The non-central chi-squared distribution
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Distribution name
Non-central chi-squared
distribution
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Common notation
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Parameters
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 =
degrees of freedom (positive integer)
 =
non-centrality parameter ( )
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Domain
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Probability density
function
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Cumulative distribution
function
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where  is the
Marcum-Q function.
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Mean
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Variance
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Skewness
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(Excess) kurtosis
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Characteristic function
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Other comments
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The non-central chi-squared distribution with degrees
of freedom and non-centrality parameter is the
distribution of the sum of the squares of independent
normal distributions each with unit standard deviation but with non-zero
means  where  . The
(standard) chi-squared
distribution is a special case of it with  .
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Nematrian web functions
This distribution is not currently supported within the Nematrian
web function library. For details of other supported probability
distributions see here.
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