cdfChinc¶
Purpose¶
Computes the cumulative distribution function for the noncentral chi-squared distribution.
Format¶
-
p =
cdfChinc(x, df, nonc)¶ - Parameters:
x (Nx1 vector) – Values at which to evaluate the cdf of the noncentral chi-squared distribution. \(x > 0\).
df (scalar) – degrees of freedom, \(df > 0\).
nonc (scalar) – noncentrality parameter, \(nonc > 0\). Note: This is the square root of the noncentrality parameter that sometimes goes under the symbol \(\lambda\). \(nonc > 0\).
- Returns:
p (Nx1 vector) – Each element in p is the noncentral chi-squared cdf value evaluated at the corresponding element in x.
Examples¶
// Values
x = { .5, 1, 5, 25 };
// Degrees of freedom
df = 4;
// Non-centrality parameter
nonc = 2;
print cdfChinc(x, df, nonc);
The code above returns:
0.0042086234
0.016608592
0.30954232
0.99441140
Remarks¶
p is the integral from 0 to x of the noncentral chi-square distribution with df degrees of freedom and noncentrality nonc.
cdfChinc() can return a vector of values, but the degrees of freedom and
noncentrality parameter must be the same for all values of x.
For invalid inputs, cdfChinc() 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.
Relation to cdfChic():
cdfChic(x, df) = 1 - cdfChinc(x, df, 0);