# Truncated Distributions

### Description

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

### Usage

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### Arguments

`n` |
This is a the number of random draws for |

`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 |

`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 |

`...` |
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.

### See Also

`lqr`

,
`SKD`

.

### Examples

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