I wish to create a function that will estimate the wealth of a person in the United States. It would be used to make a table with each decile and their estimated wealth.
This estimate will be based on very rudimentary data, and is only for personal interest. The data is:
- The total wealth of the bottom 90% is equal to the total wealth of the top 0.1%.
- Both proportions have 22% of the total wealth.
- The total wealth under the distribution is $80 trillion.
- The total population is 160 million households.
Given this data, how would I create parameter estimates for the exponent and scale of a pareto distribution? What would be $f(x)$ where $x$ is from $(0, 1)$, and the solution is the wealth of someone richer than that proportion of people? For example $f(0.1)$ is someone richer than or equal to exactly 10% of the least wealthy, and could equal 1,000 dollars. $F(0.5)$ is the median wealth, and could be 200,000 dollars. $F(0.9999)$ is richer than 99.99% and would be somewhere in the tens or hundreds of millions of dollars.