dist.Truncated {LaplacesDemon} R Documentation

## Truncated Distributions

### Description

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

### Usage

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 pertain to the probability distribution specified in the spec argument.

### 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. For more information on propriety, see is.proper. 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 dtrunc function is often used in conjunction with the interval function to truncate prior probability distributions in the model specification function for use with these numerical approximation functions: LaplaceApproximation, LaplacesDemon, and PMC.

The R code of Nadarajah and Kotz (2006) has been modified to work with log-densities.

### 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.

interval, is.proper, LaplaceApproximation, LaplacesDemon, and PMC.
library(LaplacesDemon)