SlicedLNormParetoMean: Sliced LogNormal Pareto mean

In NetSimR: Actuarial Functions for Non-Life Insurance Modelling

Sliced LogNormal Pareto mean

Description

Gives the expected claim amount of a sliced severity distribution, with LogNormal attritional claims below the slice point and a Pareto tail above it.

Usage

SlicedLNormParetoMean(mu, sigma, SlicePoint, shape)

Arguments

mu	A real number - the first parameter of the attritional Claim Severity's LogNormal distribution.
sigma	A positive real number - the second parameter of the attritional Claim Severity's LogNormal distribution.
SlicePoint	A positive real number - the slice point and the scale parameter of the tail Claim Severity's Pareto distribution. An infinite slice point gives the LogNormal distribution.
shape	A positive real number - the shape parameter of the tail Claim Severity's Pareto distribution.

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The mean of the claim severity with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape. The mean is Inf when shape <= 1 (and SlicePoint is finite), as the Pareto tail then has no finite mean. A non-numeric argument or a non-positive sigma, SlicePoint or shape is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), dSlicedGammaPareto(), dSlicedLNormPareto(), pSlicedGammaPareto(), pSlicedLNormPareto(), qSlicedGammaPareto(), qSlicedLNormPareto()

Examples

SlicedLNormParetoMean(6,1.5,1000,1.2)
SlicedLNormParetoMean(6.5,1.4,2000,1.6)
SlicedLNormParetoMean(7,1.6,3000,1.4)

NetSimR documentation built on Sept. 30, 2026, 5:13 p.m.