nhygepdf

Negative hypergeometric probability density function.

This m-function returns the negative hypergeometric probability density function with parameters M, N and A at the values in X. Note: The density function is zero unless M, N and A are integers.

If a lot consists of M acceptable items and N defective ones. Suppose that items are drawn at random one by one without replacement and x defectives are observed before the a'th acceptable one. According to Johnson et al. (2005), in an inspection sampling, instead of taking a sample of fixed size from a batch of items and then accepting the batch if the observed number of defectives is less than or equal to some predetermined value (otherwise rejecting). Here, items are drawn one at a time until either defectives are observed (at which point the batch is rejected) or nondefectives are observed (and the batch is accepted). The number of observations required to reach a decision then has a negative hypergeometric distribution.

This discrete distribution is also known as Beta-Binomial, Inverse hypergeometric, Hypergeometric waiting time, and Markov-Polya.

Its distribution function is expresed as,

f(x) = P(X=x) = (x+a-1_C_x)(m+n-a-x_C_m-x)/(m+n_C_m)

'Probability of x failures one will have before the a success(es)'

where: m=number of acceptables, n=number of not acceptables (defectives), x=number of observed defectives, before a=acceptable ones. C means combination. m+n=N, total number of elements.

Syntax: function y = nhygepdf(x,m,n,a)

Inputs:
m - number of acceptables
n - number of not acceptables (defectives)
x - number of observed defectives, before
a - acceptable ones

Output:
y - negative hypergeometric probability value