# bonferroni: Point and synthetic Bonferroni indexes In ineqJD: Inequality Joint Decomposition

## Description

Computes the decomposition of the Bonferroni point inequality indexes of a statistical variable Y described in the object `x`.

## Usage

 `1` ```bonferroni(x) ```

## Arguments

 `x ` An object of class `"dataProcessed"`. `x` is usually the result of `dataProcessing` function. More details are given in the "Details" section and `dataProcessing` help page.

## Details

`bonferroni` computes the decomposition of the Bonferroni point inequality indexes from the object `x` of class `"dataProcessed"`. `x` is usually the result of `dataProcessing` function.

## Value

 `index ` String denoting computed index. `decomposition ` Array containing the decompositions. The dimensions of `decomposition` are `c(g, g, r, s)` where `g` is the number of groups, `r` the number of different values of Y and `s` the number of sources. `x ` Object of class `dataProcessed` passed as input.

## Author(s)

Alberto Arcagni, Igor Valli.

## References

Zenga M., Valli I. (2017). Joint decomposition by Subpopulations and Sources of the Point and Synthetic Bonferroni Inequality Measures. Statistics and Applications, XV (2), pp. 83-120.

`gini` and `zenga` for other inequality indexes and `dataProcessing` for the class `"dataProcessed"`.
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```G <- c(1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 3, 3) # vector denoting group membership X1 <- c(0, 0, 0, 500, 700, 300, 750, 1000, 500, 500, 500, 1000) # vector of the first source X2 <- c(0, 0, 0, 500, 300, 700, 750, 500, 700, 700, 1000,600) # vector of the second source data <- data.frame(G, X1, X2) # no sample weights are considered x <- dataProcessing( # data preparation units = data[, c('X1', 'X2')], groups = data[, 'G'], ) decomposition <- bonferroni(x) decomposition ```