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ncx2cdf

Noncentral chi-square cumulative distribution function

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Syntax

p = ncx2cdf(x,v,delta)
p = ncx2cdf(x,v,delta,'upper')

Description

p = ncx2cdf(x,v,delta) computes the noncentral chi-square cdf at each value in x using the corresponding degrees of freedom in v and positive noncentrality parameters in delta. x, v, and delta can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of p. A scalar input for x, v, or delta is expanded to a constant array with the same dimensions as the other inputs.

p = ncx2cdf(x,v,delta,'upper') returns the complement of the noncentral chi-square cdf at each value in x, using an algorithm that more accurately computes the extreme upper tail probabilities.

Some texts refer to this distribution as the generalized Rayleigh, Rayleigh-Rice, or Rice distribution.

The noncentral chi-square cdf is

F(x|ν,δ)=∑j=0∞((12δ)jj!e−δ2)Pr[χν+2j2≤x]

Examples

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Open Live Script

Compare the noncentral chi-square cdf with DELTA = 2 to the chi-square cdf with the same number of degrees of freedom (4): 

x = (0:0.1:10)';
ncx2 = ncx2cdf(x,4,2);
chi2 = chi2cdf(x,4);

plot(x,ncx2,'b-','LineWidth',2)
hold on
plot(x,chi2,'g--','LineWidth',2)
legend('ncx2','chi2','Location','NW')

Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent ncx2, chi2.

References

[1] Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 130–148.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a

See Also

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