Sharp bounds for the bias of trimmed means of progressively censored order statistics

• Autorzy: Bieniek M.
• Języki publikacji: EN

Abstrakty

EN

We provide sharp upper and lower bounds on the bias of trimmed means of progressively censored type II order statistics from general distributions in various scale units. The results are illustrated with numerical examples. We also discuss this problem for distributions with decreasing density or failure rate, as well as for generalized order statistics.

Słowa kluczowe

EN

trimmed mean; progressive censoring; generalized order statistics; sharp bounds; bias

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 1
• Strony: 99--112
• Opis fizyczny: Bibliogr. 15 poz., tab.

Twórcy

autor

Bieniek M.

• Institute of Mathematics, University of Maria Curie-Skłodowska, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [1] N. Balakrishnan, Progressive censoring methodology: an appraisal, Test 16 (2007), pp. 211-259.
• [2] N. Balakrishnan and R. Aggarwala, Progressive Censoring: Theory, Methods, and Applications, Birkhäuser, Boston 2000.
• [3] N. Balakrishnan and E. Cramer, The Art of Progressive Censoring: Applications to Reliability and Quality, Springer, New York 2014.
• [4] N. Balakrishnan, E. Cramer, and U. Kamps, Bounds for means and variances of progressive type II censored order statistics, Statist. Probab. Lett. 54 (2001), pp. 301-315.
• [5] M. Bieniek, Variation diminishing property of densities of uniform generalized order statistics, Metrika 65 (2007), pp. 297-309.
• [6] M. Bieniek, Bounds for expectations of differences of generalized order statistics based on general and life distributions, Comm. Statist. Theory Methods 36 (2007), pp. 59-72.
• [7] M. Bieniek, On families of distributions for which optimal bounds on expectations of GOS can be derived, Comm. Statist. Theory Methods 37 (2008), pp. 1997-2009.
• [8] K. Danielak, Sharp upper mean-variance bounds for trimmed means from restricted families, Statistics 37 (2003), pp. 305-324.
• [9] K. Danielak and T. Rychlik, Exact bounds for the bias of trimmed means, Aust. N. Z. J. Stat. 45 (2003), pp. 83-96.
• [10] A. Goroncy, Lower bounds on positive L-statistics, Comm. Statist. Theory Methods 38 (2009), pp. 1989-2002.
• [11] A. Goroncy and T. Rychlik, Lower bounds on the expectations of upper record values, J. Statist. Plann. Inference 141 (2011), pp. 2726-2737.
• [12] U. Kamps and E. Cramer, On distributions of generalized order statistics, Statistics 35 (2001), pp. 269-280.
• [13] S. Moriguti, A modification of Schwarz’s inequality with applications to distributions, Ann. Math. Statist. 24 (1953), pp. 107-113.
• [14] M. Z. Raqab, p-norm bounds for moments of progressive type II censored order statistics, Statist. Probab. Lett. 64 (2003), pp. 393-402.
• [15] T. Rychlik, Projecting Statistical Functionals, Springer, New York 2001.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).