hfigt {ig}R Documentation

Hazard function of the IGTD

Description

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

Usage

hfigt(x, mu = 1.0, lambda = 1.0, nu = 1.0, kernel = "normal")

Arguments

x Vector of observations.
mu Mean.
lambda Scale parameter.
nu Shape parameter corresponding to the degrees of freedom of the t distribution. In the case of the Laplace, logistic, normal kernels, nu can be fixed at the value 1.0 since this parameter is not involved in these kernels.
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.

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; victor.leiva@yahoo.com>,
Hugo Hernández <hugo.hernandez.p@gmail.com> and
Antonio Sanhueza <asanhueza@ufro.cl>.

References

Sanhueza, A., Leiva, V., Balakrishnan, N. (2008). A new class of inverse Gaussian type distributions. Metrika (in press).

Examples

## Computes the hf of the IGTD with normal kernel for a vector x with mu = 1.0, 
## lambda = 1.0
x  <- seq(0.01, 4, by = 0.01)
hx <- hfigt(x, mu = 1.0, lambda = 1.0, nu = 1.0, kernel = "normal")
print(hx)

## At the end there is the graph of this pdf
plot(x, hx, main = "hf of the IGTD (classical case)", ylab = "h(x)")

[Package ig version 1.2 Index]