Questions tagged [lilliefors-test]

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Goodness-of-fit Tests

I wish to test whether a large number of observations $X_i$ follows an exponential distribution with parameter $\lambda=1$. I also wish to test this hypothesis exactly, and intend that if the ...
pecer10012's user avatar
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1 answer
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What is the distribution of the test statistics for Shapiro Wilk, Anderson-Darling, and Lilliefors (KS) tests for normality under null?

Have been researching tests for normality, and have some idea of how some of these tests work from Wikipedia. However, they leave out explaining the distributions of the test statistics under the null ...
jojorabbit's user avatar
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71 views

Frequentists tests to check for normality

Let $X_1,...,X_n\sim X$ be $n$ i.i.d. random variables. I want to to test if they follow a normal distribution, in other words, check if their distribution belongs to the Gaussian family. These are ...
pecer10012's user avatar
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0 answers
429 views

Help understanding lilliefors test

I need some help understanding the meaning of the lilliefors test. As far as I know, the lilliefors method provides a measure of normality of a data set. That is, a measure of how the images (values) ...
GGChe's user avatar
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Simulating p-value statistics for Liliefors test (Python statsmodels)

Python statsmodels has an implementation of Lilliefors' test for goodness of fit (i.e. if the parameters of the distribution were obtained from fitting the data and not per-determined as in the ...
maschu's user avatar
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1 vote
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Goodness Of Fit Testing When Multiple Parameters Are Estimated

I am working with independent data points $X_1,...,X_N$ each of which, under my model assumptions, is a sum of exponential waiting times with different rates, and so should come from gamma ...
adstephanides's user avatar
6 votes
1 answer
2k views

How can one compute Lilliefors' test for arbitrary distributions?

My question is actually a follow-up to Glen_b's answer to the question "Simulation of KS-test with estimated parameters." I am mostly interested on how to compute Lilliefors' test (or, more exactly, ...
Cesar's user avatar
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2 votes
0 answers
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Help me understand a step of the procedure for KS test with estimated parameters

I read the following procedure to perform KS test with estimated parameters Testing whether data follows T-Distribution At first I couldn't make head or tails of it, partly because I mistaked the ...
DeltaIV's user avatar
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3 votes
1 answer
565 views

KS test for normality on residuals from OLS vs. MLE

This is a conceptual issue. Suppose, one wants to test the residuals $e_t$ from the regression for normality. So, he runs the regression, obtains the estimates of error variance $\sigma^2$, and forms ...
Aksakal's user avatar
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5 votes
1 answer
371 views

Adapt Kolmogorov-Smirnov Test to Lilliefors Test

I'm using EasyFit to fit distributions to a sample of data and test with the Kolmogorov-Smirnov test whether the null hypothesis may be rejected or not. But as this test estimates the parameters from ...
Bloodporc's user avatar
11 votes
2 answers
347 views

What is this trick with adding 1 here?

I was looking at this page on Lillefors test's Monte Carlo implementation. I don't understand this sentence: There is random error in this calculation from the simulation. However, because of the ...
Aksakal's user avatar
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2 votes
1 answer
619 views

Help understanding the results of the Lilliefors test

I have a set of annual rainfall data for Thailand which is gridded, so I have approximately 30x18 grid squares. I am trying to test whether the gamma distribution is suitable for my data, so I am ...
emmalgale's user avatar
6 votes
1 answer
5k views

Simulation of KS-test with estimated parameters

We know that the original KS-test has a limitation, requiring the Null hypothesis testing underlying distribution to be fully specified, rather than estimated. But in practice, we usually need to test ...
Vincent's user avatar
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