The shorthand X ∼ Pascal(n, p) is used to indicate
that the random variable X has the Pascal distribution positive
integer parameter n and real parameter p satisfying 0 < p < 1.
A Pascal random variable X has probability mass function
f (x) = ?n − 1 + x? p n (1 − p)x x = 0, 1, 2, . . . . x
The Pascal distribution is also known as the negative binomial distribution. The Pascal distribution can be used to model the number of failures before the nth success in repeated mutually independent Bernoulli trials, each with probability of success p. Applications include acceptance sampling in quality control and modelling demand for a product. The probability mass function for three different parameter settings is illustrated below.
f (x) = ?n − 1 + x? p n (1 − p)x x = 0, 1, 2, . . . . x
The Pascal distribution is also known as the negative binomial distribution. The Pascal distribution can be used to model the number of failures before the nth success in repeated mutually independent Bernoulli trials, each with probability of success p. Applications include acceptance sampling in quality control and modelling demand for a product. The probability mass function for three different parameter settings is illustrated below.
