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nctcdf

Noncentral t cumulative distribution function

Syntax

p = nctcdf(x,nu,delta)
p = nctcdf(x,nu,delta,'upper')

Description

p = nctcdf(x,nu,delta) computes the noncentral t cdf at each value in x using the corresponding degrees of freedom in nu and noncentrality parameters in delta. x, nu, and delta can be vectors, matrices, or multidimensional arrays that have the same size, which is also the size of p. A scalar input for x, nu, or delta is expanded to a constant array with the same dimensions as the other inputs.

p = nctcdf(x,nu,delta,'upper') returns the complement of the noncentral t cdf at each value in x, using an algorithm that more accurately computes the extreme upper tail probabilities.

Examples

expand all

Compute Noncentral t Distribution cdf

Compare the noncentral t cdf with DELTA = 1 to the t cdf with the same number of degrees of freedom (10).

```x = (-5:0.1:5)';
p1 = nctcdf(x,10,1);
p = tcdf(x,10);
plot(x,p,'-',x,p1,':')```

References

[1] Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed., Hoboken, NJ: John Wiley & Sons, Inc., 1993, pp. 147–148.

[2] Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 201–219.