The inormcdf function calculates the inverse normal cumulative distribution function (CDF).

Synopsis

inormcdf(prob,mean,std_dev)

Summary

The inverse normal CDF, corresponding to the cumulative probability of prob given a normal distribution with the specified mean and std_dev.

Example

The standard normal distribution has mean μ = 0 and standard deviation σ = 1. This example shows the cumulative probabilities that corresponds to probabilities from 0.25 up to 0.975.

Create a 1-dimensional array of size 20 to hold probabilities, and fill it with probability values from 0.25 to 0.975:

AFL% store(build(<prob:double>[x=0:19], (x+0.5)/20.0), probabilities);

The output is:

{x} prob
{0} 0.025
{1} 0.075
{2} 0.125
{3} 0.175
{4} 0.225
{5} 0.275
{6} 0.325
{7} 0.375
{8} 0.425
{9} 0.475
{10} 0.525
{11} 0.575
{12} 0.625
{13} 0.675
{14} 0.725
{15} 0.775
{16} 0.825
{17} 0.875
{18} 0.925
{19} 0.975

Calculate the inverse normal CDF using the values in the probabilities array:

apply(probabilities, standard_deviations, inormcdf(prob,0,1));

The output is:

{x} prob,standard_deviations
{0} 0.025,-1.95996
{1} 0.075,-1.43953
{2} 0.125,-1.15035
{3} 0.175,-0.934589
{4} 0.225,-0.755415
{5} 0.275,-0.59776
{6} 0.325,-0.453762
{7} 0.375,-0.318639
{8} 0.425,-0.189118
{9} 0.475,-0.0627068
{10} 0.525,0.0627068
{11} 0.575,0.189118
{12} 0.625,0.318639
{13} 0.675,0.453762
{14} 0.725,0.59776
{15} 0.775,0.755415
{16} 0.825,0.934589
{17} 0.875,1.15035
{18} 0.925,1.43953
{19} 0.975,1.95996

Note that more than 95% of values fall within two standard deviations of the mean for the standard normal distribution. That is, for the standard normal distribution, two standard deviations comprise a 95% confidence interval.

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