A Kolmogorov-Smirnov type test for two inter-dependent random variables

02/27/2018

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by   Tommy Liu, et al.

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Consider n iid random variables, where ξ_1, ..., ξ_n are n realisations of a random variable ξ and ζ_1, ..., ζ_n are n realisations of a random variable ζ. The distribution of each realisation of ξ, that is the distribution of one ξ_i, depends on the value of the corresponding ζ_i, that is the probability P(ξ_i≤ x)=F(x,ζ_i). We develop a statistical test to see if the ξ_1, ..., ξ_n are distributed according to the distribution function F(x,ζ_i). We call this new statistical test the condition Kolmogorov-Smirnov test.