16. Pascal

Blaise Pascal, a prominent French mathematician of the 1600s, was the first to formulate the Pascal distribution. The distribution is also often referred as the negative binomial distribution. When an experiment is run whose outcome could be a success or a failure with probabilities of p and (1 − p), respectively, and the analyst is seeking k successes of the experiment, the random variable is the minimum number of fails that occur to achieve the goal of k successes. This distribution is called the Pascal distribution. Some analysts working with the Pascal are interested when the random variable is the minimum number of trials to achieve the k successes. An example is when a production facility needs to produce k successful units for a customer order and the probability of a successful unit is less than one. The number of fails till the k successful units becomes the random variable. The chapter describes how to measure the probabilities for each situation. When the probability of a success per trial is not known, sample data may be used to estimate the probability. On other occasions, no sample data is available and an approximation on the distribution is used to estimate the probability.