tpt: Truncated positive t
| tpt | R Documentation |
Truncated positive t
Description
Density, distribution function and random generation for the slash truncated positive student-t (tpt) distribution.
Usage
dtpt(x, sigma, lambda, nu, log = FALSE)
ptpt(x, sigma, lambda, nu, lower.tail=TRUE, log=FALSE)
rtpt(n, sigma, lambda, nu)
Arguments
x |
vector of quantiles |
n |
number of observations |
sigma |
scale parameter for the distribution |
lambda |
shape parameter for the distribution |
nu |
nu parameter for the distribution |
log |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x]. |
Details
Random generation is based on the inverse transformation method.
Value
dtpt gives the density, ptpt gives the distribution function and rtpt generates random deviates.
The length of the result is determined by n for rtpt, and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
A variable have tpt distribution with parameters \sigma>0, \lambda \in R and \nu>0 if its probability density
function can be written as
f(y; \sigma, \lambda, q) = \frac{t_\nu\left(\frac{y}{\sigma}-\lambda\right)}{\sigma T_\nu(\lambda)}, y>0,
where t_\nu(\cdot) and T_\nu(\cdot) denote the density and cumultative distribution functions for the standard t distribution with \nu degrees of freedom.
Author(s)
Gallardo, D.I. and Gomez, H.J.
Examples
dtpt(c(1,2), sigma=1, lambda=-1, nu=5)
ptpt(c(1,2), sigma=1, lambda=-1, nu=5)
rtpt(n=10, sigma=1, lambda=-1, nu=5)
