La loi de Pascal restreinte et ses cas particuliers; Constrained Pascal distribution and its special cases

Pascal distribution, Pa(r, /pi), also called Negative binomial distribution, pertains to the trial number n at which the first r successes have been obtained, each trial being the realization of a Bernoulli variable with success probability /pi. We review basic concepts of the Bernoulli process and delve into the constrained Pascal distribution, or Negative binomial distribution of order k, Pa(r, k, /pi), which concerns the trial number n at which r successes have been recorded within the last k trials for the first time. Practical functions and procedures are given for producing probability mass and distribution functions, along with indications for estimating the p parameter.