| InvGaussSupp {actuar} | R Documentation |
Raw moments, limited moments and moment generating function for the
Inverse Gaussian distribution with parameters nu and
lambda.
minvGauss(order, nu, lambda) levinvGauss(limit, nu, lambda, order = 1) mgfinvGauss(x, nu, lambda, log= FALSE) minvgauss(order, nu, lambda) levinvgauss(limit, nu, lambda, order = 1) mgfinvgauss(x, nu, lambda, log= FALSE)
order |
order of the moment. Only order = 1 is
supported by levinvGauss. |
limit |
limit of the loss variable. |
nu, lambda |
parameters. Must be strictly positive. |
x |
numeric vector. |
log |
logical; if TRUE, the cumulant generating function
is returned. |
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)^k] and the moment generating function is E[e^{xX}].
minvGauss gives the kth raw moment,
levinvGauss gives the kth moment of the limited loss
variable, and
mgfinvGauss gives the moment generating function in x.
Invalid arguments will result in return value NaN, with a warning.
Vincent Goulet vincent.goulet@act.ulaval.ca, Christophe Dutang
Chhikara, R. S. and Folk, T. L. (1989), The Inverse Gaussian Distribution: Theory, Methodology and Applications, Decker.
Seshadri, D. N. (1989), The Inverse Gaussian Distribution: Statistical Theory and Applications, Springer.
invGauss in package SuppDists for the
density function, distribution function, quantile function and random
number generator.
minvGauss(2, 3, 4) levinvGauss(10, 3, 4) mgfinvGauss(1,3,2)