dist.Truncated: Truncated Distributions In lqr: Robust Linear Quantile Regression

Description

Density, distribution function, quantile function and random generation for truncated distributions.

Usage

 ```1 2 3 4 5 6``` ```dtrunc(x, spec, a=-Inf, b=Inf, log=FALSE, ...) extrunc(spec, a=-Inf, b=Inf, ...) ptrunc(x, spec, a=-Inf, b=Inf, ...) qtrunc(p, spec, a=-Inf, b=Inf, ...) rtrunc(n, spec, a=-Inf, b=Inf, ...) vartrunc(spec, a=-Inf, b=Inf, ...) ```

Arguments

 `n` This is a the number of random draws for `rtrunc`. `p` This is a vector of probabilities. `x` This is a vector to be evaluated. `spec` The base name of a probability distribution is specified here. For example, to estimate the density of a truncated normal distribution, enter `norm`. `a` This is the lower bound of truncation, which defaults to negative infinity. `b` This is the upper bound of truncation, which defaults to infinity. `log` Logical. If `log=TRUE`, then the logarithm of the density is returned. `...` Additional arguments to pass.

Details

A truncated distribution is a conditional distribution that results from a priori restricting the domain of some other probability distribution. More than merely preventing values outside of truncated bounds, a proper truncated distribution integrates to one within the truncated bounds. In contrast to a truncated distribution, a censored distribution occurs when the probability distribution is still allowed outside of a pre-specified range. Here, distributions are truncated to the interval [a,b], such as p(theta) in [a,b].

The R code of Nadarajah and Kotz (2006) has been modified to work with log-densities. This code was also available in the (extinct) package LaplacesDemon.

Value

`dtrunc` gives the density, `extrunc` gives the expectation, `ptrunc` gives the distribution function, `qtrunc` gives the quantile function, `rtrunc` generates random deviates, and `vartrunc` gives the variance of the truncated distribution.

References

Nadarajah, S. and Kotz, S. (2006). "R Programs for Computing Truncated Distributions". Journal of Statistical Software, 16, Code Snippet 2, p. 1–8.

`lqr`, `SKD`.
 ```1 2``` ```x <- seq(-0.5, 0.5, by = 0.1) y <- dtrunc(x, "norm", a=-0.5, b=0.5, mean=0, sd=2) ```