# Polarisation Measure from Esteban, Gradin and Ray (2007) This function computes the polarisation measure proposed in Esteban, Gradin and Ray (2007) which accounts for deviations from an n-spike representation of strata in society. ```r polarisation.EGR(alpha, beta, rho, y, f = NULL, dist = NULL, weights = NULL, pm0 = NA, lower = NULL, upper = NULL, ...) ``` ## Arguments - `alpha`: a scalar containing the alpha parameter from Esteban and Ray (1994) on the sensitivity to polarisation. - `beta`: a scalar containing the beta parameter from Esteban, Gradin and Ray (2007) on the weight assigned to the error in the n-spike representation. - `rho`: a dataframe with the group means in the first column and their respective population shares in the second. The groups need to be exogenously defined. Note: the two columns should be named `means` and `shares` respectively. Otherwise a warning will appear. - `y`: a vector of incomes. If f is NULL and dist is NULL, this includes all incomes of all observations in the sample, i.e. all observations comprising the aggregate distribution. If either f or dist is not NULL, then this gives the incomes where the density is evaluated. - `f`: a vector of user-defined densities of the aggregate distribution for the given incomes in y. - `dist`: character string with the name of the distribution used. Must be equivalent to the respective function of that distribution, e.g. norm for the normal distribution. - `weights`: an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. If non-NULL, observations in y are weighted accordingly. - `pm0`: the point mass for zero incomes used in the gini.den function. If not specified no point mass is assumed. - `lower`: the lower bound of the income range considered used in the gini.den function. - `upper`: the upper bound of the income range considered used in the gini.den function. - ``...``: arguments to be passed to the distribution function used, e.g. mean and sd for the normal distribution. ## Returns - **P**: the polarisation measure proposed by Esteban, Gradin and Ray (2007). - **PG**: the adjusted polarisation measure proposed by Gradin (2000). - **alpha**: the alpha parameter used. - **beta**: the beta parameter used. - **beta**: the distribution option used, i.e. whether only y, f or dist was used. ## References Esteban, J. and Ray, D. (1994): On the Measurment of Polarization, in: Econometrica, Vol. 62(4), pp. 819-851. Esteban, J., Gradin, C. and Ray, D. (2007): Extensions of a Measure of Polarization, with an Application to the Income Distribution of five OECD Countries. Gradin, C. (2000): Polarization by Sub-populations in Spain, 1973-91, in Review of Income and Wealth, Vol. 46(4), pp.457-474. ## Author(s) Alexander Sohn ## See Also `polarisation.ER` ## Examples ```r ## example 1 y<-rnorm(1000,5,0.5) y<-sort(y) m.y<-mean(y) sd.y<-sd(y) y1<-y[1:(length(y)/4)] m.y1<-mean(y1) sd.y1<-sd(y1) y2<-y[(length(y)/4+1):length(y)] m.y2<-mean(y2) sd.y2<-sd(y2) means<-c(m.y1,m.y2) share1<- length(y1)/length(y) share2<- length(y2)/length(y) shares<- c(share1,share2) rho<-data.frame(means=means,shares=shares) alpha<-1 beta<-1 den<-density(y) polarisation.ER(alpha,rho,comp=FALSE) polarisation.EGR(alpha,beta,rho,y)$P polarisation.EGR(alpha,beta,rho,y=den$x,f=den$y)$P polarisation.EGR(alpha,beta,rho,y=seq(0,10,by=0.1),dist="norm", mean=m.y,sd=sd.y)$P polarisation.EGR(alpha,beta,rho,y=seq(0,10,by=0.1),dist="norm", mean=m.y,sd=sd.y)$PG ## example 2 y1<-rnorm(100,5,1) y2<-rnorm(100,1,0.1) y <- c(y1,y2) m.y1<-mean(y1) sd.y1<-sd(y1) m.y2<-mean(y2) sd.y2<-sd(y2) means<-c(m.y1,m.y2) share1<- length(y1)/length(y) share2<- length(y2)/length(y) shares<- c(share1,share2) rho<-data.frame(means=means,shares=shares) alpha<-1 beta<-1 polarisation.EGR(alpha,beta,rho,y=seq(0,10,by=0.1),dist="norm", mean=c(m.y1,m.y2),sd=c(sd.y1,sd.y2))$P ```

polarisation.EGR function