hfig {ig}R Documentation

function (hf) of the inverse Gaussian type distribution

Description

Hazard function or failure rate for the IGTD with mean parameter mu, scale parameter lambda and associated kernel g.

Usage

hfig(t, mu = 1, lambda = 1, kernel = "normal", parameter.nu = 1)

Arguments

t Vector of quantiles.
mu Mean.
lambda Scale parameter.
kernel Kernel of the pdf of the associated symmetrical distribution by means of which the IGTD is obtained. The kernels: "Laplace", "logistic", "normal" and "t" are available.
parameter.nu Additional parameter of the IGTD when the t kernel is used. This parameter corresponds to a shape parameter and it is also known as "degree of freedom". For default nu=1, in which case the Cauchy distribution is obtained. The Student-t distribution has always degrees of kurtosis greater than normal distribution. This aspect is transferred to the IGTD and produces robust parameter estimates for the IGTD.

Details

The IGTD has hf given by

h_T(t)=frac{f_Z(a_{t}) , frac{sqrt{λ}}{sqrt{t^{3}}}}{F_Z(-a_t)-int^{infty}_{b_t} c , g(u^2- frac{4 , λ}{μ}) mbox{footnotesize d}u}.

Value

hfig() gives the hf of an IGTD.

Author(s)

Víctor Leiva <victor.leiva@uv.cl>, Hugo Hernández <hugo.hernandez@msn.com>, and Antonio Sanhueza <asanhue@ufro.cl>.

Examples

## Computes the hf of the IGTD with g="normal" for a vector x with mu=1, lambda=1 and g="normal"
## At the end we have the graph of the IGTD hf 
x <- seq(0, 4,by=0.01)
hx <- hfig(x,mu=1.0,lambda=1.0,kernel="normal")
print(hx)
plot(x, hx, main = "Hazard function of the IGTD (classical case)", ylab="h(x)")

[Package ig version 1.0 Index]