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

Pareto Distribution

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