# Monetary Laeken Indicators under the GB2 Functions to calculate four primary social welfare indicators under the GB2, i.e. the at-risk-of-poverty threshold, the at-risk-of-poverty rate, the relative median at-risk-of-poverty gap, and the income quintile share ratio. 2.1 ```r arpt.gb2(prop, shape1, scale, shape2, shape3) arpr.gb2(prop, shape1, shape2, shape3) rmpg.gb2(arpr, shape1, shape2, shape3) qsr.gb2(shape1, shape2, shape3) main.gb2(prop, shape1, scale, shape2, shape3) main2.gb2(prop, shape1, scale, shape12, shape13) ``` ## Arguments - `prop`: numeric; proportion (in general is set to 0.6). - `arpr`: numeric; the value of the at-risk-of-poverty rate. - `shape1`: numeric; positive parameter. - `scale`: numeric; positive parameter. - `shape2, shape3`: numeric; positive parameters of the Beta distribution. - `shape12`: numeric; the product of the two parameters `shape1` and `shape2`. - `shape13`: numeric; the product of the two parameters `shape1` and `shape3`. ## Details In June 2006, the Social Protection Committee, which is a group of officials of the European Commisiion, adopts a set of common indicators for the social protection and social inclusion process. It consists of a portfolio of 14 overarching indicators (+11 context indicators) meant to reflect the overarching objectives (a) "social cohesion" and (b) "interaction with the Lisbon strategy for growth and jobs (launched in 2000) objectives"; and of three strand portfolios for social inclusion, pensions, and health and long-term care. The at-risk-of-poverty threshold (or ARPT) is defined as 60% of the median national equivalized income. The at-risk-of-poverty rate (or ARPR) is defined as the share of persons with an equivalised disposable income below the ARPT. The relative median at-risk-of-poverty gap (or RMPG) is defined as the difference between the median equivalised income of persons below the ARPT and the ARPT itself, expressed as a percentage of the ARPT. The income quintile share ratio (or QSR) is defined as the ratio of total income received by the 20% of the country's population with the highest income (top quintile) to that received by the 20% of the country's population with the lowest income (lowest quintile). Let $x_0.5$ be the median of a GB2 with parameters `shape1` $= a$, `scale` $= b$, `shape2` $= p$ and `shape3` $= q$. Then, $$ ARPT(a,b,p,q)=0.6 x_{0.5}ARPT(a,b,p,q)=0.6 x_0.5. $$ The ARPR being scale-free, $b$ can be chosen arbitrarily and can be fixed to 1. The QSR is calculated with the help of the incomplete moments of order 1. `main.gb2` and `main2.gb2` return a vector containing the following set of GB2 indicators: the median, the mean, the ARPR, the RMPG, the QSR and the Gini coefficient. The only difference is in the input parameters. ## Returns `arpt.gb2` gives the ARPT, `arpr.gb2` the ARPR, `rmpg.gb2` the RMPG, and `qsr.gb2` calculates the QSR. `main.gb2` returns a vector containing the median of the distribution, the mean of the distribution, the ARPR, the RMPG, the QSR and the Gini coefficient. `main2.gb2` produces the same output as `main.gb2`. ## References [https://ec.europa.eu/social/main.jsp?langId=en&catId=750](https://ec.europa.eu/social/main.jsp?langId=en&catId=750) ## Author(s) Monique Graf ## See Also `qgb2`, `incompl.gb2` ## Examples ```r a <- 3.9 b <- 18873 p <- 0.97 q <- 1.03 ap <- a*p aq <- a*q arpt <- arpt.gb2(0.6, a, b, p, q) arpr <- arpr.gb2(0.6, a, p, q) rmpg <- rmpg.gb2(arpr, a, p, q) qsr <- qsr.gb2(a, p, q) ind1 <- main.gb2(0.6, a, b, p, q) ind2 <- main2.gb2(0.6, a, b, ap, aq) ```

Indicators function