Klebanov, Lev (Leo) Borisovich

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Total publications: 55
Scientific articles: 54

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Doctor of physico-mathematical sciences (1986)
Speciality: 01.01.05 (Probability theory and mathematical statistics)
Birth date: 21.09.1946
Keywords: probability, statistics, biostatistics, bioinformatics, finance, characterization of probability distributions, statistical estimation theory, probability distances, integral and functional equations for haracterizations, limit theorems, heavytailed distributions, applications to finance, applications to biology.
UDC: 519.2, 517.91/.93, 517.968, 519.21, 519.281, 621.391.1
MSC: 60-XX, 62-XX, 39-XX, 45-XX, 92-XX


The main specialization is probability theory and statistics and their applications to biology, medicine, economics and ensurance. A number of papers and a monograph were devoted to the description of loss-function satisfying to the condition of comleteness of classes of natural estimators. There was proposed the method of intensively monotone operators to prove the uniqueness of a solution of a wide class of characterization problems of statisitics. There was constructed a stochastic model of latent time distributions for radiation carcinogenesis. There was given an explanation of computer tomography paradox. Some methods of recovering of a measure from a finite set of the values of its Radon transform were proposed. There were proposed some models for pre-limit approximation of sums of random variables. There are introduced analogues of stable law for the case of sums of a random number of random variables, and for the case of discrete variables


Graduated from Faculty of Mathematics and Mechanics Leningrad State University 1970. Ph.D. thesis was defended in 1973. D. Sci. thesis was defended in 1986. A list of my works containes more than 230 titles. Was scientific adviser of 8 Ph.D. students and of 1 person working for doctor of science degree. A menber of advicer board of the editors of journal Statistics & Decisions. Was repeatedly a referee for Theory of Probability and Applications, Statistics and Probability Letters, Statistics & Decisions, The Annals of the Institute of Statistical Mathematics, and other journals.

Main publications:
  • Khalfin L. A., Klebanov L. B. A solution of the computer tomography paradox and estimating the distances between the densities of measures with the same marginals // The Annals of Probability, 1994, vol. 22, no. 4, 2235–2241.
  • Klebanov L. B., Rachev S. T. Sums of a random number of random variables an their approximations with $\nu$-accompanying infinitely divisible laws // Serdica Math. J., v. 22, no. 4, 1996, 471–496.
  • Klebanov L. B., Rachev S. T., Yakovlev A. Yu. A stochastic model of radiation carcinogenesis: latent time distributions and their properties // Mathematical Biosciences, 1993, v. 113, 51–75.
  • Klebanov L. B., Rachev S. T. Computer tomography and quantum mechanics // Advances in Applied Probability, v. 29, no. 3, 1997, 595–606.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. I. V. Volchenkova, L. B. Klebanov, “Characterizations of Pareto distribution by the properties of neighboring order statistics”, Zap. Nauchn. Sem. POMI, 486 (2019),  63–70  mathnet
2. I. V. Volchenkova, L. B. Klebanov, “A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests”, Zap. Nauchn. Sem. POMI, 474 (2018),  63–76  mathnet
3. I. V. Volchenkova, L. B. Klebanov, “On the characterization of distributions of symmetric dependent random variables”, Zap. Nauchn. Sem. POMI, 466 (2017),  81–95  mathnet
4. A. Karlová, L. B. Klebanov, “Estimation of the tail of probability distribution through its characteristic function”, Zap. Nauchn. Sem. POMI, 454 (2016),  176–182  mathnet  mathscinet; J. Math. Sci. (N. Y.), 229:6 (2018), 714–718  scopus
5. Ya. I. Belopol'skaya, V. È. Volkovich, L. B. Klebanov, “Characterization of Elliptic Distributions”, Zap. Nauchn. Sem. POMI, 294 (2002),  19–28  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 127:1 (2005), 1682–1686
6. A. Gupta, L. B. Klebanov, “Ill-Posed probelms in statistical estimation theory”, Zap. Nauchn. Sem. POMI, 278 (2001),  36–62  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 118:6 (2003), 5525–5540
7. L. B. Klebanov, L. A. Khalfin, “On reconstruction of the density based on the finite set of Radon's transformation”, Zap. Nauchn. Sem. POMI, 244 (1997),  181–185  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 99:2 (2000), 1127–1129
8. L. B. Klebanov, J. F. Crouzed, “The quasi-convolutions and the applications to the coded images”, Zap. Nauchn. Sem. POMI, 244 (1997),  167–180  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 99:2 (2000), 1120–1126
9. L. B. Klebanov, L. A. Khalfin, “What information about a wave function give its measurement by the tomograph method of a Wigner distribution restoration?”, Zap. Nauchn. Sem. POMI, 228 (1996),  189–200  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 93:3 (1999), 372–378
10. L. B. Klebanov, “On a generalization of stable distributions”, Uspekhi Mat. Nauk, 50:5(305) (1995),  173–182  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:5 (1995), 1015–1024  isi
11. L. B. Klebanov, J. A. Melamed, “On the location parameter confidence intervals based on a random size sample from a partially known population”, Zap. Nauchn. Sem. POMI, 207 (1993),  98–100  mathnet  mathscinet  zmath; J. Math. Sci., 81:1 (1996), 2421–2423
12. A. A. Zinger, L. B. Klebanov, “On a condition of constancy of regression of a polynomial statistic on sample mean”, Zap. Nauchn. Sem. LOMI, 184 (1990),  106–114  mathnet  mathscinet  zmath; J. Math. Sci., 68:4 (1994), 469–474
13. L. B. Klebanov, M. V. Neupokoeva, “A Characterization of Distributions by a Property of Mean Values of Order Statistics”, Teor. Veroyatnost. i Primenen., 34:4 (1989),  780–785  mathnet  mathscinet  zmath; Theory Probab. Appl., 34:4 (1989), 715–720  isi
14. L. B. Klebanov, “On renewal of a distribution by the mean values of the minima of a random number of random variables”, Zap. Nauchn. Sem. LOMI, 166 (1988),  60–62  mathnet  zmath
15. L. B. Klebanov, R. V. Januskevičus, “Estimation of Stability in S. N. Bernshtein's theorem”, Teor. Veroyatnost. i Primenen., 30:2 (1985),  358–360  mathnet  mathscinet  zmath; Theory Probab. Appl., 30:2 (1986), 383–386  isi
16. A. V. Kakocian, L. B. Klebanov, R. V. Yanushkevichius, “Probabilistic applications of an analogue of an inequality of A. N. Kolmogorov”, Dokl. Akad. Nauk SSSR, 279:3 (1984),  535–538  mathnet  mathscinet  zmath
17. L. B. Klebanov, G. M. Maniya, I. A. Melamed, “A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a sheme for summing of a random number of random variables”, Teor. Veroyatnost. i Primenen., 29:4 (1984),  757–760  mathnet  mathscinet  zmath; Theory Probab. Appl., 29:4 (1985), 791–794  isi
18. A. A. Zinger, L. B. Klebanov, J. A. Melamed, “Characterizations of probability laws by the properties of indentically distributions of linear forms with random coefficients”, Zap. Nauchn. Sem. LOMI, 136 (1984),  58–73  mathnet  mathscinet  zmath
19. L. B. Klebanov, R. V. Yanuškjavičus, “$\varepsilon$-independence of the sample mean and the tubular statistics”, Teor. Veroyatnost. i Primenen., 28:1 (1983),  157–163  mathnet  mathscinet  zmath; Theory Probab. Appl., 28:1 (1984), 165–172  isi
20. L. B. Klebanov, S. T. Mkrtchyan, “An estimator of a distance between distributions in terms of a distance between their characteristic functions in finite interval”, Zap. Nauchn. Sem. LOMI, 108 (1981),  111–118  mathnet  mathscinet  zmath; J. Soviet Math., 25:3 (1984), 1181–1186
21. L. B. Klebanov, “Einige Ergebnisse, die mit Charakterisierung der Exponentialvertellung verbunden sind”, Teor. Veroyatnost. i Primenen., 25:3 (1980),  628–633  mathnet  mathscinet  zmath; Theory Probab. Appl., 25:3 (1981), 617–622  isi
22. L. B. Klebanov, “Some estimators of a distance between distributions in terms of characteristic functions”, Zap. Nauchn. Sem. LOMI, 98 (1980),  86–97  mathnet  mathscinet  zmath; J. Soviet Math., 21:1 (1983), 57–64
23. L. B. Klebanov, “Unbiased parametric estimate of probability distribution”, Mat. Zametki, 25:5 (1979),  743–750  mathnet  mathscinet  zmath; Math. Notes, 25:5 (1979), 383–387  isi
24. L. B. Klebanov, “When has a quadratic statistics a constant regression on the sample mean?”, Teor. Veroyatnost. i Primenen., 24:3 (1979),  646–648  mathnet  mathscinet  zmath; Theory Probab. Appl., 24:3 (1980), 649–651  isi
25. L. B. Klebanov, “Once more on stability estimation in the problem of reconstructing the additive type of a distribution”, Zap. Nauchn. Sem. LOMI, 87 (1979),  74–78  mathnet  mathscinet  zmath; J. Soviet Math., 17:6 (1981), 2265–2269
26. L. B. Klebanov, “The stability of the problem of statistical estimation and a choice of the loss function”, Zap. Nauchn. Sem. LOMI, 87 (1979),  62–73  mathnet  mathscinet  zmath; J. Soviet Math., 17:6 (1981), 2255–2264
27. L. B. Klebanov, “Characterization of distributions by a property of modified $\chi^2$-statistic”, Mat. Zametki, 24:4 (1978),  583–588  mathnet  mathscinet  zmath; Math. Notes, 24:4 (1978), 811–814
28. L. B. Klebanov, “Bayesian estimates, stable with respect to the choice of the loss function”, Mat. Zametki, 23:2 (1978),  327–334  mathnet  mathscinet  zmath; Math. Notes, 23:2 (1978), 175–179
29. L. B. Klebanov, “Einige Aufgaben der Verteilungscharakterisierung, die in der Zuverlässigkeitstheorie entstehen”, Teor. Veroyatnost. i Primenen., 23:4 (1978),  828–831  mathnet  mathscinet  zmath; Theory Probab. Appl., 23:4 (1979), 798–801  isi
30. L. B. Klebanov, “Parametric estimates of a density function and characterization of the families of distributions with a location parameter admitting sufficient statistic”, Zap. Nauchn. Sem. LOMI, 79 (1978),  11–16  mathnet  mathscinet  zmath; J. Soviet Math., 36:5 (1987), 576–580
31. L. B. Klebanov, “$L_k^{(2)}$-sufficient subspaces for families with shift and scale parameters”, Mat. Zametki, 20:2 (1976),  279–291  mathnet  mathscinet  zmath; Math. Notes, 20:2 (1976), 714–720
32. L. B. Klebanov, I. A. Melamed, “On Asymptotic Behavior of Certain Estimates of Shift and Scale Parameters”, Probl. Peredachi Inf., 12:3 (1976),  41–56  mathnet  mathscinet  zmath; Problems Inform. Transmission, 12:3 (1976), 193–204
33. L. B. Klebanov, “Eine allgemeine Definition der erwartungstreuen Schätzung”, Teor. Veroyatnost. i Primenen., 21:3 (1976),  584–598  mathnet  mathscinet  zmath; Theory Probab. Appl., 21:3 (1977), 571–585
34. L. B. Klebanov, I. A. Melamed, “Asymptotic $\varepsilon$-admissibility of the sample variance as an estimator of the population variance”, Zap. Nauchn. Sem. LOMI, 61 (1976),  75–83  mathnet  mathscinet  zmath; J. Soviet Math., 16:5 (1981), 1390–1395
35. A. M. Kagan, L. B. Klebanov, “Estimating stability in the problem of reconstructing the additive type of a distribution”, Zap. Nauchn. Sem. LOMI, 61 (1976),  68–74  mathnet  mathscinet  zmath; J. Soviet Math., 16:5 (1981), 1385–1389
36. L. B. Klebanov, “Characterization of loss functions in the statistical theory of estimation”, Zap. Nauchn. Sem. LOMI, 53 (1975),  130–141  mathnet  mathscinet  zmath
37. L. B. Klebanov, A. L. Rukhin, “On families of distributions with location parameter admitting a sufficient statistic of rank not greater that two”, Teor. Veroyatnost. i Primenen., 19:3 (1974),  604–611  mathnet  mathscinet  zmath; Theory Probab. Appl., 19:3 (1975), 577–584
38. L. B. Klebanov, “Unbiased estimates and sufficient statistics”, Teor. Veroyatnost. i Primenen., 19:2 (1974),  392–397  mathnet  mathscinet  zmath; Theory Probab. Appl., 19:2 (1975), 379–383
39. L. B. Klebanov, “On conditions for the zero regression of one linear statistic with respect to another”, Teor. Veroyatnost. i Primenen., 19:1 (1974),  206–210  mathnet  mathscinet  zmath; Theory Probab. Appl., 19:1 (1974), 200–204
40. L. B. Klebanov, I. A. Melamed, “On characterization of the normal and Gamma distributions by properties of Fisher information”, Zap. Nauchn. Sem. LOMI, 43 (1974),  53–58  mathnet  mathscinet
41. L. B. Klebanov, “Unbiased estimators and convex loss functions”, Zap. Nauchn. Sem. LOMI, 43 (1974),  40–52  mathnet  mathscinet
42. A. M. Kagan, L. B. Klebanov, S. M. Fintushal, “Asymptotic behaviour of the polynomial Pitman estimators”, Zap. Nauchn. Sem. LOMI, 43 (1974),  30–39  mathnet  mathscinet
43. L. B. Klebanov, “Inadmissibility of polynomial estimates of the shift parameter”, Mat. Zametki, 14:6 (1973),  885–893  mathnet  mathscinet  zmath; Math. Notes, 14:6 (1973), 1068–1073
44. L. B. Klebanov, “Reconstituting the distribution of the components of a random Vector from distributions of certain statistics”, Mat. Zametki, 13:6 (1973),  889–892  mathnet  mathscinet  zmath; Math. Notes, 13:6 (1973), 531–532
45. L. B. Klebanov, “A characterization of the normal distribution by a property of order statistics”, Mat. Zametki, 13:1 (1973),  121–124  mathnet  mathscinet  zmath; Math. Notes, 13:1 (1973), 71–73
46. L. B. Klebanov, “On the Characterization of a Family of Distributions by the Property of Independence of Statistics”, Teor. Veroyatnost. i Primenen., 18:3 (1973),  639–642  mathnet  mathscinet  zmath; Theory Probab. Appl., 18:3 (1974), 608–611
47. L. B. Klebanov, “The Admissibility of the Sample Mean As an Estimate of the Location Parameter for Non-Quadratic Risk Functions”, Teor. Veroyatnost. i Primenen., 18:2 (1973),  339–349  mathnet  mathscinet  zmath; Theory Probab. Appl., 18:2 (1973), 329–339
48. L. B. Klebanov, ““Universal” loss functions and unbiased estimates”, Dokl. Akad. Nauk SSSR, 203:6 (1972),  1249–1251  mathnet  mathscinet  zmath
49. L. B. Klebanov, Yu. V. Linnik, A. L. Rukhin, “Unbiased estimation and matrix loss functions”, Dokl. Akad. Nauk SSSR, 200:5 (1971),  1024–1025  mathnet  mathscinet  zmath
50. L. B. Klebanov, “Local behavior of the solutions of ordinary differential equations”, Differ. Uravn., 7:8 (1971),  1393–1397  mathnet  mathscinet  zmath
51. L. B. Klebanov, “A remark on independence of a tubular statistic and the sample mean”, Teor. Veroyatnost. i Primenen., 16:4 (1971),  753–755  mathnet  mathscinet  zmath; Theory Probab. Appl., 16:4 (1971), 732–733
52. L. B. Klebanov, “A certain generalization of Craig's theorem”, Dokl. Akad. Nauk SSSR, 195:4 (1970),  763–764  mathnet  mathscinet  zmath
53. L. B. Klebanov, “Admissibility of a sample mean as estimate of the shift parameter in the presence of polynomial losses”, Dokl. Akad. Nauk SSSR, 194:3 (1970),  508–509  mathnet  mathscinet  zmath
54. A. A. Zinger, A. M. Kagan, L. B. Klebanov, “The sample mean as an estimator of the shift parameter in the presence of certain losses which differ from the quadratic”, Dokl. Akad. Nauk SSSR, 189:1 (1969),  29–30  mathnet  mathscinet  zmath

55. L. B. Klebanov, “Н. V. Robert, Ed. «Stadies in Statistics» (book review)”, Teor. Veroyatnost. i Primenen., 26:1 (1981),  218  mathnet; Theory Probab. Appl., 26:1 (1981), 212–215

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