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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

### 7.15.4 Probability functions

The probability functions for the Normal or Gaussian distribution are described in Abramowitz & Stegun, Section 26.2.

Function: double gsl_sf_erf_Z (double x)
Function: int gsl_sf_erf_Z_e (double x, gsl_sf_result * result)
These routines compute the Gaussian probability density function Z(x) = (1/\sqrt{2\pi}) \exp(-x^2/2).
Function: double gsl_sf_erf_Q (double x)
Function: int gsl_sf_erf_Q_e (double x, gsl_sf_result * result)
These routines compute the upper tail of the Gaussian probability function Q(x) = (1/\sqrt{2\pi}) \int_x^\infty dt \exp(-t^2/2).

The hazard function for the normal distribution, also known as the inverse Mill's ratio, is defined as,

h(x) = Z(x)/Q(x) = \sqrt{2/\pi} \exp(-x^2 / 2) / \erfc(x/\sqrt 2)


It decreases rapidly as x approaches -\infty and asymptotes to h(x) \sim x as x approaches +\infty.

Function: double gsl_sf_hazard (double x)
Function: int gsl_sf_hazard_e (double x, gsl_sf_result * result)
These routines compute the hazard function for the normal distribution.
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition