cdft

Scilab Function
Last update : Dec 1997

cdft - cumulative distribution function Student's T distribution

### Calling Sequence

  `[P,Q]=cdft("PQ",T,Df)`
  `[T]=cdft("T",Df,P,Q)`
  `[Df]=cdft("Df",P,Q,T)`

### Parameters

- `P,Q,T,Df`: six real vectors of the same size.
- `P,Q (Q=1-P)` : The integral from -infinity to t of the t-density. Input range: (0,1].
- `T`: Upper limit of integration of the t-density. Input range: ( -infinity, +infinity). Search range: [ -1E150, 1E150 ]
- `DF:` Degrees of freedom of the t-distribution. Input range: (0 , +infinity). Search range: [1e-300, 1E10]

### Description

Calculates any one parameter of the T distribution given values for the others.

Formula 26.5.27 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to reduce the computation of the cumulative distribution function to that of an incomplete beta.

Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.