# Pareto Distribution

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The Pareto Distribution is a continuous probability distribution used to describe many empirical observations. It was originally used by the Italian economist Vilfredo Pareto who used it to model the distribution of wealth in cities.

### Density Curve of the Pareto Distribution:

The probability distribution function is given as:

where xm is the minimum possible value of x and α is the shape parameter.

The probability density curve when plotted looks like a rectangular hyperbola with the graph becoming asymptotic to the x-axis as x tends to infinity. The graph is “long-tailed”.

### Mean and Variance of the Pareto Distribution:

The mean and variance of the Pareto distribution can be calculated as follows,

### Pareto Principle:

The Pareto principle or the 80-20 rules states that wealth is distributed in such a way that 20% of the population has 80% of the riches. It has been observed empirically that richer people tend to own a greater amount of wealth in comparison to the rest of the population.

So a substantial portion of the total wealth(80% of the total wealth) lies in the hands of the extremely rich(the top 20%). The bottom 80% of the people own only 20% of the total wealth.

### Applications of the Pareto Distribution:

The Pareto distribution is widely used in:

1. The modelling of wealth distribution in countries.
2. Modelling the spread of population.
3. Modelling the gains made in the stock market.

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