dig.kotz {ig}R Documentation

Probability density function (pdf) of the inverse Gaussian type distribution generated from the Kotz kernel

Description

Compute the probabilility density function of inverse Gaussian distribution generated from the Kotz distribution with parameters q, r and s.

Usage

dig.kotz(t, mu, lambda, parameters = c(1, 1, 1), log = FALSE)

Arguments

t Vector of observations.
mu Mean.
lambda Scale parameter.
parameters Parameters of the Kotz distribution.
log Logical; if TRUE, probabilities p are given as log(p).

Details

The IGTD has pdf given by

f_T(t)=f_Z(a_{t}) sqrt{λ}/sqrt{t^{3}},

with t > 0, μ>0 and λ>0, where f_Z(cdot)= c,g(cdot) is the pdf of the Kotz distribution a_{t} = a_{t}(μ,λ) = sqrt{λ/μ} [sqrt{t/μ} - sqrt{μ/t}].

Value

dig.kotz() gives the pdf of an IGTD generated from the Kotz kernel.

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

x<-seq(-3,3,by=0.01)
y<-dig.kotz(x,1.0,1.0,c(1,2,3))
plot(x,y,type="l",xlab="x",ylab="f(x)")

[Package ig version 1.0 Index]