Two flexible functional form approaches for approximating the Lorenz curve

Ryu, Hang K.; Slottje, Daniel J.

doi:10.1016/0304-4076(94)01722-0

Cited by 69 publications

(43 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(see Ryu (1993) for the continuous version of ONB, and Ryu and Slottje (1996) and Milne (1949) for a discussion of the discrete version of ONB). The…”

Section: Orthonormal Basis Expansion Of the Logarithm Of Income Sharementioning

confidence: 99%

A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries

2017

Self Cite

View full text Add to dashboard Cite

There is a vast literature on the selection of an appropriate index of income inequality and on what desirable properties such a measure (or index) should contain. The Gini index is, of course, the most popular. There is a concurrent literature on the use of hypothetical statistical distributions to approximate and describe an observed distribution of incomes. Pareto and others observed early on that incomes tend to be heavily right-tailed in their distribution. These asymmetries led to approximating the observed income distributions with extreme value hypothetical statistical distributions, such as the Pareto distribution. But these income distribution functions (IDFs) continue to be described with a single index (such as the Gini) that poorly detects the extreme values present in the underlying empirical IDF. This paper introduces a new inequality measure to supplement, but not to replace, the Gini that measures more accurately the inherent asymmetries and extreme values that are present in observed income distributions. The new measure is based on a third-order term of a Legendre polynomial from the logarithm of a share function (or Lorenz curve). We advocate using the two measures together to provide a better description of inequality inherent in empirical income distributions with extreme values. Keywords AbstractThere is a vast literature on the selection of an appropriate index of income inequality and on what desirable properties such a measure (or index) should contain. The Gini index is, of course, the most popular. There is a concurrent literature on the use of hypothetical statistical distributions to approximate and describe an observed distribution of incomes. Pareto and others observed early on that incomes tend to be heavily right-tailed in their distribution. These asymmetries led to approximating the observed income distributions with extreme value hypothetical statistical distributions, such as the Pareto distribution. But these income distribution functions (IDFs) continue to be described with a single index (such as the Gini) that poorly detect the extreme values present in the underlying empirical IDF. This paper introduces a new inequality measure to supplement, but not to replace, the Gini that measures more accurately the inherent asymmetries and extreme values that are present in observed income distributions. The new measure is based on a third-order term of a Legendre polynomial from the logarithm of a share function (or Lorenz curve). We advocate using the two measures together to provide a better description of inequality inherent in empirical income distributions with extreme values. JEL Classification: D31, D63

show abstract

“…(see Ryu (1993) for the continuous version of ONB, and Ryu and Slottje (1996) and Milne (1949) for a discussion of the discrete version of ONB). The…”

Section: Orthonormal Basis Expansion Of the Logarithm Of Income Sharementioning

confidence: 99%

A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…Various procedures have been developed to assess the usefulness of rankings and to determine "ties" when specific estimates appear to be the same [e.g., 8,9,16,18,19,[31][32][33]41]. The issue of consistent and careful ranking is important in other domains, as well.…”

Section: Literature Reviewmentioning

confidence: 98%

Ranking inequality: Applications of multivariate subset selection

2006

View full text Add to dashboard Cite

show abstract

“…Different parametric models for the Lorenz curve have been proposed by Kakwani and Podder (1976), Rasche et al (1980), Aggarwal (1984), Aggarwal and Singh (1984), Gupta (1984), Arnold (1986), Pakes (1986), Arnold et al (1987), Villaseñor and Arnold (1989), Basmann et al (1990), Ortega et al (1991), Chotikapanich (1993), Holm (1993), Ryu and Slottje (1996), Sarabia (1997), Sarabia et al (1999), Sarabia et al (2001), Ogwang and Rao (1996), Ogwang and Rao (2000), Sarabia and Pascual (2002), Sarabia et al (2010a,b), Rohde (2009), Helene (2010, Wang et al (2009Wang et al ( , 2011, and recently, Sarabia et al (2013). As we show in this section, a number of these models have been obtained by distorting a baseline Lorenz curve L .…”

Section: Distorted Lorenz Curves: Modelsmentioning

confidence: 99%

Distorted Lorenz curves: models and comparisons

2013

View full text Add to dashboard Cite

The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve L by a function h, giving rise to a distorted Lorenz curve L = h • L. In this paper, we study, in a unified framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aaberge (2001) for orderings on the set of Lorenz curves. Then, we describe some particular models and investigate how changes in the parameters in the baseline Lorenz curve L affect the transformed curve L. Our results are stated in terms of preservation of some stochastic orders between two Lorenz curves when both are distorted by a common function.

show abstract

Two flexible functional form approaches for approximating the Lorenz curve

Cited by 69 publications

References 12 publications

A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries

A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries

Ranking inequality: Applications of multivariate subset selection

Distorted Lorenz curves: models and comparisons

Contact Info

Product

Resources

About