Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

## Pareto Distribution

 Definition Normally, the parameter K is known and represents the lower border of the data. The parameter λ has to be adjusted to the data to obtain a best fit. The Pareto distribution has been described for the first time by V. Pareto, an Italian economist, who discovered that a small portion of the population owns a large portion of the gross national capital (80-20-rule: 20% of the population own 80% of the capital). Graphic Representation The diagram at the left shows the Pareto distribution with the parameters K=1 and λ=2, 3, 5 and 10 Applications A few examples of data following a Pareto distribution: the size of meteorites (many small, few large ones) the size of settlements (few mega cities, many small villages) the wealth of persons the size of sand grains Mean μ = Kλ/(λ-1); λ > 1 Variance σ = K2λ/(λ-1)2/(λ-2); λ > 2