Moments and Moment Generating Function of the (non-central) Chi-Squared Distribution
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)
order |
order of the moment. |
limit |
limit of the loss variable. |
df |
degrees of freedom (non-negative, but can be non-integer). |
ncp |
non-centrality parameter (non-negative). |
t |
numeric vector. |
log |
logical; if |
The kth raw moment of the random variable X is E[X^k], the kth 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).
mchisq gives the kth raw moment,
levchisq gives the kth 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.
Christophe Dutang, Vincent Goulet vincent.goulet@act.ulaval.ca
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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