Parameters for negbinomial Function?

[mark4flies]

I do not understand the description of the negbinomial function in the Help system. My understanding of this probability mass function is that it provides the probability of r successes out of x trials when the probability of a success is equal to p. The HP Prime computation is P(X=x) = COMB(x-1,r-1)*(p^r)*(1-p)^(x-r). I defined a user function this way and confirmed its results.

I want to use the built-in function negbinomial(n,k,x) but I do not understand the parameters. How do n, k, and x here relate to the x, r, and p above?

Thanks!

[Eddie W. Shore]

How is the negbinomial distribution different from the regular binomial distribution?

[mark4flies]

They share a common basis: the Bernoulli trial. The binomial distribution is for n independent Bernoulli trials, each with the same probability of success p. The PMF is the probability of y successes given n trials and p.

The negbinomial distribution is for the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures occurs. This distribution is useful in QA work, for example.

Similar names but the negbinomial distribution is related more closely with the geometric and hypergeometric distributions than it is the binomial distribution.

With both distributions, 'success' and 'failure' can be substituted with any dichotomous outcomes or switched.