# (Kolmogorov-) Lilliefors (K-L) distribution

**URL:** <https://discourse.julialang.org/t/kolmogorov-lilliefors-k-l-distribution/31086>\
**Category:** Statistics\
**Created:** [November 14, 2019, 3:42pm UTC](https://discourse.julialang.org/t/kolmogorov-lilliefors-k-l-distribution/31086 "2019-11-14T15:42:20Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![sylvaticus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sylvaticus/32/203883_2.png) [@sylvaticus](https://discourse.julialang.org/u/sylvaticus)\
**Post date:** [November 14, 2019, 3:42pm UTC](https://discourse.julialang.org/t/kolmogorov-lilliefors-k-l-distribution/31086/1 "2019-11-14T15:42:20Z")

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Hello, does any Julia packages provides the [(Kolmogorov-)Lilliefors distribution](https://en.wikipedia.org/wiki/Lilliefors_test) ?

This should be used in hypothesis testing when we want to perform a goodness of fit test against a generic probability family, once we have used a MLE as best fit of its specific parameters, in place of the Kolmogorov-Smirnov test.

The reference I have is as follow:

 ![image](https://global.discourse-cdn.com/julialang/original/3X/1/4/14e06115283e60f288208486e06e1473e6eec9f8.png)

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**Author:** ![longemen3000](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/longemen3000/32/7298_2.png) [@longemen3000](https://discourse.julialang.org/u/longemen3000)\
**Post date:** [November 14, 2019, 8:33pm UTC](https://discourse.julialang.org/t/kolmogorov-lilliefors-k-l-distribution/31086/2 "2019-11-14T20:33:32Z")

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For what i know, the standard is just a set of tables, not a distribution function, so the best way to implement that is to use a spline or something like that. There is an excel site that has the following approximation:  
 ![image](https://global.discourse-cdn.com/julialang/original/3X/a/a/aaa0d26f4445993a6a578478d6d5bd1cf25eb9fd.png)