×

Convergence criteria for interval-valued inequality indices. (English) Zbl 1040.62070

Summary: We introduce an interval-valued inequality index for random intervals based on a convex function. We show that if this function does not grow faster than \(x^p\), then the inequality index is continuous on the space of random intervals with finite \(p\)th moment. A bound for the distance between the inequality indices of two random intervals is also constructed. An example is presented to motivate and illustrate the developments in this paper.

MSC:

62L99 Sequential statistical methods
62L20 Stochastic approximation
41A25 Rate of convergence, degree of approximation
62P10 Applications of statistics to biology and medical sciences; meta analysis
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Eichhorn W., Applied Mathematics-Optimization and Operations Research pp pp. 657–693– (1982)
[2] Atkinson A., The Economics of Inequality (1983)
[3] DOI: 10.1093/0198289286.001.0001 · doi:10.1093/0198289286.001.0001
[4] DOI: 10.1016/0022-247X(65)90049-1 · Zbl 0163.06301 · doi:10.1016/0022-247X(65)90049-1
[5] Molchanov I., CWI Quarterly 11 pp 371– (1998)
[6] DOI: 10.1016/0047-259X(77)90037-9 · Zbl 0368.60006 · doi:10.1016/0047-259X(77)90037-9
[7] Csiszár I., Studia Sci. Math. Hungar. 2 pp 299– (1967)
[8] Cascos-Fernández I., Soft Methods in Probability, Statistics and Data Analysis pp pp. 98–104– (2002)
[9] DOI: 10.2307/1914138 · Zbl 0424.90013 · doi:10.2307/1914138
[10] López-García H., Statist. Probab. Lett. 46 pp 149– (2000) · Zbl 0955.60011 · doi:10.1016/S0167-7152(99)00100-5
[11] AIDAon-line2(2001) [wwwhttp://www.2aida.net]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.