Q1) How do we model distributions that represent the wealth or income of populations?
Pareto
The Pareto distribution is used to model distributions that have a “heavy tail”, often found in wealth or income distributions. Its parameters are:
- Scale parameter ( x_m )
- Shape parameter ( \alpha )
- Expected value (mean) (for ( \alpha > 1 )) = ( \frac{\alpha x_m}{\alpha-1} )
- Variance (for ( \alpha > 2 )) = ( \frac{x_m^2\alpha}{(\alpha-1)^2(\alpha-2)} )