# dapprox_unif: Compute Density Function of Approximated (Differentiably)... In sdPrior: Scale-Dependent Hyperpriors in Structured Additive Distributional Regression

## Description

Compute Density Function of Approximated (Differentiably) Uniform Distribution.

## Usage

 1 dapprox_unif(x, scale, tildec = 13.86294) 

## Arguments

 x denotes the argument of the density function. scale the scale parameter originally defining the upper bound of the uniform distribution. tildec denotes the ratio between scale parameter θ and s. The latter is responsible for the closeness of the approximation to the uniform distribution. See also below for further details and the default value.

## Details

The density of the uniform distribution for τ is approximated by

p(τ)=(1/(1+exp(τ\tilde{c}/θ-\tilde{c})))/(θ(1+log(1+exp(-\tilde{c}))))

. This results in

p(τ^2)=0.5*(τ^2)^(-1/2)(1/(1+exp((τ^2)^(1/2)\tilde{c}/θ-\tilde{c})))/(θ(1+log(1+exp(-\tilde{c}))))

for tau^2. \tilde{c} is chosen such that P(τ<=θ)>=0.95.

the density.

## Author(s)

rapprox_unif,papprox_unif