The noncentral chisquared distribution with noncentrality parameter is given by
(1)
 
(2)
 
(3)

where is a modified Bessel function of the first kind and is a regularized confluent hypergeometric limit function. It is implemented in the Wolfram Language as NoncentralChiSquareDistribution[r, lambda].
The mean, variance, skewness, and kurtosis excess are
(4)
 
(5)
 
(6)
 
(7)

The raw moments can be calculated analytically as
(8)

The first few are therefore
(9)
 
(10)
 
(11)

The first few central moments are
(12)
 
(13)
 
(14)
