bradfordr

The goal of bradfordr is to implement probability functions from the Standardized Bradford Distribution in the same way other distributions are implemented in the {stats} package. Its definition and functionality were taken from SciPy.

Definition of the Standardized Bradford Distribution

A continuous random variable follows the Standardized Bradford Distribution if it’s probability density function is given as the following:

For 0 <= x <= 1 and c > 0.

It comes primarily from Bradford’s law of scattering, which states that, if journals in a specific field are sorted into three groups (each with one third of all articles of that field), the number of journals in each group will be proportional to 1 : n : n2. The Bradford Distribution itself is a special case of the Pareto Distribution, and has some relations with the Exponential Distribution.

Installation

You can install the development version of bradfordr from GitHub with:

# install.packages("devtools")
devtools::install_github("victordogo/bradfordr")

Example

bradfordr contains 4 basic functions, exemplified below. More in depth applications can be seen in the vignettes of this package.

rbradford

The rbradford function generates a vector of values from the Standardized Bradford Distribution with length n and parameter c using the Inverse Transform Sampling Method.

The standard value for c is 5:

library(bradfordr)

rbradford(n=10)
#>  [1] 0.185216959 0.100725128 0.931113765 0.184023942 0.003606418 0.637271882
#>  [7] 0.031869913 0.581854982 0.743135455 0.274802504

If the value of c is less or equal than 0, the function returns an error (this is true to all functions in this package).

pbradford

The pbradford function returns the probabilities calculated from the accumulated distribution function of the Standardized Bradford Distribution:

If lower.tail=FALSE, however, it returns 1 − F(x; c). It also has the option to return probabilities in the logarithmic scale.

# Calculating P(X <= 0.7) when c = 10

pbradford(q=0.7,c=10)
#> [1] 0.8671945

# Now, calculating P(X > 0.7) when c = 10

pbradford(q=0.7,c=10, lower.tail=FALSE)
#> [1] 0.1328055

dbradford

The dbradford function gives the distribution’s pdf. By definition, we can’t really calculate probabilities like we do with discrete distributions (think like P(X = 10)), so this is the least useful function in the package.

qbradford

The qbradford function gives the distribution’s quantile function. It’s useful for discovering what value would satisfy P(X ≤ x) = p. The same arguments from pbradford apply here.

# What value of x satisfies P(X <= x) = 0.8 when c=100?

qbradford(p=0.8, c=100)
#> [1] 0.3912889

Acknowledgments

  • Many thanks to Prof. Dr. Danilo Lourenço Lopes, who gave me the assignment to create functions for the Standardized Bradford Distribution and inadvertently inspired me to create this package;
  • A huge shoutout to all instructors at curso-r.com, specially Beatriz Milz and Caio Lente who taught the R Packages Course. It was great!;
  • Also, many thanks to Athos Damiani and Julio Trecenti who, in 2019, taught a one-time mini course in R in which I’ve helped as event committee member (to the best of my abilities at that time, I was very shy). They encouraged me a lot! You can see that in this video (in portuguese).