digkotz {ig} | R Documentation |
This function computes the probabilility density function of inverse Gaussian
distribution generated from the Kotz distribution with parameters q
,
r
and s
.
digkotz(x, mu = 1.0, lambda = 1.0, parameters = c(1.0, 1.0, 1.0), log = FALSE)
x |
Vector of observations. |
mu |
Mean. |
lambda |
Scale parameter. |
parameters |
Parameters of the Kotz distribution, c(q, r, s) . |
log |
Logical; if TRUE, probabilities p are given as log(p). |
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}].
digkotz()
gives the pdf of an IGTD generated from the Kotz kernel.
Víctor Leiva <victor.leiva@uv.cl; victor.leiva@yahoo.com>,
Hugo Hernández <hugo.hernandez.p@gmail.com> and
Antonio Sanhueza <asanhueza@ufro.cl>.
Sanhueza, A., Leiva, V., Balakrishnan, N. (2008). A new class of inverse Gaussian type distributions. Metrika (in press).
# Produces a graphical plot for the IGD from the Kotz kernel # with parameters q = 1, r = 2 and s = 3 x <- seq(-3, 3, by = 0.01) y <- digkotz(x, 1.0, 1.0, parameters = c(1, 2, 3)) plot(x, y, type = "l", xlab = "x", ylab = "f(x)")