cdfChincInv

Purpose

Computes the quantile or inverse of noncentral chi-squared cumulative distribution function.

Format

x = cdfChincInv(p, df, nonc)
Parameters:
  • p (NxK matrix, Nx1 vector or scalar) – Probabilities at which to compute the inverse of noncentral chi-squared cumulative distribution function. \(0 < p < 1\).
  • df (ExE conformable with p) – The degrees of freedom. \(df > 0\).
  • nonc (ExE conformable with p) – The noncentrality parameter. Note: This is the squared root of the noncentrality parameter that sometimes goes under the symbol \(\lambda\). \(nonc > 0\).
Returns:

x (NxK matrix, Nx1 vector or scalar) – each value of x is the value such that the noncentral chi-squared cdf with df degrees of freedom and nonc noncentrality evaluated at x is equal to the corresponding value of p.

Examples

// Probabilities
p = { .05, .1, .25, .5, .75, 0.90, 0.95 };

// Degrees of freedom
df = 4;

// Non-centrality parameter
nonc = 2;

print cdfChincInv(p, df, nonc);

The code above returns:

1.7650
2.5583
4.3564
7.1016
10.6736
14.6157
17.3093

Remarks

For invalid inputs, cdfChincinv() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr() will return a 1; if the second is out of range, scalerr will return a 2; etc.