Questions tagged [lilliefors]

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Statistical power of the Lilliefors test: how to compare results for samples of different sizes?

The power of the Lilliefors test (LT) strongly depends on the sample size. I need to apply LT to a discrete distribution to find the minimum value m_min above which it is exponential. I need to do it ...
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41 views

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 ...
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0answers
49 views

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 ...
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1answer
978 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, ...
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0answers
472 views

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 ...
3
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1answer
261 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 ...
4
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1answer
254 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 ...
11
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2answers
284 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 ...
2
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1answer
360 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 ...
4
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1answer
3k 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 ...