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Simulation of Pareto Distributed Budgets+Peak over Threshold

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Project Description

I would like to use Excel to simulate a Pareto distribution of corporate budgets (Monte-Carlo simulation) and vary the degree of inequality.

You start with a list of 60 000 firms. They are ranked in size, beginning with the largest firm. The list is generated by the following rules:

The biggest firm has a size of N0=600 000 employees.

The size of each subsequent firm has the size of

N = (1/Rank * N0) (Zipf Plot)

In each size class, the average budget of each firm is calculated like this:

The average budget per employee equals the logarithm of firm-size multiplied by a factor of x0=1008 €

Within each size group, the budgets of the firms are Pareto distributed, most have a small budget, very few have a big budget. The degree of the inequality a is a function of the company size. It is smaller among the big firms and increases among smaller firms. (Small firms differ more among each other)

After the list is finished, you need to perform a “peak over threshold analysis”

You take the 500 largest budgets of the list (peak over the threshold = budget of the spender nr 1000) and compare them with the attached list.

Change the inequality a(size) and/or the value of x0 until the simulation ideally matches the 1000 budgets.

Draw a diagram of the 1000 simulated firms (budget per employee on y axis, size on x-axis) and a diagram of the firms from my list

Inform me, how you found the values for a(size) and x0 and send me the Excel sheet.

(On the Internet I found an Excel spreadsheet that calculates the probability density function of the Pareto function: [url removed, login to view] but

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