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Tests for specific nonparametric relations between two distribution functions with applications
Author(s) -
Deshpande JV,
Dewan Isha,
Lam KF,
NaikNimbalkar UV
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2375
Subject(s) - mathematics , nonparametric statistics , null hypothesis , kolmogorov–smirnov test , wilcoxon signed rank test , empirical distribution function
Let ( X , Y ) be a random vector and let G and H be the marginal distributions of X and Y , respectively. In this paper, we propose two tests, one of Kolmogorov‐Smirnov type and the other of Wilcoxon type, for the null hypothesis Ψ( G ) = H against the alternative Ψ( G ) < H , where Ψ() is a function such that Ψ( G ) is a distribution function. The tests are based on the empirical distribution functions of the observations on X and Y , which are dependent. We obtain their asymptotic null distributions. A suspected relationship between the distribution functions of two dependent outcomes can be specified as a hypothesis to be tested in examples like the load sharing models, record values, and auction bidding models. As an application, we consider in detail the problem of testing the effect of load sharing in two component parallel systems.