ORDER RESTRICTED STATISTICAL INFERENCE ON LORENZ CURVES OF PARETO DISTRIBUTIONS

  • Oh, Myongsik (Department of Statistics, Pusan University of Foreign)
  • Published : 2003.09.01

Abstract

The comparison of two or more Lorenz curves of Pareto distributions of first kind under arbitrary order restriction is studied. The problem is turned out to be a statistical inference problem concerning scale parameters under order restriction. We assume that the location parameters of Palate distributions are completely unknown. In this paper the maximum likelihood estimation and likelihood ratio tests for and against order restriction are proposed.

Keywords

References

  1. Lecture Notes in Statistics no.43 Majorization and Lorenz Order Arnold.B.C.
  2. Journal of American Statistical Association v.70 A Two-Moment Chi-Square Approximation for the Statistic log($(\~{x}/\~{x})$) Bain,L.J.;Engelhardt,M.
  3. Encyclopedia of Statistical Siences v.5 Lorenz Curve Dagum,C.;S.Kotz(ed.);N.L.Johnson(ed.);C.B.Read(ed.)
  4. Monthly Notice of Royal Astronomical Society v.245 The Distribution of Cometary Magnitudes Donnison,J.R.
  5. Monthly Notice of Royal Astronomical Society v.256 An Approach to trend Analysis in Data with Special Reference to Cometary Magnitudes Donnison,J.R.;Peers,H.W.
  6. Testig for trends in a nonhomogeneous Poisson process Technical report Guffey,J.M;Wright,F.T.
  7. Metrika v.15 Estimation of the Parameter of the Pareto Distribution Malik,H.J.
  8. Ph. D. Thesis, The University of Iowa Statistical Tests Concerning a Set of Multinomial Parameters under Order Restrictions: Approximations to Null Hypotheses Distributions Oh,M
  9. Journal of the Royal Statistical Society, Series D, The Statistician v.42 Inferences about Ordered Parameters - An Astronomical Problem Pettit,L.I.
  10. The Annals of Statistics v.6 Likelihood ratio tests for order restrictions in exponential families Robertson,T.;Wegman,E.J.
  11. Order Restricted Statistical Inference Robertson,T.;F.T.Wright;R.L.Dykstra
  12. Stochastic Orders and their Applications Shaked,M.;Shanthikumar,J.G.