cdfSummary

Compute CDFs to ultimate claims for developmentTriangle object

Syntax

selectedLinkRatiosTable = cdfSummary(developmentTriangle)

Description

selectedLinkRatiosTable = cdfSummary(developmentTriangle) calculates the cumulative development factors (CDFs) and the percentage of total claims.

Examples

Calculate CDFs and Percentage of Total Claims for Development Triangle

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

developmentTriangle — Development triangle

developmentTriangle object

Development triangle, specified as a previously created developmentTriangle object.

Data Types: object

Output Arguments

selectedLinkRatiosTable — CDF to ultimate claims

table

CDF to ultimate claims, returned as a table. The table shows the selected ratios, CDFs, and percentage of total claims.

More About

Cumulative Development Factors

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

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