I am testing the significance of observed data sampled ($n\approx50$) using a multinomial distribution with known probabilities (with ~20 categories). Given the probability of observing the sample $P_{sam}$, I would like to compute the p-value, which is defined as the sum of all probabilities lower than this observed $P_{sam}$ i.e. $Sum\{p \mid p < P_{sam}, p \in Multinomial-distribution\}$.

One way to find this is to generate a large number of random samples from the given distribution and calculate the above sum using this set. But I am wondering if there exist any exact results and whether there are any good approximations which are less computationally intensive.


  • 4
    $\begingroup$ The $p$-value is always related to a hypothesis test. What is the null hypothesis ? $\endgroup$ Oct 9 '12 at 20:49
  • $\begingroup$ Sorry for the late reply, but the null hypothesis is that the observed samples are drawn from a multinomial distribution characterized by known frequencies of ~20 categories. $\endgroup$ Mar 17 '13 at 22:17

You say you know the probability of each side of the die and there are about 20 sides. Let's denote the sides $i$ for $ i = 1, 2, ..., 20$. So your answer is exactly the definition-- $p$-value$(i_0) =$ $$ \sum_{ \{ i : p(i) \leq p(i_0)\} } p(i). $$

Note that I disagree slightly with your definition. I think the $<$ in your sum should be $\leq$.


Try approximating the distribution by multivariate normal and then make use of Mahalanobis distnace.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.