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Spline-functions for investigating and forecasting systems. (English. Russian original) Zbl 1302.65038

Cybern. Syst. Anal. 47, No. 1, 134-139 (2011); translation from Kibern. Sist. Anal. 2011, No. 1, 146-151 (2011).
Summary: An explicit formula of a multivariate \(B\)-spline, some useful investigations in the field of linear transformations of independent exponentially distributed random variables, representation of theirs density functions with the help of multivariate exponential spline functions, and their usage are considered. The consideration is illustrated by an appropriate example.

MSC:

65C50 Other computational problems in probability (MSC2010)
65D07 Numerical computation using splines
60G25 Prediction theory (aspects of stochastic processes)
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References:

[1] A. A. Akopian and B. D. Bojanov, Theory of Spline Functions [in Bulgarian], Publishing House ”Nauka i izkustvo,” Sofia (1990).
[2] S. R. Kostadinova and Tz. Ignatov, ”Linear transformations of exponentially distributed random quantities and multidimensional exponential splines,” in: Annual of St. Kliment Ohridski University of Sofia, Faculty of Economics and Business Administration, Vol. 5, (2006), pp. 109–114.
[3] M. M. Ali and E. R. Mead, ”On the distribution of several linear combinations of order statistics from the uniform distribution,” in: Bulletin of the Institute of Statistical Research and Training, Vol. 3, University of Dacca (1968), pp. 22–41.
[4] W. Dahmen and C. A. Micchelli, ”On the linear independence of mulivariate B-splines. II. Complete configurations,” in: Mathematics of Computation, Vol. 41, No. 163 (1983), pp. 143–163. · Zbl 0525.41012
[5] C. De Boor, ”Splines as Linear Combinations of B-Splines,” in: G.G. Lorentz, C. K. Chui, and L. L. Shumaker (eds.), Approximation Theory II, Acad. Press, New York (1976), pp. 1–47. · Zbl 0343.41011
[6] Zv. G. Ignatov, M. O. Dialo, and S. R. Kostadinova, ”The density of linear transformations of independent exponential random variables,” in: Proc. XXXIVth Spring Conf. of UBM (2005), pp. 164–168. · Zbl 1374.60010
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