Noncentral Chi-Squared Distribution
المؤلف:
Stuart, A.; and Ord, J. K.
المصدر:
Kendall,s Advanced Theory of Statistics, Vol. 2A: Classical Inference & the Linear Model, 6th ed. New York: Oxford University Press
الجزء والصفحة:
p. 865
10-4-2021
1434
Noncentral Chi-Squared Distribution
The noncentral chi-squared distribution with noncentrality parameter 
is given by
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
The raw moments can be calculated analytically as
 |
(8)
|
The first few are therefore
The first few central moments are
REFERENCES:
Stuart, A.; and Ord, J. K. Kendall's Advanced Theory of Statistics, Vol. 2A: Classical Inference & the Linear Model, 6th ed. New York: Oxford University Press, p. 865, 1999.
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