ChisqSupp | R Documentation |
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 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
).
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.
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.
Chisquare
mchisq(2, 3, 4)
levchisq(10, 3, order = 2)
mgfchisq(0.25, 3, 2)
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