dlognPareto {lognGPD} | R Documentation |
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)
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.
Value
ysim (n x 1) vector: numerical values of the truncated lognormal-Pareto spliced distribution at x.
References
Scollnik DPM (2007). “On composite lognormal-Pareto models.” Scandinavian Actuarial Journal, 1, 20-33.
Examples
ysim <- dlognPareto(seq(0,20,length.out=500),1,5,2)