Kolmogorov–Smirnov test¶
The null hypothesis of the Kolmogorov–Smirnov test is that a dataset comes from
a certain distribution; the reference distribution can be specified explicitely
(onesample test) or by an empirical sample (twosample test). The alternative
hypothesis is that the cumulative distributions of the sample is different
(tail=:both
; default), smaller (tail=:left`), or larger (``tail:=right
)
than the reference cumulative distribution. The exact test is based on the exact
distribution of the differences whereas the approximate test is derived from its
asymptotic distribution.

ExactOneSampleKSTest{T<:Real}(x::AbstractVector{T}, d::UnivariateDistribution)
Perform a one sample Kolmogorov–Smirnovtest of the null hypothesis that the data in vector
x
comes from the distributiond
against the alternative hypothesis that the sample is not drawn fromd
.Implements: pvalue

ApproximateOneSampleKSTest{T<:Real}(x::AbstractVector{T}, d::UnivariateDistribution)
Perform an asymptotic one sample Kolmogorov–Smirnovtest of the null hypothesis that the data in vector
x
comes from the distributiond
against the alternative hypothesis that the sample is not drawn fromd
.Implements: pvalue

ApproximateTwoSampleKSTest{T<:Real, S<:Real}(x::AbstractVector{T}, y::AbstractVector{S})
Perform an asymptotic two sample Kolmogorov–Smirnovtest of the null hypothesis that
x
andy
are drawn from the same distribution against the alternative hypothesis that the distribution comes from different distributions.Implements: pvalue
References:
 Approximation of onesided test: http://www.encyclopediaofmath.org/index.php/KolmogorovSmirnov_test