LN_LIKE

Purpose

This function calculates the log-likelihood of the data, under a
lognormal model. This distribution is given by
f(x) = C * 1 / x * exp(-(ln(x) - mu)^2 / sigma^2)
C = sqrt(2) / (sigma sqrt(pi)) /
erfc( (ln(xmin) - mu) / sqrt(2 sigma) )
C simplifies to 1 / sqrt(2 pi sigma^2) if xmin = 0

Calling Sequence

result = ln_like([params, derivs, data = data, xmin = xmin, sigma =
sigma, mu = mu])

Optional Inputs

params: A two element vector specifying [alpha, xmin].
derivs: A named variable to hold the partial derivative of the
log-likelihood with respect to alpha and xmin.

Keyword Parameters

data: A vector of data values, assumed to be >= xmin
alpha: Another way to specify alpha. This takes precedence over any
variable stored in params[0].
xmin: Another way to specify xmin. This takes precedence over any
variable stored in params[1].

Outputs

Ln(Product( f(data_i) ) )

Restrictions

To maximize speed, the function does not check for values of data <
xmin. However, the output is useless when any data are < xmin.

Modification History

June 2009 Written by Chris Beaumont