# dist.Truncated: Truncated Distributions In LaplacesDemon: Complete Environment for Bayesian Inference

## 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 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`.

## Examples

 ```1 2 3``` ```library(LaplacesDemon) x <- seq(-0.5, 0.5, by = 0.1) y <- dtrunc(x, "norm", a=-0.5, b=0.5, mean=0, sd=2) ```

### Example output

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LaplacesDemon documentation built on July 9, 2021, 5:07 p.m.