Estimating the Renewal Function When the Second Moment Is Infinite

REFERENCES

• Baltrūnas , A. ; Omey , E. Second order renewal theorem in the finite-means case . Theory Probab. Appl. 2003 , 47 , 127 – 132 .
   Web of Science ®Google Scholar
• Baxter , L.A. ; Li , L. Non-parametric confidence intervals for the renewal function and the point availability . Scand. J. Statist. 1994 , 21 , 277 – 287 .
   Web of Science ®Google Scholar
• Frees , E.W. Nonparametric renewal function estimation . Ann. Statist. 1986 , 14 , 1366 – 1378 .
   Web of Science ®Google Scholar
• Grübel , R. ; Pitts , S.M. Nonparametric estimation in renewal theory I: the empirical renewal function . Ann. Statist. 1993 , 21 , 1431 – 1451 .
   Web of Science ®Google Scholar
• Guerin , C.A. ; Nyberg , H. ; Perrin , O. ; Resnick , S. ; Rootzén , H. ; Stărică , C. Empirical testing of the infinite source Poisson data traffic model . Stochastic Models 2003 , 19 , 151 – 200 .
   Web of Science ®Google Scholar
• Heath , D. ; Resnick , S. ; Samorodnitsky , G. Heavy tails and long range dependence in on/off processes and associated fluid models . Math. Oper. Res. 1998 , 23 , 145 – 165 .
   Web of Science ®Google Scholar
• LePage , R. ; Woodroofe , M. ; Zinn , J. Convergence to a stable distribution via order statistics . Ann. Probab. 1981 , 9 , 624 – 632 .
   Web of Science ®Google Scholar
• Markovitch , N.M. ; Krieger , U.R. Nonparametric estimation of long-tailed density functions and its application to the analysis of World Wide Web traffic . Performance Evaluation 2000 , 42 , 205 – 222 .
   Web of Science ®Google Scholar
• Markovitch , N.M. ; Krieger , U.R. Estimating basic characteristics of arrival processes in telecommunication networks by empirical data . Telecommunication Systems 2002 , 20 , 11 – 31 .
   Web of Science ®Google Scholar
• Schneider , H. ; Lin , B.S. ; O'Cinneide , C. Comparison of nonparametric estimators for the renewal function . J. Royal Statist. Soc., Series C. 1990 , 39 , 55 – 61 .
   Web of Science ®Google Scholar
• Sgibnev , M.S. Renewal theorem in the case of an infinite variance. Siberian Math. J. 1981, 22, 787–796.
   Web of Science ®Google Scholar
• Taqqu , M.S. The modeling of ethernet data and of signals that are heavy tailed with infinite variance . Scand. J. Statist. 2002 , 29 , 273 – 295 .
   Web of Science ®Google Scholar
• Willinger , W. ; Taqqu , M.S. ; Leland , M. ; Wilson , D. Self-similarity through high variability: statistical analysis of ethernet LAN traffic at the source level . Comput. Commun. Rev. 1995 , 25 , 100 – 113 .
   Google Scholar
• Willinger , W. ; Taqqu , M.S. ; Leland , M. ; Wilson , D. Self-similarity in high-speed packet traffic: analysis and modeling of ethernet traffic measurements . Statistical Science 1995 , 10 , 67 – 85 .
   Web of Science ®Google Scholar
• Zhao , Q. ; Subba Rao , S. Nonparametric renewal function estimation based on estimated densities . Asia-Pacific J. Oper. Res. 1997 , 14 , 115 – 126 .
   Web of Science ®Google Scholar
• Zolotarev , V.M. One-dimensional Stable Distributions ; Translations of Mathematical Monographs, 65 . American Mathematical Society : Providence, RI , 1986 .
   Google Scholar