When large n is not enough – Distribution-free interval estimators for ratios of quantiles

Luke A. Prendergast () and Robert G. Staudte ()
Additional contact information
Luke A. Prendergast: La Trobe University
Robert G. Staudte: La Trobe University

The Journal of Economic Inequality, 2017, vol. 15, issue 3, No 4, 277-293

Abstract: Abstract Ratios of sample percentiles or of quantiles based on a single sample are often published for skewed income data to illustrate aspects of income inequality, but distribution-free confidence intervals for such ratios are not available in the literature. Here we derive and compare two large-sample methods for obtaining such intervals. They both require good distribution-free estimates of the quantile density at the quantiles of interest, and such estimates have recently become available. Simulation studies for various sample sizes are carried out for Pareto, lognormal and exponential distributions, as well as fitted generalized lambda distributions, to determine the coverage probabilities and widths of the intervals. Robustness of the estimators to contamination or a positive proportion of zero incomes is examined via influence functions and simulations. The motivating example is Australian household income data where ratios of quantiles measure inequality, but of course these results apply equally to data from other countries.

Keywords: Generalized lambda distribution; Influence function; Mixture distribution; Quantile density; Ratio of percentiles (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10888-017-9347-9 Abstract (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:jecinq:v:15:y:2017:i:3:d:10.1007_s10888-017-9347-9

Ordering information: This journal article can be ordered from
http://www.springer. ... th/journal/10888/PS2

DOI: 10.1007/s10888-017-9347-9

Access Statistics for this article

The Journal of Economic Inequality is currently edited by Stephen Jenkins

More articles in The Journal of Economic Inequality from Springer, Society for the Study of Economic Inequality Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().