Log-concavity of generalized order statistics
Generalized order statistics have been introduced as a unification of several models of random variables arranged in ascending order of magnitude with different interpretations and statistical applications. The purpose of this note is to investigate conditions on the underlying distribution function and on the parameters under which the generalized order statistics and their spacings have log-concave joint densities, respectively. Several well-known results in the literature are complemented and strengthened.
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Volume (Year): 79 (2009)
Issue (Month): 3 (February)
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References listed on IDEAS
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- Bagnoli, M. & Bergstrom, T., 1989.
"Log-Concave Probability And Its Applications,"
89-23, Michigan - Center for Research on Economic & Social Theory.
- Balakrishnan, N. & Papadatos, N., 2002. "The use of spacings in the estimation of a scale parameter," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 193-204, April.
- N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
- N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
- Cramer, Erhard, 2004. "Logconcavity and unimodality of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 83-90, June.
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