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 \(a\),
\(\gamma_a(\mu)\), 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) \(beta(x)\).