dig {ig} | R Documentation |
Probability density function for the inverse Gaussian type distribution with mean parameter mu,
scale parameter lambda and associated kernel g. The IGTD is a generalization of the inverse Gaussian
type distribution; for details see Sanhueza, Leiva and Balakrishnan (2007).
The g function corresponds to the kernel of the pdf of the associated symmetrical distribution.
In the ig package, the IGTD can be obtained from the following kernels: Laplace, logistic, normal
(classical case) and Student-t. All these kernels are implemented in the R
software.
The Laplace or double exponential distribution is obtained from the normalp package developed by Mineo (2005).
dig(x, mu = 1, lambda = 1, kernel = "normal", parameter.nu = 1, log = FALSE)
x |
Vector of observations. |
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. This parameter corresponds to a shape parameter known as "degree of freedom" . For default nu=1 , in which case the Cauchy distribution is obtained. The Student-t distribution has always degrees of kurtosis greater than normal distribution. This aspect is transferred to the IGTD and produces robust parameter estimates for the IGTD. |
log |
Logical; if TRUE, probabilities p are given as log(p). |
If mu, lambda or g are not specified, then they assume the default values 0, 1 and "normal"
, respectively. 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 associated symmetrical about zero distribution and a_{t} = a_{t}(μ,λ) = sqrt{λ/μ} [sqrt{t/μ} - sqrt{μ/t}].
dig()
gives the pdf of an IGTD.
Víctor Leiva <victor.leiva@uv.cl>, Hugo Hernández <hugo.hernandez@msn.com>, and Antonio Sanhueza <asanhue@ufro.cl>.
Mineo, A. (2003). A new package for the general error distribution. R News 3, 13-16.
Sanhueza, A., Leiva, V. and Balakrishnan, N. (2007). A new class of inverse Gaussian type distributions. Metrika (in press).
## Compute the pdf of the IGTD with g="normal" for a vector x with mu=1, lambda=1 ## At the end we have the graph of this pdf x <- seq(0, 4,by=0.01) fx <- dig(x,mu=1.0,lambda=1.0,kernel="normal") print(fx) plot(x, fx, main = "pdf of the IGTD (classical case)", ylab="f(x)")