Aggregate Loss Distribution Calculator

Work out aggregate loss distribution instantly with clear inputs, formula shown and shareable results.

About Aggregate Loss Distribution Calculator

For a compound Poisson model the aggregate loss has mean λμ and variance λ(σ² + μ²), so both claim count and claim size volatility feed the spread. A normal approximation then gives a working 95th percentile for capital setting.

Formula

Compound Poisson moments

E[S] = λμ; Var[S] = λ(σ² + μ²); VaR₉₅ ≈ E[S] + 1.645·SD[S]

λ: Claim count
μ: Mean severity
σ: Severity SD

Worked example

With the default values below, Aggregate Loss Distribution Calculator returns Expected Aggregate Loss of $1,800,000.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Expected Claim Countaccepts 0.1–1,000,000: 120
Mean Claim Severityminimum 0: 15,000
Severity Standard Deviationminimum 0: 20,000

Results

Expected Aggregate Loss: $1,800,000.00
Standard Deviation Of Aggregate Loss: $273,861.28
95th Percentile (Normal Approximation): $2,250,474.42
Coefficient Of Variation: 15.215%

Step by step

1Values used
2Compound Poisson moments
3Expected Aggregate Loss= 1,800,000.00
4Standard Deviation Of Aggregate Loss= 273,861.28
595th Percentile (Normal Approximation)= 2,250,474.42
6Coefficient Of Variation= 15.215

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does severity variance matter twice?

The variance term carries both σ² and μ², because random claim counts alone already create spread even with fixed severities.

Is the normal approximation safe?

Only for large, well-diversified portfolios. Skewed books need translated gamma, Panjer recursion or simulation.