dlognPareto: Density of the lognormal-Pareto spliced distribution
Description
This function evaluates the density of the continuous and
differentiable version of the truncated lognormal-Pareto spliced
distribution proposed by Scollnik (2007).
Usage
dlognPareto(x, sigma, xmin, alpha)
Value
ysim (n x 1) vector: numerical values of the
truncated lognormal-Pareto spliced distribution at x.
Arguments
x
vector (nx1): points where the function is evaluated.
sigma
positive real: log-standard deviation of the truncated
lognormal distribution.
xmin
positive real: scale parameter of the Pareto distribution.
alpha
positive real: shape parameterof the Pareto distribution.
Details
To get a continuous and differentiable density, it is necessary to enforce constraints that reduce the number
of free parameters of the model; in particular, the mixing weight and the log-mean of the lognormal distirbution are
functions of the reamining parameters. See Scollnik (2007) for details.