tnorm | R Documentation |

Density, distribution function, quantile function, and random generation for the left and/or right truncated normal distribution.

```
dtnorm(x, mean = 0, sd = 1, left = -Inf, right = Inf, log = FALSE)
ptnorm(q, mean = 0, sd = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
qtnorm(p, mean = 0, sd = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
rtnorm(n, mean = 0, sd = 1, left = -Inf, right = Inf)
```

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

`mean` |
vector of means. |

`sd` |
vector of standard deviations. |

`left` |
left censoring point. |

`right` |
right censoring point. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`lower.tail` |
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x]. |

If `mean`

or `sd`

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

and `1`

, respectively. `left`

and `right`

have the defaults `-Inf`

and `Inf`

respectively.

The truncated normal distribution has density

```
f(x) = 1/\sigma \phi((x - \mu)/\sigma) /
(\Phi((right - \mu)/\sigma) - \Phi((left - \mu)/\sigma))
```

for `left \le x \le right`

, and 0 otherwise.

`\Phi`

and `\phi`

are the cumulative distribution function
and probability density function of the standard normal distribution
respectively, `\mu`

is the mean of the distribution, and `\sigma`

the standard deviation.

`dtnorm`

gives the density, `ptnorm`

gives the distribution
function, `qtnorm`

gives the quantile function, and `rtnorm`

generates random deviates.

`dnorm`

crch documentation built on March 31, 2023, 11:08 p.m.

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