theor.Lc {ineq}R Documentation

Theoretical Lorenz Curves

Description

theoretical Lorenz curves of income distributions

Usage

theor.Lc(p,parameter=0,type=c("Singh-Maddala","Dagum","lognorm","Pareto","exponential"))

Lc.dagum(p, parameter=c(2,2))
Lc.singh(p, parameter=c(2,2))
Lc.pareto(p, parameter=2)
Lc.lognorm(p, parameter=1)
Lc.exp(p)

Arguments

p vector with elements from [0,1]
parameter vector containing parameter(s) of the distributions
type character string giving the income distribution. must be one of the strings in the default argument (the first character is sufficient). defaults to "Singh-Maddala".

Details

theor.Lc is just a wrapper for the theoretical Lorenz curves of income distributions Lc.dagum, Lc.singh, Lc.pareto, Lc.lognorm, Lc.exp.

Lc.dagum is the Lorenz curve of the Dagum distribution (2 parameters), Lc.singh the one of the Singh-Maddala distribution (2 parameters), Lc.pareto the one of the Pareto distribution (1 parameter), Lc.lognorm the one of the Lognormal distribution (1 parameter) and Lc.exp the Lorenz curve of the exponential distribution (no parameter).

Value

value of the theoretical Lorenz curve at p

Author(s)

Achim Zeileis zeileis@ci.tuwien.ac.at

References

C Dagum: Income Distribution Models, 1983, in: Johnson / Kotz (Eds): Encyclopedia of Statistical Sciences Vol.4, 27-34.

J B McDonald: Some generalized functions for the size distribution of income, 1984, Econometrica 52, 647-664.

See Also

Lc, Lc.plot, theor.Lc.plot

Examples

# vector of percentages
p <- (1:10)*0.1
# compute values of theoretic Lorenz curve of a Dagum-distribution
theor.Lc(p, parameter=c(3.4,2.6), type="Dagum")
# or
Lc.dagum(p, parameter=c(3.4,2.6))