The beta rank function (BRF), is the normalized and continuous rank of an observation has wide applications in fitting real-world data. The underlying probability density function (pdf) is not expressible in terms of elementary functions... more
The beta rank function (BRF), is the normalized and continuous rank of an observation has wide applications in fitting real-world data. The underlying probability density function (pdf) is not expressible in terms of elementary functions except for specific parameter values. We show however that it is approximately a unimodal skewed two-sided power law, or double -Pareto, or log-Laplacian distribution. We give closed-form expressions of both pdf's in terms of Fox-H functions and propose numerical algorithms to approximate them. We suggest a way to elucidate if a data set follows a one-sided power law, a lognormal, a two-sided power law or a BRF. Finally, we illustrate the usefulness of these distributions in data analysis through a few examples.
