invGauss: Inverse Gaussian distribution

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

Inverse Gaussian distribution

Usage

pIG(x,mu,vsi)  # cdf with mean parameter mu and second parameter vsi
dIG(x,mu,vsi)  # density
qIG(p,mu,vsi,mxiter=10,eps=1e-06,mxstep=5,iprint=F)  # inverse cdf
rIG(n,mu,vsi)  # simulation of random variables

Arguments

x	positive value; could be a vector
p	value in (0,1); could be a vector
mu	mean parameter m of inverse Gaussian
vsi	second parameter varsigma=lambda of inverse Gaussian
mxiter	maximum number of iterations
eps	tolerance for convergence
mxstep	bound on step size for Newton-Raphson iterations
iprint	print flag for iterations
n	simulation sample size

Details

Seshadri (1993): with mu>0, vsi>0 means the pdf is: f(x;mu,vsi)= [sqrt(vsi)/sqrt(2*pi*x^3)] * exp[-(vsi/[2mu^2])*(x-mu)^2/x] for x>0.

Reparametrization has mu=zeta*eta as the mean and vsi=eta^2 where eta=convolution parameter; zeta is like a scale parameter that can be set to 1 for the copula

Property of the cdf is pIG(x,mu,vsi)=pIG(x/mu,1,vsi/mu)

Value

cdf or pdf or quantile or random sample

References

Seshadri V (1993). The Inverse Gaussian Distribution. Clarendon Press.

See Also

invGaussconvfactor

Examples

mu=3; vsi=2
x=1:10
p=pIG(x,mu,vsi)
xx=qIG(p,mu,vsi)
print(cbind(x,p,xx))
eps=1.e-5
peps=pIG(x+eps,mu,vsi)
print(cbind((peps-p)/eps,dIG(x,mu,vsi)))
set.seed(123)
n=10000
x=rIG(n,mu,vsi)
print(summary(x))
print(var(x))
cat("theoretical values mean=", mu, " var=", mu^3/vsi,"\n")

YafeiXu/CopulaModel documentation built on May 9, 2019, 11:07 p.m.