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# linkRatios

Compute link ratios for `developmentTriangle` object

Since R2020b

## Syntax

``LinkRatiosTable = linkRatios(developmentTriangle)``

## Description

example

````LinkRatiosTable = linkRatios(developmentTriangle)` calculates the link ratios between the current development period and the next for each origin period. You can plot the link ratios using `linkRatiosPlot`.```

## Examples

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Calculate the link ratios (age-to-age factors) for a `developmentTriangle` object containing 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 the `linkRatios` function to calculate link ratios between the current development period and the next period.

`LinkRatiosTable = linkRatios(dT)`
```LinkRatiosTable=10×9 table 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 _____ _____ _____ _____ _____ _____ _____ ______ _______ 2010 1.16 1.05 1.02 1.01 1.005 1.004 1.003 1.002 1.001 2011 1.18 1.06 1.02 1.01 1.005 1.003 1.003 1.002 NaN 2012 1.2 1.06 1.027 1.009 1.005 1.004 1.003 NaN NaN 2013 1.19 1.06 1.026 1.014 1.007 1.004 NaN NaN NaN 2014 1.18 1.06 1.028 1.011 1.005 NaN NaN NaN NaN 2015 1.17 1.05 1.027 1.01 NaN NaN NaN NaN NaN 2016 1.16 1.05 1.026 NaN NaN NaN NaN NaN NaN 2017 1.18 1.06 NaN NaN NaN NaN NaN NaN NaN 2018 1.17 NaN NaN NaN NaN NaN NaN NaN NaN 2019 NaN NaN NaN NaN NaN NaN NaN NaN NaN ```

## Input Arguments

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

Data Types: `object`

## Output Arguments

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Link ratios, returned as a table.

## More About

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### Link Ratios

Link ratios, also called age-to-age factors or loss development factors (LDFs), represent the ratio of loss amounts from one valuation date to another, and they are intended to capture growth patterns of losses over time.

## Version History

Introduced in R2020b