INEQUALITIES FOR LINEAR COMBINATIONS OF ORDER STATISTICS FROM RESTRICTED FAMILIES

作者: Richard E. Barlow , Frank Proschan

DOI: 10.1214/AOMS/1177699149

关键词: Failure rateProbability distributionMathematicsCombinatoricsStatisticsMonotone polygonDistribution (mathematics)Regular polygonLinear combinationLinear programmingOrder statistic

摘要: Abstract : Comparisons are obtained between a linear combination of order statistics from distribution F and corresponding G where G-1F is (a) convex, (b) starshaped. The results have applications in life testing the underlying has monotone failure rate or on average.

参考文章(13)
Richard E. Barlow, Albert W. Marshall, Bounds for Distributions with Monotone Hazard Rate, II Annals of Mathematical Statistics. ,vol. 35, pp. 1234- 1257 ,(1964) , 10.1214/AOMS/1177703281
Van Zwet, Convex transformations of random variables MC Tracts. ,vol. 7, pp. 1- 116 ,(1964)
Samuel Karlin, Total positivity, absorption probabilities and applications Transactions of the American Mathematical Society. ,vol. 111, pp. 33- 107 ,(1964) , 10.1090/S0002-9947-1964-0168010-2
Richard E. Barlow, Frank Proschan, Mathematical theory of reliability ,(1965)
G. H. Hardy, Some simple inequalities satisfied by convex functions Messenger Math.. ,vol. 58, pp. 145- 152 ,(1929)
Richard E. Barlow, Albert W. Marshall, Frank Proschan, Properties of Probability Distributions with Monotone Hazard Rate Annals of Mathematical Statistics. ,vol. 34, pp. 375- 389 ,(1963) , 10.1214/AOMS/1177704147
Benjamin Epstein, Statistical Life Test Acceptance Procedures Technometrics. ,vol. 2, pp. 435- 446 ,(1960) , 10.1080/00401706.1960.10489910
Benjamin Epstein, Estimation from Life Test Data IRE Transactions on Reliability and Quality Control. ,vol. RQC-9, pp. 104- 107 ,(1960) , 10.1109/IRE-PGRQC.1960.5007277
Albert W Marshall, Frank Proschan, An inequality for convex functions involving G-majorization☆☆☆ Journal of Mathematical Analysis and Applications. ,vol. 12, pp. 603- 606 ,(1965) , 10.1016/0022-247X(65)90056-9
Richard E. Barlow, Frank Proschan, Tolerance and Confidence Limits for Classes of Distributions Based on Failure Rate Annals of Mathematical Statistics. ,vol. 37, pp. 1593- 1601 ,(1966) , 10.1214/AOMS/1177699150