cdfSummary
Compute CDFs to ultimate claims for developmentTriangle
object
Description
calculates the cumulative development factors (CDFs) and the percentage of total
claims.selectedLinkRatiosTable
= cdfSummary(developmentTriangle
)
Examples
Calculate the CDFs and the percentage of total claims for a developmentTriangle
object using simulated insurance claims data.
load InsuranceClaimsData.mat;
head(data)
OriginYear DevelopmentYear ReportedClaims PaidClaims __________ _______________ ______________ __________ 2010 12 3995.7 1893.9 2010 24 4635 3371.2 2010 36 4866.8 4079.1 2010 48 4964.1 4487 2010 60 5013.7 4711.4 2010 72 5038.8 4805.6 2010 84 5059 4853.7 2010 96 5074.1 4877.9
Use developmentTriangle
to convert the data to a development triangle, which is the standard form for representing claims data.
dT = developmentTriangle(data)
dT = developmentTriangle with properties: Origin: {10×1 cell} Development: {10×1 cell} Claims: [10×10 double] LatestDiagonal: [10×1 double] Description: "" TailFactor: 1 CumulativeDevelopmentFactors: [1.3069 1.1107 1.0516 1.0261 1.0152 1.0098 1.0060 1.0030 1.0010 1] SelectedLinkRatio: [1.1767 1.0563 1.0249 1.0107 1.0054 1.0038 1.0030 1.0020 1.0010]
Use linkRatioAverages
function to calculate the different link ratio averages.
LinkRatioAveragesTable = linkRatioAverages(dT)
LinkRatioAveragesTable=8×9 table
12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120
______ ______ ______ ______ ______ ______ _____ ______ _______
Simple Average 1.1767 1.0563 1.0249 1.0107 1.0054 1.0038 1.003 1.002 1.001
Simple Average - Latest 5 1.172 1.056 1.0268 1.0108 1.0054 1.0038 1.003 1.002 1.001
Simple Average - Latest 3 1.17 1.0533 1.027 1.0117 1.0057 1.0037 1.003 1.002 1.001
Medial Average - Latest 5x1 1.1733 1.0567 1.0267 1.0103 1.005 1.004 1.003 1.002 1.001
Volume-weighted Average 1.1766 1.0563 1.025 1.0107 1.0054 1.0038 1.003 1.002 1.001
Volume-weighted Average - Latest 5 1.172 1.056 1.0268 1.0108 1.0054 1.0038 1.003 1.002 1.001
Volume-weighted Average - Latest 3 1.1701 1.0534 1.027 1.0117 1.0057 1.0037 1.003 1.002 1.001
Geometric Average - Latest 4 1.17 1.055 1.0267 1.011 1.0055 1.0037 1.003 1.002 1.001
Use the cdfSummary
function to calculate CDFs and the percentage of total claims and return a table with the selected link ratios, CDFs, and percent of total claims.
dT.SelectedLinkRatio = [1.1755, 1.0577, 1.0273, 1.0104, 1.0044, 1.0026, 1.0016, 1.0006, 1.0004]; selectedLinkRatiosTable = cdfSummary(dT)
selectedLinkRatiosTable=3×10 table
12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 Ultimate
_______ _______ _______ _______ _______ _______ ______ ______ _______ ________
Selected 1.1755 1.0577 1.0273 1.0104 1.0044 1.0026 1.0016 1.0006 1.0004 1
CDF to Ultimate 1.303 1.1084 1.048 1.0201 1.0096 1.0052 1.0026 1.001 1.0004 1
Percent of Total Claims 0.76747 0.90216 0.95422 0.98027 0.99046 0.99482 0.9974 0.999 0.9996 1
Input Arguments
Development triangle, specified as a previously created developmentTriangle
object.
Data Types: object
Output Arguments
CDF to ultimate claims, returned as a table. The table shows the selected ratios, CDFs, and percentage of total claims.
More About
Calculating the cumulative development factors (CDFs) of a random variable is a method to describe the distribution of random variables.
The CDF of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X takes a value less than or equal to x.
Ultimate claims are the total sum the insured, its insurer(s), and/or its reinsurer(s) pay for a fully developed loss. A fully developed loss is the paid losses plus outstanding and reported losses and incurred-but-not-reported (IBNR) losses.
Version History
Introduced in R2020b
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