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

1. 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

2. 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

3. 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

4. Remove the example arrays:

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