multpdf

Multinomial probability density function.

This m-file returns the multinomial probability density function value with parameters N and P at the values in X. Note that the density function is zero unless X is an integer.

Let {X1, X2, . . . , Xk}, k > 1, be a set of random variables, each of which can take the values 0, 1, . . . , n. Suppose there are k nonnegative numbers {p1, p2, . . . , pk} that sum to one, such that for every set of k nonnegative integers {n1, . . . , nk} whose sum is n, P( X1 = n1 and X2 = n1 and . . . and Xk = nk ) =

n!
------------------------×p1^n1×p2^n2×..×pk^nk .
n1!×n2!×..×nk!

Then {X1, X1, . . . , Xk} have a multinomial joint distribution with parameters n and p1, p2, . . . , pk. The parameter n is called the number of trials; the parameters p1, p2, . . . , pk are called the category probabilities; k is called the number of categories.

File needs to input n-number of trials, p-vector of associated probabilities and x-vector of the interested values.

It output the multinomial probability density value.