cdft

Arguments

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.

In certain cases, the degrees of freedom are not integers. Scilab then issues a warning.

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

Examples

In the following example, we compute the probability of the event T=5 for the Student's T distribution function with Df=2.

T = 5;
Df = 2;
// Expected : P = 0.9811252 and Q = 1-P
[P, Q] = cdft("PQ", T, Df)

See also

• cdfbet — cumulative distribution function Beta distribution
• cdfbin — cumulative distribution function Binomial distribution
• cdfchi — cumulative distribution function chi-square distribution
• cdfchn — cumulative distribution function non-central chi-square distribution
• cdff — cumulative distribution function Fisher distribution
• cdffnc — cumulative distribution function non-central f-distribution
• cdfgam — cumulative distribution function gamma distribution
• cdfnbn — cumulative distribution function negative binomial distribution
• cdfnor — cumulative distribution function normal distribution
• cdfpoi — cumulative distribution function poisson distribution