pig {ig}R Documentation

Cumulative distribution function (cdf) of the inverse Gaussian type distribution

Description

Cumulative distribution function for the IGDT with mean mu, scale parameter lambda and associated kernel g.

Usage

pig(q, mu = 1, lambda = 1, kernel = "normal", parameter.nu = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

q 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.
lower.tail Logical; if TRUE (default), probabilities are P[X <= x],
otherwise, P[X > x].
log.p Logical; if TRUE, probabilities p are given as log(p).

Details

The IGTD has cdf given by

F_T(t) = F_Z(a_t)+int^{infty}_{b_t} c , g(u^2- frac{4 , λ}{μ}) mbox{d}u,

where b_t=sqrt{λ/μ} [sqrt{t/μ} + sqrt{μ/t}], μ is the mean, λ the scale parameter, g is the kernel of the pdf of the associated symmetrical distribution, c the normalization constant and F_Z(cdot) denotes the cdf of the associated symmetrical distribution.

Value

pig() gives the cdf of an IGTD.

Author(s)

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

References

Sanhueza, A., Leiva, V. and Balakrishnan, N. (2007). A new class of inverse Gaussian type distributions. Metrika (in press).

Examples

## Compute the cdf for a vector q with mu=1, lambda=1 and g="normal"
## At the end we have the graph of the cdf of the IGTD with g="normal".
x <- seq(0, 4,by=0.01)
px <- pig(x,mu=1.0,lambda=1.0,kernel="normal")
print(px)
plot(x, px, main = "cdf of the IGTD (g='normal')", ylab="F(x)")

[Package ig version 1.0 Index]