Characterizations of Aging Classes in Terms of Spacings Between Record Values

REFERENCES

• Abu-Youssef , S.E. On characterization of certain distributions of record values . Appl. Math. Computation 2003 , 145 , 443 – 450 .
   Web of Science ®Google Scholar
• Ahsanullah , M. Introduction to Record Values ; Ginn Press : Needham Heights , MA , 1988 .
   Google Scholar
• Ahsanullah , M. Record Statistics ; Nova Science Publishers : New York , 1995 .
   Google Scholar
• Ahsanullah , M. ; Wesolowski , J. Linearity of best predictors for non-adjacent record values . Sankuyā (Ser. B) 1998 , 60 , 221 – 227 .
   Google Scholar
• Arnold , B.C. ; Balakrishnan , N. ; Nagaraja , H.N. Records ; Wiley : New York , 1998 .
   Google Scholar
• Balakrishnan , N. ; Stepanov , A. Two characterizations based on order statistics and records . J. Statist. Plann. Inference 2004 , 124 , 273 – 287 .
   Google Scholar
• Barlow , R.E. ; Proschan , F. Statistical Theory of Reliability and Life Testing ; To Begin With : Silver Spring , 1981 .
   Google Scholar
• Belzunce , F. ; Franco , M. ; Ruiz , J.M. On ageing properties based on the residual life of k-out-of-n systems . Probab. Eng. Inform. Sci. 1999 , 13 , 193 – 199 .
   Google Scholar
• Block , H.W. ; Savits , T.H. ; Singh , H. The reversed hazard rate function . Probab. Eng. Inform. Sci. 1998 , 12 , 69 – 90 .
   Web of Science ®Google Scholar
• Bryson , M.C. ; Siddiqui , M.M. Some criteria for aging . J. Amer. Statist. Assoc. 1969 , 64 , 1472 – 1483 .
   Web of Science ®Google Scholar
• Cao , J. ; Wang , Y. The NBUC and NWUC classes of life distributions . J. Appl. Prob. 1991 , 28 , 473 – 479 [ Correction. J. Appl. Prob. 1992, 29, 753 ].
   Web of Science ®Google Scholar
• Dembińska , A. ; Wesolowski , J. Linearity of regression for non-adjacent record values . J. Statist. Plann. Inference 2000 , 90 , 195 – 205 .
   Web of Science ®Google Scholar
• Franco , M. ; Ruiz , J.M. On characterization of distributions by expected values of order statistics and record values with gap . Metrika 1997 , 45 , 107 – 119 .
   Google Scholar
• Hu , T. ; Zhuang , W. Stochastic properties of p-spacings of generalized order statistics . Probab. Eng. Inform. Sci. 2005 , 19 , 257 – 276 .
   Google Scholar
• Hu , T. ; Zhuang , W. Stochastic orderings between p-spacings of generalized order statistics from two samples . Probab. Eng. Inform. Sci. 2006 , 20 , 465 – 479 .
   Web of Science ®Google Scholar
• Joag-dev , K. ; Kochar , S. ; Proschan , F. A general composition theorem and its applications to certain partial orderings of distributions . Statist. Prob. Lett. 1995 , 22 , 111 – 119 .
   Web of Science ®Google Scholar
• Karlin , S. Total Positivity ; University Press : Palo Alto , CA , 1968 .
   Google Scholar
• Langberg , N.A. ; León , R.V. ; Proschan , F. Characterization of nonparametric classes of life distributions . Ann. Prob. 1980 , 8 , 1163 – 1170 .
   Web of Science ®Google Scholar
• Lōpez-Blāzquez , F. ; Moreno-Rebollo , J.L. A characterization of distributions based on linearity of regression for order statistics and record values . Sankhyā (Ser. A) 1997 , 59 , 311 – 323 .
   Google Scholar
• Müller , A. Stochastic orders generated by integrals: a unified study . Adv. Appl. Prob. 1997 , 29 , 414 – 428 .
   Web of Science ®Google Scholar
• Müller , A. ; Stoyan , D. Comparison Methods for Stochastic Models and Risks ; John Wiley & Sons, Ltd .: West Sussex , 2002 .
   Google Scholar
• Nagaraja , H.N. Some characterizations of continuous distributions based on regression of adjacent order statistics and record values . Sankhyā (Ser. A) 1988 , 50 , 70 – 73 .
   Google Scholar
• Nagaraja , H.N. ; Nevzorov , V.B. On characterizations based on reord values and order statistics . J. Statist. Plann. Inference 1997 , 63 , 271 – 284 .
   Web of Science ®Google Scholar
• Pellerey , F. ; Shaked , M. ; Zinn , J. Nonhomogeneous Poisson processes and logconcavity . Probab. Eng. Inform. Sci. 2000 , 14 , 353 – 373 .
   Web of Science ®Google Scholar
• Shaked , M. ; Shanthikumar , J.G. Characterization of some first passage times using log-concavity and log-convexity as aging notions . Probab. Eng. Inform. Sci. 1987 , 1 , 279 – 291 .
   Google Scholar
• Shaked , M. ; Shanthikumar , J.G. Stochastic Orders and their Applications; Academic Press : New York , 1994 .
   Google Scholar
• Shaked , M. ; Shanthikumar , J.G. Stochastic Orders ; Springer : New York , 2007 .
   Google Scholar
• Stepanov , A. A characterization theorem for weak records . Theory Prob. Appl. 1994 , 38 , 762 – 764 .
   Web of Science ®Google Scholar