J. M. Sarabia Alegría, F. J. Girón, C. Trueba
A new methodology for stochastic comparison of composite indices is proposed. The stochastic component of the index is introduced in the weights vector using a Dirichlet distribution. The exact probability distribution of the index is obtained. Several probabilistic properties of the stochastic indices are obtained, including raw moments, which can be written in terms of the confluent and Lauricella functions. A method for the elicitation of the parameters of the Dirichlet distribution is proposed. The stochastic composite indices can be easily estimated by simulation. A matrix of pairwise probabilistic comparisons between countries is defined and several stochastic orderings are proposed and compared. The new methodology is used to construct a stochastic version of the Human Development Index (HDI). The method is illustrated with data of the OECD countries for 2010. The new stochastic orderings are consistent with the ranking established by PNUD to classify the OECD countries by HDI.
Palabras clave: composite index, stochastic comparisons, Dirichlet distribution, human development index
Programado
XC1a Pósters (Estadística)
18 de abril de 2012 12:00
Salón Madrid
