Cauchy Distribution, Using Multiple Draws

Density, distribution function, quantile function and random generation for the Cauchy distribution, modified to work with rvecs.

Usage

dcauchy_rvec(x, location = 0, scale = 1, log = FALSE)

pcauchy_rvec(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)

qcauchy_rvec(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)

rcauchy_rvec(n, location = 0, scale = 1, n_draw = NULL)

Arguments

x: Quantiles. Can be an rvec.
location: Center of distribution. Default is 0. See dcauchy(). Can be an rvec.
scale: Scale parameter. Default is 1. See dcauchy(). Can be an rvec.
log, log.p: Whether to return results on a log scale. Default is FALSE. Cannot be an rvec.
q: Quantiles. Can be an rvec.
lower.tail: Whether to return \(P[X \le x]\), as opposed to \(P[X > x]\). Default is TRUE. Cannot be an rvec.
p: Probabilities. Can be an rvec.
n: The length of random vector being created. Cannot be an rvec.
n_draw: Number of random draws in the random vector being created. Cannot be an rvec.

Value

If any of the arguments are rvecs, or if a value for n_draw is supplied, then an rvec; otherwise an ordinary R vector.

Details

Functions dcauchy_rvec(), pcauchy_rvec(), pcauchy_rvec() and rcauchy_rvec() work like base R functions dcauchy(), pcauchy(), qcauchy(), and rcauchy(), except that they accept rvecs as inputs. If any input is an rvec, then the output will be too. Function rcauchy_rvec() also returns an rvec if a value for n_draw is supplied.

dcauchy_rvec(), pcauchy_rvec(), pcauchy_rvec() and rcauchy_rvec() use tidyverse vector recycling rules:

Vectors of length 1 are recycled
All other vectors must have the same size

Examples

x <- rvec(list(c(3, -5.1),
               c(0, -2.3)))
dcauchy_rvec(x)
#> <rvec_dbl<2>[2]>
#> [1] 0.03183,0.01178 0.3183,0.05061 
pcauchy_rvec(x)
#> <rvec_dbl<2>[2]>
#> [1] 0.8976,0.06163 0.5,0.1305    

rcauchy_rvec(n = 2,
             location = c(-5, 5),
             n_draw = 1000)
#> <rvec_dbl<1000>[2]>
#> [1] -5 (-23, 9.9) 5 (-3.5, 16)