Density, distribution function, quantile function and random generation for the
scaled and shifted Student's t distribution, parameterized by degrees of freedom (`df`

),
location (`mu`

), and scale (`sigma`

).

dstudent_t(x, df, mu = 0, sigma = 1, log = FALSE) pstudent_t(q, df, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qstudent_t(p, df, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rstudent_t(n, df, mu = 0, sigma = 1)

x | vector of quantiles. |
---|---|

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

mu | Location parameter (median) |

sigma | Scale parameter |

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

q | vector of quantiles. |

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

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

p | vector of probabilities. |

n | number of observations. If |

`dstudent_t`

gives the density`pstudent_t`

gives the cumulative distribution function (CDF)`qstudent_t`

gives the quantile function (inverse CDF)`rstudent_t`

generates random draws.

The length of the result is determined by `n`

for `rstudent_t`

, and is the maximum of the lengths of
the numerical arguments for the other functions.

The numerical arguments other than `n`

are recycled to the length of the result. Only the first elements
of the logical arguments are used.

`parse_dist()`

and parsing distribution specs and the `stat_dist_slabinterval()`

family of stats for visualizing them.

library(dplyr) library(ggplot2) library(forcats) expand.grid( df = c(3,5,10,30), scale = c(1,1.5) ) %>% ggplot(aes(y = 0, dist = "student_t", arg1 = df, arg2 = 0, arg3 = scale, color = ordered(df))) + stat_dist_slab(p_limits = c(.01, .99), fill = NA) + scale_y_continuous(breaks = NULL) + facet_grid( ~ scale) + labs( title = "dstudent_t(x, df, 0, sigma)", subtitle = "Scale (sigma)", y = NULL, x = NULL ) + theme_ggdist() + theme(axis.title = element_text(hjust = 0))