BenfordDistribution

Generate a set of pseudorandom numbers that are Benford distributed:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness is defined for :

Kurtosis is defined for :

Hazard function:

Quantile function:

CDF of BenfordDistribution is an example of a right continuous function:

Benford's distribution approximates distributions of values spanning multiple orders of magnitude. Consider a sample from a heavy-tailed distribution:

Find the order of magnitude between minimum and maximum:

Extract first digits:

Compare the histogram with the PDF of the corresponding BenfordDistribution:

Now consider a sample from a light-tailed distribution:

Find the order of magnitude between minimum and maximum:

Compare the histogram with the PDF of the corresponding BenfordDistribution:

Check whether the population of the largest cities in the United States follows Benford distribution:

The population of the 100 largest cities does not follow Benford distribution very well:

Consider physical constants:

Find the first digits, not taking units into account:

The first digits are not uniformly distributed; more likely their distribution follows Benford's law: