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István Vincze (1912–1999) and his contribution to lattice path combinatorics and statistics. (English) Zbl 1075.60004

Summary: A brief account of the life and work of István Vincze, a prominent Hungarian statistician, is given. His contributions in various topics are discussed. They include empirical distribution, Kolmogorov-Smirnov statistics, information theory, Cramér-Fréchet-Rao inequality, estimation of density, and a characterization problem.

MSC:

60C05 Combinatorial probability
30D20 Entire functions of one complex variable (general theory)
60G50 Sums of independent random variables; random walks
62B10 Statistical aspects of information-theoretic topics
62F10 Point estimation
62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions
94A17 Measures of information, entropy
60-03 History of probability theory

Biographic References:

Vincze, István
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[2] Cramér, H., Mathematical Methods of Statistics (1946), Princeton University Press: Princeton University Press Princeton · Zbl 0063.01014
[3] Csáki, E.; Vincze, I., On some problems connected with the Galton test, Publ. Math. Inst. Hungar. Acad. Sci., 6, 97-109 (1961) · Zbl 0202.47304
[4] Csáki, E.; Vincze, I., On some combinatorial relations concerning the symmetric random walk, Acta Sci. Math. (Szeged), 24, 231-235 (1963) · Zbl 0119.14104
[5] Csáki, E.; Vincze, I., Two joint distribution laws in the theory of order statistics, Mathematica (Cluj), 5, 27-37 (1963) · Zbl 0192.26104
[6] Csáki, E.; Vincze, I., On some distributions connected with the arcsine law, Publ. Math. Inst. Hungar. Acad. Sci., 8, 281-291 (1964) · Zbl 0133.41102
[7] Csáki, E.; Vincze, I., A lemma on real functions and its application in the nonparametric theory, (Bartoszyński, R.; Fidelis, E.; Klonecki, W., Proceedings of the Symposium to Honour Jerzy Neyman (1977), Polish Scientific Publishers: Polish Scientific Publishers Warsaw), 83-92 · Zbl 0364.62034
[8] Csáki, E.; Vincze, I., On limiting distribution laws of statistics analogous to Pearson’s chi-square, Math. Operationsforsch. Statist., Ser. Statist., 9, 531-548 (1978) · Zbl 0407.62022
[9] Csordás, G.; Vincze, I., Convexity properties of power series with logarithmically s-concave coefficients, Anal. Math., 18, 3-13 (1992) · Zbl 0786.26008
[10] Fréchet, M., Sur l’extension de certaines evaluations statistiques au case de petits echantillons, Rev. Inst. Internat. Statist., 11, 182-205 (1943) · Zbl 0060.30702
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[12] Govindarajulu, Z.; Vincze, I., The Cramér-Fréchet-Rao inequality for sequential estimation in non-regular case, (Dodge, Y., Statistical Data Analysis and Inference (1989), North Holland: North Holland Amsterdam), 257-268 · Zbl 0733.62085
[13] Gupta, A.K., Vincze, I., 1991. Approximation of higher order derivatives of a real function. In: Szabados, J., Tandori, K. (Eds.), Approximation Theory, Kecskemét, Hungary, 1990; Colloquia Mathematica Societatis János Bolyai, vol. 58. North-Holland, Amsterdam, pp. 339-342.; Gupta, A.K., Vincze, I., 1991. Approximation of higher order derivatives of a real function. In: Szabados, J., Tandori, K. (Eds.), Approximation Theory, Kecskemét, Hungary, 1990; Colloquia Mathematica Societatis János Bolyai, vol. 58. North-Holland, Amsterdam, pp. 339-342. · Zbl 0777.41008
[14] Hall, R.R., Vincze, I., 1981. On a simultaneous characterization of the Poisson law and the gamma distribution. In: Dugué, D., Lukács, E., Rohatgi, V.K. (Eds.), Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol. 861. Springer, Berlin, pp. 54-59.; Hall, R.R., Vincze, I., 1981. On a simultaneous characterization of the Poisson law and the gamma distribution. In: Dugué, D., Lukács, E., Rohatgi, V.K. (Eds.), Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol. 861. Springer, Berlin, pp. 54-59. · Zbl 0454.60017
[15] Hayman, W. K., Research Problems in Function Theory (1967), The Athlone Press, University of London: The Athlone Press, University of London London · Zbl 0158.06301
[16] Hayman, W. K.; Vincze, I., A problem on entire functions, (Bogoljubov, N. N.; Lavrent’ev, M. A.; Bicadze, A. V., Complex Analysis and its Applications (dedicated to I.N. Vekua on his 70th Birthday) (1978), Izd. Nauka: Izd. Nauka Moscow), 591-594 · Zbl 0435.30024
[17] Hayman, W.K., Vincze, I., 1979. Markov-type inequalities and entire functions. In: Gyires, B. (Ed.), Analytic Function Methods in Probability Theory, Debrecen, Hungary, 1977; Colloquia Mathematica Societatis János Bolyai, vol. 21. North-Holland, Amsterdam, pp. 153-163.; Hayman, W.K., Vincze, I., 1979. Markov-type inequalities and entire functions. In: Gyires, B. (Ed.), Analytic Function Methods in Probability Theory, Debrecen, Hungary, 1977; Colloquia Mathematica Societatis János Bolyai, vol. 21. North-Holland, Amsterdam, pp. 153-163. · Zbl 0416.60019
[18] Jaynes, E. T., Information theory and statistical mechanics, Phys. Rev., 106, 2, 620-630 (1957) · Zbl 0084.43701
[19] Koul, H. L.; Quine, M. P., The Bahadur efficiency of the Reimann-Vincze statistics, Studia Sci. Math. Hungar., 9, 399-403 (1974) · Zbl 0332.62037
[20] Kullback, S., Information Theory and Statistics (1959), Wiley: Wiley New York · Zbl 0149.37901
[21] Miles, J.; Williamson, J., A characterization of the exponential function, J. London Math. Soc., 33, 2, 110-116 (1986) · Zbl 0545.30017
[22] Puri, M. L.; Vincze, I., On the Cramér-Fréchet-Rao inequality for translation parameter in the case of finite support, Statistics, 16, 495-506 (1985) · Zbl 0595.62016
[23] Puri, M. L.; Vincze, I., Information and mathematical statistics, (Mandl, P.; Hušková, M., Proceedings of the Fourth Prague Symposium on Asymptotic Statistics Prague, 1988 (1989), Charles University: Charles University Prague), 447-456 · Zbl 0708.62007
[24] Puri, M. L.; Vincze, I., Measure of information and contiguity, Statist. Probab. Lett., 9, 223-228 (1990) · Zbl 0689.62006
[25] Puri, M. L.; Vincze, I., The Neyman-Pearson probability ratio and information, (Schach, S.; Trenkler, G., Data Analysis and Statistical Inference (1992), Verlag Josef Eul: Verlag Josef Eul Bergisch Gladbach), 53-64 · Zbl 0790.62011
[26] Rao, C. R., Information and accuracy attainable in the estimation of statistical parameter, Bull. Calcutta Math. Soc., 37, 81-91 (1945) · Zbl 0063.06420
[27] Reimann, J.; Vincze, I., On the comparison of two samples with slightly different sizes, Publ. Math. Inst. Hungar. Acad. Sci., 5, 293-309 (1960) · Zbl 0201.52701
[28] Sanov, I. N., On the probability of large deviations of random magnitudes (Russian), Mat. Sbornik (N.S.), 42, 84, 11-44 (1957), (English translation: selected Transl. Math. Statist. Probab., Amer. Math. Soc. 1, 213-244)
[29] Vincze, I., Determination of distributions by means of their conditional expectations (Hungarian), Magyar Tud. Akad. Mat. Fiz. Oszt. Közl., 4, 513-523 (1954) · Zbl 0059.12503
[30] Vincze, I., Einige zweidimensionale Verteilungs- und Grenzverteilungssätze in der Theorie der geordneten Stichproben, Publ. Math. Inst. Hungar. Acad. Sci., 2, 183-209 (1958) · Zbl 0086.34005
[31] Vincze, I., On some joint distribution and joint limiting distribution in the theory of order statistics, II, Publ. Math. Inst. Hungar. Acad. Sci., 4, 29-47 (1959) · Zbl 0086.34101
[32] Vincze, I., 1960. An interpretation of the I-divergence of information theory. In: Kozesnik, J. (Ed.), Transactions of the Second Prague Conference on Information Theory, Statistical Decision Functions and Random Processes. Publ. House Czechoslovak Acad. Sci., Prague, pp. 681-684.; Vincze, I., 1960. An interpretation of the I-divergence of information theory. In: Kozesnik, J. (Ed.), Transactions of the Second Prague Conference on Information Theory, Statistical Decision Functions and Random Processes. Publ. House Czechoslovak Acad. Sci., Prague, pp. 681-684. · Zbl 0100.13303
[33] Vincze, I., On two sample tests based on order statistics, (Neyman, J., Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. I (1961), University of California Press: University of California Press Berkeley), 695-705 · Zbl 0121.36303
[34] Vincze, I., Some questions concerning the probabilistic concept of information (Hungarian), Magyar Tud. Akad. Mat. Fiz. Oszt. Közl., 12, 7-14 (1962) · Zbl 0138.14802
[35] Vincze, I., A generating function in the theory of order statistics, Publ. Math., 10, 82-87 (1963) · Zbl 0122.37004
[36] Vincze, I., On the power function of the Kolmogorov-Smirnov and other non-parametric tests (Hungarian), Magyar Tud. Akad. Mat. Fiz. Oszt. Közl., 15, 97-105 (1965) · Zbl 0149.15103
[37] Vincze, I., Some questions connected with two sample tests of Smirnov type, (Le-cam, L. M.; Neyman, J., Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1 (1967), University of California PressBerkeley), 654-666 · Zbl 0212.21904
[38] Vincze, I., On the power of the Kolmogorov-Smirnov two-sample test and related nonparametric tests, (Sarkadi, K.; Vincze, I., Studies in Mathematical Statistics: Theory and Applications (1968), Publishing House of the Hung. Acad. Sci.: Publishing House of the Hung. Acad. Sci. Budapest), 201-210 · Zbl 0187.16002
[39] Vincze, I., On the information-theoretical foundation of mathematical statistics, (Rényi, A., Proceedings of the Colloquium on Information Theory, vol. II (1968), János Bolyai Mathematical Society: János Bolyai Mathematical Society Budapest), 503-509 · Zbl 0192.55901
[40] Vincze, I., On Kolmogorov-Smirnov type distribution theorems, (Puri, M. L., Nonparametric Techniques in Statistical Inference (1970), Cambridge University Press: Cambridge University Press London), 385-401
[41] Vincze, I., On some results and problems in connection with statistics of the Kolmogorov-Smirnov type, (Le-cam, L. M.; Neyman, J.; Scott, E. L., Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. I (1972), University of California Press: University of California Press Berkeley), 459-470 · Zbl 0237.62036
[42] Vincze, I., 1974. On the maximum probability principle in statistical physics. In: Gani, J., Sarkadi, K., Vincze, I. (Eds.), Progress in Statistics, Colloquia Mathematica Societatis János Bolyai, Vol. 9, North Holland, Amsterdam, pp. 869-893.; Vincze, I., 1974. On the maximum probability principle in statistical physics. In: Gani, J., Sarkadi, K., Vincze, I. (Eds.), Progress in Statistics, Colloquia Mathematica Societatis János Bolyai, Vol. 9, North Holland, Amsterdam, pp. 869-893. · Zbl 0299.62001
[43] Vincze, I., On some problems in connection with the Bose-Einstein statistic, Sankhyā, 37, 355-362 (1975) · Zbl 0371.60016
[44] Vincze, I., On the Cramér-Fréchet-Rao inequality in the non-regular case, (Jurečková, J., Contributions to Statistics, Journal of Hájek Memorial Volume (1979), Reidel: Reidel Dordrecht), 253-262 · Zbl 0419.62029
[45] Vincze, I., 1981. Remark to the derivation of the Cramér-Fréchet-Rao inequality in the regular case. In: Révész, P., Schmetterer, L., Zolotarev, V.M. (Eds.), Proceedings of the First Pannonian Symposium on Mathematical Statistics, Lecture Notes in Statistics, vol. 8. Springer, Berlin, pp. 284-289.; Vincze, I., 1981. Remark to the derivation of the Cramér-Fréchet-Rao inequality in the regular case. In: Révész, P., Schmetterer, L., Zolotarev, V.M. (Eds.), Proceedings of the First Pannonian Symposium on Mathematical Statistics, Lecture Notes in Statistics, vol. 8. Springer, Berlin, pp. 284-289. · Zbl 0476.62031
[46] Vincze, I., Contribution to a characterization problem, (Mogyoródi, J.; Vincze, I.; Wertz, W., Proceedings of the Third Pannonian Symposium on Mathematical Statistics, Visegrád, Hungary, 1982 (1984), Reidel: Reidel Dordrecht), 353-361 · Zbl 0552.62006
[47] Vincze, I., On a probabilistic characterization theorem, (Grossmann, W.; Mogyoródi, J.; Vincze, I.; Wertz, W., Proceedings of the Fifth Pannonian Symposium on Mathematical Statistics, Visegrád, Hungary, 1985 (1988), Reidel: Reidel Dordrecht), 213-219 · Zbl 0668.60017
[48] Vincze, I., On nonparametric Cramér-Rao inequalities, (Sen, P. K.; Salama, I. A., Order Statistics and Nonparametrics: Theory and Applications (1992), North Holland: North Holland Amsterdam), 439-454
[49] Vincze, I., Cramér-Rao type inequality and a problem of mixture of distributions. ProbaStat ’94, Smolenice Castle, 1994, Tatra Mt. Math. Publ., 7, 237-245 (1996) · Zbl 0920.62027
[50] Vincze, I.; Tőrös, R., The joint energy distributions of the Bose-Einstein and of the Fermi-Dirac particles, (Balakrishnan, N., Advances in Combinatorial Methods and Applications to Probability and Statistics (1997), Birkhäuser: Birkhäuser Boston), 441-449 · Zbl 0885.60095
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