Raw moments, limited moments and moment generating function for the
chi-squared (\(\chi^2\)) distribution with df degrees
of freedom and optional non-centrality parameter ncp.
mchisq(order, df, ncp = 0)
levchisq(limit, df, ncp = 0, order = 1)
mgfchisq(t, df, ncp = 0, log= FALSE)mchisq gives the \(k\)th raw moment,
levchisq gives the \(k\)th moment of the limited loss
variable, and
mgfchisq gives the moment generating function in t.
Invalid arguments will result in return value NaN, with a warning.
order of the moment.
limit of the loss variable.
degrees of freedom (non-negative, but can be non-integer).
non-centrality parameter (non-negative).
numeric vector.
logical; if TRUE, the cumulant generating function
is returned.
Christophe Dutang, Vincent Goulet vincent.goulet@act.ulaval.ca
The \(k\)th raw moment of the random variable \(X\) is \(E[X^k]\), the \(k\)th limited moment at some limit \(d\) is \(E[\min(X, d)]\) and the moment generating function is \(E[e^{tX}]\).
Only integer moments are supported for the non central Chi-square
distribution (ncp > 0).
The limited expected value is supported for the centered Chi-square
distribution (ncp = 0).
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.
Johnson, N. L. and Kotz, S. (1970), Continuous Univariate Distributions, Volume 1, Wiley.
mchisq(2, 3, 4)
levchisq(10, 3, order = 2)
mgfchisq(0.25, 3, 2)
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