tt | R Documentation |

Density, distribution function, quantile function, and random generation
for the left and/or right truncated student-t distribution with `df`

degrees of freedom.

```
dtt(x, location = 0, scale = 1, df, left = -Inf, right = Inf, log = FALSE)
ptt(q, location = 0, scale = 1, df, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
qtt(p, location = 0, scale = 1, df, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
rtt(n, location = 0, scale = 1, df, left = -Inf, right = Inf)
```

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

`location` |
location parameter. |

`scale` |
scale parameter. |

`df` |
degrees of freedom (> 0, maybe non-integer). |

`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 `location`

or `scale`

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 student-t distribution has density

```
f(x) = 1/\sigma \tau((x - \mu)/\sigma) /
(T((right - \mu)/\sigma) - T((left - \mu)/\sigma))
```

for `left \le x \le right`

, and 0 otherwise.

where `T`

and `\tau`

are the cumulative distribution function
and probability density function of the student-t distribution with
`df`

degrees of freedom respectively, `\mu`

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

the scale.

`dtt`

gives the density, `ptt`

gives the distribution
function, `qtt`

gives the quantile function, and `rtt`

generates random deviates.

`dt`

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