# 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 ...
• 107
87 views

### 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 ...
• 153
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 ...
• 107
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) ...
• 165
347 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 ...
• 101
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 ...
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, ...
• 1,003
510 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 ...
• 18k
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 ...
• 61.3k
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 ...
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 ...
• 61.3k