NAG Library Function Document
nag_cumul_normal_complem (s15acc) returns the value of the complement of the cumulative Normal distribution function, .
||nag_cumul_normal_complem (double x)
evaluates an approximate value for the complement of the cumulative Normal distribution function
The function is based on the fact that
and it calls nag_erfc (s15adc)
to obtain the necessary value of
, the complementary error function.
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, then in principle they are related by
For negative or small positive this factor is always less than one and accuracy is mainly limited by machine precision. For large positive we find and hence to a certain extent relative accuracy is unavoidably lost. However the absolute error in the result, , is given by
and since this factor is always less than one absolute accuracy can be guaranteed for all
Parallelism and Performance
nag_cumul_normal_complem (s15acc) 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 (s15acce.c)
Program Data (s15acce.d)
Program Results (s15acce.r)