R: Truncated Distributions

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.

### See Also

`interval`, `is.proper`, `LaplaceApproximation`, `LaplacesDemon`, and `PMC`.

### Examples

    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)

[Package LaplacesDemon version 16.1.1 Index]