SlicedGammaParetoMean: Sliced Gamma Pareto mean

In NetSimR: Actuarial Functions for Non-Life Insurance Modelling

Sliced Gamma Pareto mean

Description

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

Usage

SlicedGammaParetoMean(GShape, GRate, SlicePoint, PShape)

Arguments

GShape	A positive real number - the shape parameter of the attritional Claim Severity's Gamma distribution.
GRate	A positive real number - the rate parameter of the attritional Claim Severity's Gamma 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 Gamma distribution.
PShape	A positive real number - the shape parameter of the tail Claim Severity's Pareto distribution.

Details

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

Value

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

See Also

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

Examples

SlicedGammaParetoMean(1,0.0005,1000,1.2)
SlicedGammaParetoMean(1.1,0.0006,2000,1.6)
SlicedGammaParetoMean(1.2,0.0004,3000,1.4)

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