digpvii {ig}R Documentation

Density of the IGTD generated from the Pearson type VII kernel

Description

Probabilility density function of the IGTD generated from the the Pearson type VII kernel with parameters q and r.

Usage

digpvii(x, mu = 1.0, lambda = 1.0, parameters = c(1.0, 1.0), log = FALSE)

Arguments

x Vector of observations.
mu Mean.
lambda Scale parameter.
parameters Parameters of the Kotz distribution, c(q, r).
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 Pearson VII distribution a_{t} = a_{t}(μ,λ) = sqrt{λ/μ} [sqrt{t/μ} - sqrt{μ/t}].

Value

digpvii() gives the pdf of an IGTD generated from the Pearson VII kernel.

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

# Produces a graphical plot for the IGD from the Pearson VII type kernel
# with parameters q = 1 y r = 2
x <- seq(-3, 3, by = 0.01)
y <- digpvii(x, 1.0, 1.0, parameters = c(1, 2))
plot(x, y, type = "l", xlab = "x", ylab = "f(x)")

[Package ig version 1.2 Index]