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8 Incomplete Gamma and Related FunctionsApplications

§8.23 Statistical Applications

The functions P(a,x) and Q(a,x) are used extensively in statistics as the probability integrals of the gamma distribution; see Johnson et al. (1994, pp. 337–414). Particular forms are the chi-square distribution functions; see Johnson et al. (1994, pp. 415–493). The function Bx(a,b) and its normalization Ix(a,b) play a similar role in statistics in connection with the beta distribution; see Johnson et al. (1995, pp. 210–275). In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of Q(a,x); see Jagerman (1974) and Cooper (1981, pp. 80, 316–319).