# dusb: Uniform scaled beta distribution In cctools: Tools for the Continuous Convolution Trick in Nonparametric Estimation

## Description

The uniform scaled beta (USB) distribution describes the distribution of the random variable

U_{b, ν} = U + θ(B - 0.5),

where U is a U[-0.5, 0.5] random variable, B is a Beta(ν, ν) random variable, and theta > 0, ν >= 1.

## Usage

 ```1 2 3``` ```dusb(x, theta = 0, nu = 5) rusb(n, theta = 0, nu = 5, quasi = FALSE) ```

## Arguments

 `x` vector of quantiles. `theta` scale parameter of the USB distribution. `nu` smoothness parameter of the USB distribution. `n` number of observations. `quasi` logical indicating whether quasi random numbers (`qrng::ghalton()`) should be used for generating uniforms (which are then transformed by the quantile function)

## References

Nagler, T. (2017). A generic approach to nonparametric function estimation with mixed data. arXiv:1704.07457

## Examples

 ```1 2 3 4 5 6 7 8``` ```# plot distribution sq <- seq(-0.8, 0.8, by = 0.01) plot(sq, dusb(sq), type = "l") lines(sq, dusb(sq, theta = 0.25), col = 2) lines(sq, dusb(sq, theta = 0.25, nu = 10), col = 3) # simulate from the distribution x <- rusb(100, theta = 0.3, nu = 0) ```

cctools documentation built on May 2, 2019, 8:51 a.m.