Fackler Distributions Excel Add-in

An Excel add-in implementing the heavy-tailed probability distributions from Fackler (2013) "Reinventing Pareto: Fits for Both Small and Large Losses".

Corroborating python functions are also included in the project.

This project is in beta. Code was produced using AI coding tools and is offered without any warranty. Please report any bugs.

Distribution Visualizations

Pareto Family Comparison

Core Distributions

Pareto Type I	GPD	Lomax

Burr Distribution

Bell-shaped	Decreasing

Spliced Distributions

Lognormal-Pareto	Lognormal-GPD

Weibull-Pareto	Exponential-Pareto	Power-Pareto

Mixture Distributions

Four-Parameter Pareto	Five-Parameter Pareto

Additional

Right-Truncated Pareto	Spliced Comparison

Installation

1. Download the appropriate XLL file from the dist folder:

   • FacklerDistributions64.xll for 64-bit Excel
   • FacklerDistributions.xll for 32-bit Excel

2. If Windows blocks the file (common for downloads), right-click the XLL file → Properties → check "Unblock" → OK

3. In Excel: File → Options → Add-ins → Manage: Excel Add-ins → Go → Browse → select the XLL file

Alternatively, double-click the XLL file to load it for the current session.

Available Functions

All functions use the FACKLER. prefix and are available in the "Fackler Distributions" category.

Pareto Type I

Function	Description
FACKLER.PARETO.PDF(x, alpha, theta)	Probability density function
FACKLER.PARETO.CDF(x, alpha, theta)	Cumulative distribution function
FACKLER.PARETO.SF(x, alpha, theta)	Survival function
FACKLER.PARETO.MEAN(alpha, theta)	Expected value

Generalized Pareto Distribution (GPD)

Function	Description
FACKLER.GPD.PDF(x, alpha, lambda, [theta])	PDF using Fackler's parametrization
FACKLER.GPD.CDF(x, alpha, lambda, [theta])	CDF
FACKLER.GPD.SF(x, alpha, lambda, [theta])	Survival function
FACKLER.GPD.LOCALALPHA(d, alpha, lambda)	Local Pareto alpha at point d

Lomax (Pareto Type II)

Function	Description
FACKLER.LOMAX.PDF(x, alpha, lambda)	PDF
FACKLER.LOMAX.CDF(x, alpha, lambda)	CDF
FACKLER.LOMAX.SF(x, alpha, lambda)	Survival function
FACKLER.LOMAX.MEAN(alpha, lambda)	Expected value

Burr Type XII

Function	Description
FACKLER.BURR.PDF(x, alpha, lambda, tau)	PDF
FACKLER.BURR.CDF(x, alpha, lambda, tau)	CDF
FACKLER.BURR.SF(x, alpha, lambda, tau)	Survival function

Lognormal-Pareto (Czeledin)

Lognormal body with Pareto tail, continuously spliced at threshold.

Function	Description
FACKLER.LNPARETO.PDF(x, mu, sigma, theta)	PDF
FACKLER.LNPARETO.CDF(x, mu, sigma, theta)	CDF
FACKLER.LNPARETO.SF(x, mu, sigma, theta)	Survival function
FACKLER.LNPARETO.ALPHA(mu, sigma, theta)	Derived tail index from C1 condition

Weibull-Pareto

Weibull body with Pareto tail.

Function	Description
FACKLER.WEIPARETO.PDF(x, k, scale, theta, r)	PDF
FACKLER.WEIPARETO.CDF(x, k, scale, theta, r)	CDF
FACKLER.WEIPARETO.SF(x, k, scale, theta, r)	Survival function
FACKLER.WEIPARETO.ALPHA(k, scale, theta, r)	Derived tail index

Exponential-Pareto

Exponential body with Pareto tail (parameters derived from continuity conditions).

Function	Description
FACKLER.EXPPARETO.PDF(x, rate, theta)	PDF
FACKLER.EXPPARETO.CDF(x, rate, theta)	CDF
FACKLER.EXPPARETO.SF(x, rate, theta)	Survival function
FACKLER.EXPPARETO.ALPHA(rate, theta)	Derived alpha = theta * rate
FACKLER.EXPPARETO.R(rate, theta)	Derived r = 1 - exp(-rate * theta)

Power-Pareto (Log-Laplace)

Power function body with Pareto tail.

Function	Description
FACKLER.POWPARETO.PDF(x, alpha, beta, theta)	PDF
FACKLER.POWPARETO.CDF(x, alpha, beta, theta)	CDF
FACKLER.POWPARETO.SF(x, alpha, beta, theta)	Survival function
FACKLER.POWPARETO.R(alpha, beta)	Derived r = alpha / (alpha + beta)

Four-Parameter Pareto

Lomax mixture with constraint alpha1 = alpha2 + 2.

Function	Description
FACKLER.PARETO4.PDF(x, alpha2, lambda1, lambda2, r)	PDF
FACKLER.PARETO4.CDF(x, alpha2, lambda1, lambda2, r)	CDF
FACKLER.PARETO4.SF(x, alpha2, lambda1, lambda2, r)	Survival function

Five-Parameter Pareto

Unconstrained Lomax mixture.

Function	Description
FACKLER.PARETO5.PDF(x, alpha1, alpha2, lambda1, lambda2, r)	PDF
FACKLER.PARETO5.CDF(x, alpha1, alpha2, lambda1, lambda2, r)	CDF
FACKLER.PARETO5.SF(x, alpha1, alpha2, lambda1, lambda2, r)	Survival function

Utility Functions

Function	Description
FACKLER.LOCALALPHA(pdf, sf, x)	Local Pareto alpha: x * pdf / sf
FACKLER.VERSION()	Add-in version
FACKLER.HELP()	Help text

Project Structure

fackler_paper_excel_addin/
├── dist/                           # Distribution files (ready to use)
│   ├── FacklerDistributions.xll    # Excel add-in (32-bit)
│   ├── FacklerDistributions64.xll  # Excel add-in (64-bit)
│   └── FacklerDistributions_Demo.xlsx
│
├── excel-addin/                    # C# source code
│   ├── Distributions.cs            # Core distribution implementations
│   ├── ExcelFunctions.cs           # Excel UDF wrappers
│   ├── FacklerDistributions.csproj # Project file
│   ├── FacklerDistributions.dna    # Excel-DNA configuration
│   └── build.ps1                   # Build script
│
├── output/                         # Distribution visualizations (PNG)
│
├── docs/                           # Documentation
│   └── fackler_distributions_summary.md
│
├── reference/                      # Reference materials
│   └── Fackler_Paper_Hague2013.pdf # Original paper
│
├── fackler_distributions.py        # Python reference implementation
├── test_fackler_distributions.py   # Python tests
├── create_excel_demo.py            # Script to generate demo workbook
├── requirements.txt                # Python dependencies
└── agents.md                       # AI agent development notes

Building from Source

Requirements:

• Windows
• .NET SDK 6.0 or later
• .NET Framework 4.8 targeting pack

cd excel-addin
.\build.ps1

Output files are placed in the dist folder.

Reference

Fackler, M. (2013). "Reinventing Pareto: Fits for Both Small and Large Losses". ASTIN Colloquium, The Hague.

License

MIT