Kropac, Oldrich Some properties and applications of probability distributions based on MacDonald function. (English) Zbl 0491.60021 Apl. Mat. 27, 285-302 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 60E99 Distribution theory 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) Keywords:MacDonald function; Bessel function of the second kind; composed distributions PDFBibTeX XMLCite \textit{O. Kropac}, Apl. Mat. 27, 285--302 (1982; Zbl 0491.60021) Full Text: DOI EuDML References: [1] H. Bateman A. Erdélyi: Higher transcendental functions. Vol. 2. New York, McGraw-Hill, 1953. [2] H. Bateman A. Erdélyi: Tables of integral transforms, Vol. I, II. New York, McGraw-Hill, 1954. [3] K. C. Chu: Estimation and decision for linear systems with elliptical random processes. IEEE Trans. Autom. Control, AC-18, 1973, pp. 499-505. · Zbl 0263.93049 · doi:10.1109/TAC.1973.1100374 [4] C. C. Craig: On the frequency function xy. Ann. Math. Statist., 7, 1936, pp. 1 - 15. · Zbl 0013.35904 · doi:10.1214/aoms/1177732541 [5] E. M. Elderton: Table of the product moment \(T_m\) function. Biometrika, 21, 1929, pp. 194-201. · JFM 55.0919.03 · doi:10.1093/biomet/21.1-4.194 [6] Jahnke-Emde-Lösch: Tafeln höherer Funktionen. Stuttgart, Teubner, 1960. · Zbl 0087.12801 [7] N. L. Johnson S. Kotz: Continuous multivariate distributions. New York, J. Wiley, 1972. · Zbl 0248.62021 [8] O. Kropáč: Relations between distributions of random vibratory processes and distributions of their envelopes. Aplik. Matem., 17, 1972, pp. 75-112. [9] O. Kropáč: Rozdělení s náhodnými parametry a jejich inženýrské aplikace. Strojn. Čas. 33, 1980, pp. 597-622. [10] O. Kropáč: A unified model for non-stationary and/or non-Gaussian random processes. J. Sound Vibr., 79, 1981, pp. 11 - 21. · Zbl 0478.60099 · doi:10.1016/0022-460X(81)90326-6 [11] O. Kropáč: Some general properties of elliptically symmetric random processes. Kybernetika, 17, 1981, pp. 401-412. [12] S. Kullback: The distribution laws of the difference and quotient of variables independently distributed in Pearson III laws. Ann. Math. Statist., 7, 1936, pp. 51 - 53. · Zbl 0014.07302 · doi:10.1214/aoms/1177732546 [13] D. K. McGraw J. F. Wagner: Elliptically symmetric distributions. IEEE Trans. Inform. Theory, IT-14, 1968, pp. 110-120. · doi:10.1109/TIT.1968.1054081 [14] K. Pearson G. B. Jeffery E. M. Elderton: On the distribution of the first product moment-coefficient, in samples drawn from an indefinitely large normal population. Biometrika, 21, 1929, pp. 164-193. · JFM 55.0919.02 · doi:10.1093/biomet/21.1-4.164 [15] K. Pearson S. A. Stouffer F. N. David: Further applications in statistics of the \(T_m (x)\) Bessel function. Biometrika, 24, 1932, pp. 293 - 350. · Zbl 0006.02201 [16] D. Teichrow: The mixture of normal distributions with different variances. Ann. Math. Statist., 28, 1957, pp. 510-512. · Zbl 0080.11905 · doi:10.1214/aoms/1177706981 [17] G. N. Watson: A treatise on the theory of Bessel functions. Cambridge, Univ. Press, 1944 (2nd edit.). · Zbl 0063.08184 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.