R: Function beta for the Laplace prior

beta.laplace {EbayesThresh} | R Documentation

## Function beta for the Laplace prior

### 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

    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

    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)

[Package EbayesThresh version 1.4-12 Index]