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NAG Toolbox

NAG Toolbox: nag_specfun_cdf_normal (s15ab)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_specfun_cdf_normal (s15ab) returns the value of the cumulative Normal distribution function, Px, via the function name.


[result, ifail] = s15ab(x)
[result, ifail] = nag_specfun_cdf_normal(x)


nag_specfun_cdf_normal (s15ab) evaluates an approximate value for the cumulative Normal distribution function
The function is based on the fact that
and it calls nag_specfun_erfc_real (s15ad) to obtain a value of erfc for the appropriate argument.


Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications


Compulsory Input Parameters

1:     x – double scalar
The argument x of the function.

Optional Input Parameters


Output Parameters

1:     result – double scalar
The result of the function.
2:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

There are no failure exits from this function. The argument ifail is included for consistency with other functions in this chapter.


Because of its close relationship with erfc, the accuracy of this function is very similar to that in nag_specfun_erfc_real (s15ad). If ε and δ are the relative errors in result and argument, respectively, they are in principle related by
ε x e -12 x2 2πPx δ  
so that the relative error in the argument, x, is amplified by a factor, xe-12x2 2πPx , in the result.
For x small and for x positive this factor is always less than one and accuracy is mainly limited by machine precision.
For large negative x the factor behaves like x2 and hence to a certain extent relative accuracy is unavoidably lost.
However the absolute error in the result, E, is given by
E x e -12 x2 2π δ  
so absolute accuracy can be guaranteed for all x.

Further Comments



This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.
function s15ab_example

fprintf('s15ab example results\n\n');

x = [-20   -1     0    1    2    20];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s15ab(x(j));

disp('      x          P(x)');
fprintf('%12.3e%12.3e\n',[x; result]);

s15ab example results

      x          P(x)
  -2.000e+01   2.754e-89
  -1.000e+00   1.587e-01
   0.000e+00   5.000e-01
   1.000e+00   8.413e-01
   2.000e+00   9.772e-01
   2.000e+01   1.000e+00

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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