# The Truncated Normal Distribution

### Description

Density, distribution function, quantile function, random generation and expected value function for the truncated normal distribution with mean equal to 'mean' and standard deviation equal to 'sd'.

### Usage

1 2 3 4 5 6 |

### Arguments

`x,q` |
vector of quantiles. |

`p` |
vector of probabilites. |

`n` |
number of observations. If 'length(n) > 1', the length is taken to be the number required. |

`a` |
vector of lower bounds. These may be |

`b` |
vector of upper bounds. These may be |

`mean` |
vector of means. |

`sd` |
vector of standard deviations. |

### Details

If `mean`

or `sd`

are not specified they assume the default values of
`0`

and `1`

, respectively. The values of `a`

, `b`

,
`mean`

and `sd`

are recycled as needed.

### Value

'dtruncnorm' gives the density, 'ptruncnorm' gives the distribution function, 'qtruncnorm' gives the quantile function, 'rtruncnorm' generates random deviates, 'etruncnorm' gives the expected value and 'vtruncnorm' the variance of the distribution.

### Author(s)

Heike Trautmann trautmann@statistik.tu-dortmund.de,
Detlef Steuer steuer@hsu-hamburg.de,
Olaf Mersmann olafm@statistik.tu-dortmund.de and
Björn Bornkamp bornkamp@statistik.tu-dortmund.de who donated a
much improved `rtruncnorm`

implementation using an accept-reject sampler.

### References

The accept-reject sampler follows the description given in

Geweke, J. (1991). *Efficient simulation from the multivariate normal
and student-t distributions subject to linear constraints*. In
Computing Science and Statistics: Proceedings of the 23rd Symposium on
the Interface, Ed. E. Keramidas and S. Kaufman, pp. 571-8. Fairfax
Station, VA: Interface Foundation of North America.