# zenga: Point and synthetic Zenga 2007 indexes In ineqJD: Inequality Joint Decomposition

## Description

Computes point and synthetic Zenga 2007 indexes on a variable Y.

## Usage

 `1` ```zenga(x) ```

## Arguments

 `x ` List containing: `'yh'`, the vector of unique values of the variable Y whose Bonferroni index is computed; `'Phl'`, the matrix of absoute cumulative frequencies; `'Qhlk'`, the matrix of cumlative sums of `y` or its sources. `x` is usually the result of `dataProcessing` function. More details are given in the "Details" section and `dataProcessing` help page.

## Details

`zenga` compute point and synthetic Zenga 2007 indexes on a variable `y`, e.g. income, on a statistical population that could be partitioned in `g` subpopultions and could be considered as sum of `c` sources, e.g. income sources.

## Value

 `index ` String denoting computed index. `decomposition ` Array containing the decompositions. `x ` Object usually of class `dataProcessed` passed as input.

## Author(s)

Alberto Arcagni, Igor Valli

## References

Zenga M. M.(2007). Inequality Curve and Inequality Index based on the Ratios between lower and upper means . Statistica and Applicazioni, V (1), 3-27.

Zenga M. (2015) Joint decomposition by subpopulations and sources of the point and synthetic Zenga(2007) Index I(Y). Statistica and Applicazioni, XIII (2), pp.163-195.

## Examples

 ``` 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 <- zenga(x) decomposition ```

ineqJD documentation built on Sept. 20, 2019, 9:06 a.m.