# beta.laplace: Function beta for the Laplace prior In EbayesThresh: Empirical Bayes Thresholding and Related Methods

## Description

Given a single value or a vector of x and s, find the value(s) of the function beta(x;s,a) = g(x;s,a)/fn(x;0,s) - 1 , where fn(x;0,s) is the normal density with mean 0 and standard deviation s, and g is the convolution of the Laplace density with scale parameter a, gamma(mu; a), with the normal density fn(x;mu,s) with mean mu and standard deviation s.

## Usage

 `1` ```beta.laplace(x, s = 1, a = 0.5) ```

## Arguments

 `x` the value or vector of data values `s` the value or vector of standard deviations; if vector, must have the same length as `x` `a` the scale parameter of the Laplace distribution

## Value

A vector of the same length as `x` is returned, containing the value(s) beta(x).

## Note

The Laplace density is given by gamma(u) = (a/2) exp(-a|u|) and is also known as the double exponential density.

## Author(s)

Bernard Silverman

## References

See `ebayesthresh` and http://www.bernardsilverman.com

## See Also

`beta.cauchy`

## Examples

 ```1 2``` ```beta.laplace(c(-2,1,0,-4,8,50), s=1) beta.laplace(c(-2,1,0,-4,8,50), s=1:6, a=1) ```

EbayesThresh documentation built on Aug. 8, 2017, 9:09 a.m.