The itcdf function calculates the inverse student's t cumulative distribution function (CDF).

Synopsis

itcdf(prob,degrees_of_freedom)

Summary

The student's t-CDF represents the probability p that a single observation from the t-distribution with ν degrees of freedom will fall in the interval [−∞, x). Thus the inverse student's t-CDF returns x, given p and ν.

Example

Create a 1-dimensional array of size 10 filled with values from 0.5 to 9.5.

AFL% store(build(<x:double>[i=0:9], i+1/2.0), inputs);

The output is:

{i} x
{0} 0.5
{1} 1.5
{2} 2.5
{3} 3.5
{4} 4.5
{5} 5.5
{6} 6.5
{7} 7.5
{8} 8.5
{9} 9.5

Apply the tcdf function to the attribute x for 4 degrees of freedom and store the result in array probabilities:

AFL% store(apply(inputs, t_4d, tcdf(x, 4)), probabilities);

The output is:

{i} x,t_4d
{0} 0.5,0.678335
{1} 1.5,0.896
{2} 2.5,0.966617
{3} 3.5,0.987552
{4} 4.5,0.994589
{5} 5.5,0.997336
{6} 6.5,0.998555
{7} 7.5,0.999155
{8} 8.5,0.999475
{9} 9.5,0.999657

Apply the inverse student's t function:

AFL% apply(probabilities, inverse, itcdf(t_4d, 4));

The output is:

{i} x,t_4d,inverse
{0} 0.5,0.678335,0.5
{1} 1.5,0.896,1.5
{2} 2.5,0.966617,2.5
{3} 3.5,0.987552,3.5
{4} 4.5,0.994589,4.5
{5} 5.5,0.997336,5.5
{6} 6.5,0.998555,6.5
{7} 7.5,0.999155,7.5
{8} 8.5,0.999475,8.5
{9} 9.5,0.999657,9.5

Remove the example arrays:

AFL% remove(inputs); remove(probabilities);