NAG AD Library g01ha_a1w_f (prob_bivariate_normal_a1w)
Note:a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype.
Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document.
Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types.
The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.
The routine may be called by the names g01ha_a1w_f or nagf_stat_prob_bivariate_normal_a1w. The corresponding t1w and p0w variants of this routine are also available.
is the adjoint version of the primal routine
g01haf returns the lower tail probability for the bivariate Normal distribution.
For further information see Section 3 in the documentation for g01haf.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Genz A (2004) Numerical computation of rectangular bivariate and trivariate Normal and probabilities Statistics and Computing14 151–160
Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
In addition to the arguments present in the interface of the primal routine,
g01ha_a1w_f includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine.
A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.
Note that the primal routine
is a function whereas g01ha_a1w_f,
is a subroutine, where the function value is returned in the additional output parameter, p.