighting functions
KW  -  Stochastic processes
KW  -  Mathematical functions
KW  -  Distribution functions
KW  -  Differential equations
KW  -  Eigenvalues
KW  -  Eigenfunctions
KW  -  Statistics
KW  -  Mathematical integrals
SN  - 0003-4851
SP  - 193
ER  -