Exercise 19 investigated Benfords law, a discrete distribution with pmf given by p(x) = log10((x + 1)/x)
Question:
Exercise 19 investigated Benford’s law, a discrete distribution with pmf given by p(x) = log10((x + 1)/x) for x = 1, 2, …, 9. Use the inverse cdf method to write a program that simulates the Benford’s law distribution. Then use your program to estimate the expected value and variance of this distribution.
Data From Exercises 19
Suppose that you read through this year’s issues of the New York Times and record each number that appears in a news article—the income of a CEO, the number of cases of wine produced by a winery, the total charitable contribution of a politician during the previous tax year, the age of a celebrity, and so on. Now focus on the leading digit of each number, which could be 1, 2, …, 8, or 9. Your first thought might be that the leading digit X of a randomly selected number would be equally likely to be one of the nine possibilities (a discrete uniform distribution). However, much empirical evidence as well as some theoretical arguments suggest an alternative probability distribution called Benford’s law:
Step by Step Answer:
Modern Mathematical Statistics With Applications
ISBN: 9783030551551
3rd Edition
Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton