# cdfSummary

Compute CDFs to ultimate claims for `developmentTriangle` object

Since R2020b

## Syntax

``selectedLinkRatiosTable = cdfSummary(developmentTriangle)``

## Description

example

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

## Examples

collapse all

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: {10x1 cell} Development: {10x1 cell} Claims: [10x10 double] LatestDiagonal: [10x1 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

collapse all

Development triangle, specified as a previously created `developmentTriangle` object.

Data Types: `object`

## Output Arguments

collapse all

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

collapse all

### 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