# Lorenz.curve: Plot a Lorenz curve from regional industrial counts In PABalland/EconGeo: Computing Key Indicators of the Spatial Distribution of Economic Activities

## Description

This function plots a Lorenz curve from regional industrial counts. This curve gives an indication of the unequal distribution of an industry accross regions.

## Usage

 `1` ```Lorenz.curve(mat, pdf = FALSE, plot = TRUE) ```

## Arguments

 `mat` An incidence matrix with regions in rows and industries in columns. The input can also be a vector of industrial regional count (a matrix with n regions in rows and a single column). `pdf` Logical; shall a pdf be saved to your current working directory? Defaults to FALSE. If set to TRUE, a pdf with all Lorenz curves will be compiled and saved to your current working directory. `plot` Logical; shall the curve be automatically plotted? Defaults to TRUE. If set to TRUE, the function will return x y coordinates that you can latter use to plot and customize the curve.

## Author(s)

Pierre-Alexandre Balland p.balland@uu.nl

## References

Lorenz, M. O. (1905) Methods of measuring the concentration of wealth, Publications of the American Statistical Association 9: 209–219

`Hoover.Gini`, `locational.Gini`, `locational.Gini.curve`, `Hoover.curve`, `Gini`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54``` ```## generate vectors of industrial count ind <- c(0, 10, 10, 30, 50) ## run the function Lorenz.curve (ind) Lorenz.curve (ind, pdf = TRUE) Lorenz.curve (ind, plot = FALSE) ## generate a region - industry matrix mat = matrix ( c (0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1), ncol = 4, byrow = T) rownames(mat) <- c ("R1", "R2", "R3", "R4", "R5") colnames(mat) <- c ("I1", "I2", "I3", "I4") ## run the function Lorenz.curve (mat) Lorenz.curve (mat, pdf = TRUE) Lorenz.curve (mat, plot = FALSE) ## run the function by aggregating all industries Lorenz.curve (rowSums(mat)) Lorenz.curve (rowSums(mat), pdf = TRUE) Lorenz.curve (rowSums(mat), plot = FALSE) ## run the function for industry #1 only (perfect equality) Lorenz.curve (mat[,1]) Lorenz.curve (mat[,1], pdf = TRUE) Lorenz.curve (mat[,1], plot = FALSE) ## run the function for industry #2 only (perfect equality) Lorenz.curve (mat[,2]) Lorenz.curve (mat[,2], pdf = TRUE) Lorenz.curve (mat[,2], plot = FALSE) ## run the function for industry #3 only (perfect unequality) Lorenz.curve (mat[,3]) Lorenz.curve (mat[,3], pdf = TRUE) Lorenz.curve (mat[,3], plot = FALSE) ## run the function for industry #4 only (top 40% produces 100% of the output) Lorenz.curve (mat[,4]) Lorenz.curve (mat[,4], pdf = TRUE) Lorenz.curve (mat[,4], plot = FALSE) Compare the distribution of the #industries par(mfrow=c(2,2)) Lorenz.curve (mat[,1]) Lorenz.curve (mat[,2]) Lorenz.curve (mat[,3]) Lorenz.curve (mat[,4]) ```