non-central chi-squared distribution

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If Z1, Z2,…, Zν are independent standard normal variables and δ1, δ2,…, δν are constants then X, given by is said to have a non-central chi-squared distribution with ν degrees of freedom and non-centrality parameter λ, where The probability density function f of X is given by where Γ is the gamma function. The distribution, which is unimodal, has mean (ν+λ) and variance 2(ν+2λ). If λ=0 then the distribution becomes the chi-squared distribution with ν degrees of freedom.

Subjects: Probability and Statistics.

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