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/σ τ((x - μ)/σ) /
(T((right - μ)/σ) - T((left - μ)/σ))*

for *left ≤ x ≤ right*, and 0 otherwise.

where *T* and *τ* are the cumulative distribution function
and probability density function of the student-t distribution with
`df`

degrees of freedom respectively, *μ* is the location of the
distribution, and *σ* 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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