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