lorenz: A generalized lorenz curve

In mjantti/incdist: A collection of functions for income distribution analysis

A generalized lorenz curve

Description

lorenz, lorenz.default, lorenz.locfit and lorenz.incdist compute a (possibly generalized) Lorenz curve. The default method assumes the data are vectors, the locfit method assumes that the function is applied to a locfit density object, and the incdist method assumes the object has been created by the incdist methods. The curve is estimated at a given number of points or at every point in the data.

Usage

lorenz(x, ...)

Arguments

x	a numerical vector whose Lorenz curve is to be estimated
w	an optional vector of non-negative integer values weights
obj	a locfit density object
ranked	an optional vector of length(x) which defines the ordering. If not x, lorenz returns the concentration curve of x for the variable given in ranked.
q	an integer or logical. If an integer, it is the number of equally spaced points at which the Lorenz curve ordinates are estimated. If FALSE, then the Lorenz curve is estimated at every point in x.
p	the population points at which the Lorenz curve is estimated. Defaults to equally spaced point on the unit interval. If given, then q is set to the length of this (minus one).
data	the data frame where the variables are found.
subset	use this subset of the data
na.rm	a logical value governing the treatment of NA:s. If true, NAs are removed.
cov	a logical indicating whether the variance covariance matrix of the lorenz curve is to be estimated
no.negatives	indicates whether or not negative incomes should be allowed
cutoffs	the values of the q-1 cutoffs for the quantile groups (may be used in within-group estimation)
group.cutoffs	a logical, indicating whether each group in the incdist object should use their own quantile cutoffs or if the overall cutoffs should be used.

Details

var.cov is a utility function, invoked when cov = T for lorenz.default, and estimates the variance-covariance matrix of the lorenz ordinates and income shares.

print and summary methods are provided, as well as coercion to data fame (can be useful when combined e.g. with lattice to produce good graphics.

dominates.lorenz compares two lorenz curves and returns (1=x L dominates y, 0 = curves cross or are identical, -1 = y L dominates x).

dominates.lorenz_list takes a list of lorenz curves and computes an upper triangular matrix with elements dominates.lorenz(row, column)

The function computes an ordinary lorenz curve. The summary and plot methods allow also a generalized (L*mean) be plotted and summarized. The weights are for the time being assumed to be positive integers, although this will hopefully change soon.

Later on this function should know about income distribution objects. I am also considering extending it to be able to handle locfit, density and ecdf objects, at least.

Simple summary, print and plot methods are provided.

There is a substantial literature on calculating standard errors for Lorenz curve ordinates. If cov = TRUE is chosen and q = FALSE, the returned object includes the variance matrix of the ordinates and of the income shares, estimated as shown in Beach and Davidson (1983) and Beach and Kaliski (1986). The R package boot is probably quite useful for doing so here, not least because all interesting work involving Lorenz curves concerns the comparison of two (or more) Lorenz curves, making it most often a two-sample problem.

Value

A object of class lorenz with elements

p	the population shares.
ordinates	the Lorenz curve ordinates.
mean	the (weighted) mean of x.
n	the sample size.
sum.weights	the sum of weights.
quintile.means	(if q is not false) the within-group means.
quintile.shares	(if q is not false) the within-group incomes shares.

Author(s)

Markus Jantti [e-mail]

References

\insertRef

lambert1993incdist \insertRefbeachanddavidson1983incdist \insertRefbeachandkaliski1986incdist

See Also

weighted_mean, tip, locfit

Examples

lorenz(runif(10), q = FALSE)
n <- 100
income <- exp(10 + rnorm(n)*sqrt(2))
weight <- rpois(n,7)
lor <- lorenz(income, weight, p = c(0, .5, .7, .9, .98, 1))
lor <- lorenz(income, weight, q = 5)
plot(lor, main = "Lorenz curve")
plot(lor, lor.type = "gen", main = "Generalized Lorenz curve")
lor.1 <- lorenz(runif(100))
lor.2 <- lorenz(rexp(100))
lor.3 <- lorenz(rexp(100), cov = TRUE)

plot.lorenz_list(list("1"=lor.1, "2"=lor.2))
dominates.lorenz(lor.1, lor.2)
dominates.lorenz_list(list("1"=lor.1, "2"=lor.2))
library(locfit)
x <- runif(500)
y <- rexp(500)
lf.1 <- lorenz(locfit(~ x))
lf.2 <- lorenz(locfit(~ y))
dominates.lorenz(lor.1, lor.2)
dominates.lorenz_list(list("1"=lor.1, "2"=lor.2))
plot.lorenz_list(list("1"=lor.1, "2"=lor.2))

mjantti/incdist documentation built on Aug. 23, 2023, 5:33 p.m.