## Afrika Statistika

### The asymptotic theory of the poverty intensity in view of extreme value theory for two simple cases

#### Abstract

Let $Y_1,Y_2\dots$ be independent observations of the income variable of some given population, with underlying distribution $G$. Given a poverty line $Z$, then for each $n\geq 1$, $q=q_n$ is the number of poor in the population. The general form of poverty measures used by economists to monitor the welfare evolution of this population is $$P_n=\frac{1}{a(q)b(n)}\sum^q_{j=1}c(n,q,j)d\left(\frac{Z-Y_{j,n}}{Z}\right).$$ This class includes the most popular poverty measures like the Sen, Shorrocks and Greer-Foster-Thorbecke statistics. We give a complete asymptotic normality theory in the framework of extreme value theory. In this paper, the poverty intensity is studied in two simple cases: Pareto and exponential distributions. Simulations and applications to the Senegalese data are given.

#### Article information

Source
Afr. Stat., Volume 2, Number 1 (2007), 44-58.

Dates
Received: 20 January 2006
Accepted: 10 May 2007
First available in Project Euclid: 26 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.as/1495766686

Digital Object Identifier
doi:10.4314/afst.v2i1.46866

Mathematical Reviews number (MathSciNet)
MR2388962

Zentralblatt MATH identifier
05939879

#### Citation

Lo, Gane Samb; Sall, Serigne Touba. The asymptotic theory of the poverty intensity in view of extreme value theory for two simple cases. Afr. Stat. 2 (2007), no. 1, 44--58. doi:10.4314/afst.v2i1.46866. https://projecteuclid.org/euclid.as/1495766686