Statistical tests of the form "is my PDF correct?"

Asked May 23 '21 at 19:28

Active May 23 '21 at 19:36

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Let's say we observe some data points $x_i$ and we hypothesize
they come from some continuous r.v. X which has PDF $f$.

I know that e.g. the Kolmogorov-Smirnov test can be applied to this kind of problems.

Do these tests/problems of the form "is my PDF correct?" have a specific name?

These problems can be viewed as continuous analogues of problems of the kind "is my PMF correct?" Example of the latter is the test if a given e.g. 6-sided die is fair. In that test our $H_0$ hypothesis is that $P(X=i) = 1/6$ which is a PMF and we ask: "Is my PMF correct?". Do these also have some name?

This question came to me while watching this last lecture of this MIT course.

https://youtu.be/rYefUsYuEp0?t=2167

edited May 23 '21 at 19:36

asked May 23 '21 at 19:28

peter.petrov

12,568

2

goodness of fit test – fGDu94 May 23 '21 at 19:30
Specification testing? – Dasherman May 23 '21 at 19:33
These are goodness-of-fit tests, including also the Anderson-Darling test and the $\chi^2$ goodness of fit test. – Clarinetist May 23 '21 at 19:35
OK... so in both cases PDF/PMF it's still a "goodness of fit test", is that what it is being said here? – peter.petrov May 23 '21 at 19:37

Statistical tests of the form "is my PDF correct?"

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