NAG Library Function Document
nag_cumul_normal (s15abc) returns the value of the cumulative Normal distribution function, .
||nag_cumul_normal (double x)
evaluates an approximate value for the cumulative Normal distribution function
The function is based on the fact that
and it calls nag_erfc (s15adc)
to obtain a value of
for the appropriate argument.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
On entry: the argument of the function.
Error Indicators and Warnings
Because of its close relationship with
, the accuracy of this function is very similar to that in nag_erfc (s15adc)
are the relative errors in result and argument, respectively, they are in principle related by
so that the relative error in the argument,
, is amplified by a factor,
, in the result.
For small and for positive this factor is always less than one and accuracy is mainly limited by machine precision.
For large negative the factor behaves like and hence to a certain extent relative accuracy is unavoidably lost.
However the absolute error in the result,
, is given by
so absolute accuracy can be guaranteed for all
Parallelism and Performance
nag_cumul_normal (s15abc) is not threaded in any implementation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
Program Text (s15abce.c)
Program Data (s15abce.d)
Program Results (s15abce.r)