The normcdf function calculates the normal cumulative distribution function (CDF).

Synopsis

normcdf(x,mean,std_dev)

Summary

The normal, or Gaussian, CDF with mean μ and standard deviation σ is:

Example

The standard normal distribution has μ = 0 and σ = 1. Any observation has a 0.5 probability of being greater than 0.

Create a 1-dimensional array of size 10 called standard_array with a double attribute called standard, and fill it with values from -2.25 to 2.25:
```
AFL% store(build(<standard:double>[x=0:9], (x-4.5)/2.0), standard_array);
```
These values represent 2.25 standard deviations on either side of the mean.

Find the cumulative probability for each value in standard_array:

AFL% apply(standard_array, prob, normcdf(standard, 0, 1));

The output is:

{x} standard,prob
{0} -2.25,0.0122245
{1} -1.75,0.0400592
{2} -1.25,0.10565
{3} -0.75,0.226627
{4} -0.25,0.401294
{5} 0.25,0.598706
{6} 0.75,0.773373
{7} 1.25,0.89435
{8} 1.75,0.959941
{9} 2.25,0.987776

Note that approximately 97.5% of values fall within 2.25 standard deviations of the mean for the standard normal distribution.

Remove the example array:
```
AFL% remove(standard_array);
```

Inverse

inormcdf: Inverse normal CDF