A discretization method for the range of values of a multidimensional random variable is considered. Its dependence on the volume, dimension of the initial information and the type of probability density is investigated. The obtained results are compared with the Scott rule for a multidimensional random variable with a normal distribution law.
Similar content being viewed by others
References
H. A. Sturges, “The choice of a class interval,” J. Am. Stat. Assoc., 21, 65–66 (1926), DOI: https://doi.org/10.1080/01621459.1926.10502161.
D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, Wiley, New York (1992).
A. Hacine Gharbi, P. Ravier, R. Harba, and T. Mohamadi, “Low bias histogram based estimation of mutual information for feature selection,” Pattern Recogn. Lett., 33, No. 10, 1302–1308 (2012), DOI: https://doi.org/10.1016/j.patrec.2012. 02.022.
V. S. Pugachev, Theory of Probability and Mathematical Statistics: Textbook, FIZMATLIT, Moscow (2002).
D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, Wiley, NJ (2015), 2nd ed.
L. Devroye and G. Lugosi, “Bin width selection in multivariate histograms by the combinatorial method,” Test., 13, No. 1, 129–145 (2004), DOI: https://doi.org/10.1007/BF02603004.
A. V. Lapko and V. A. Lapko, “Optimal choice of the number of discretization intervals for the domain of variation of a one-dimensional random variable when estimating the probability density,” Izmer. Tekhn., No. 7, 24–27 (2013).
A. V. Lapko and V. A. Lapko, “Selection of the optimal number of discretization intervals for the range of values of a two-dimensional random variable,” Izmer. Tekhn., No. 2, 14–17 (2016).
A. V. Lapko and V. A. Lapko, “Comparison of the efficiency of discretization methods for the range of values of dependent random variables in the synthesis of a non-parametric estimate of two-dimensional probability density,” Izmer. Tekhn., No. 4, 15–18 (2017).
A. V. Lapko and V. A. Lapko, “Regression estimate of multidimensional probability density and its properties,” Optoelectr., Instrum. Data Proc., 50, No. 2, 148–153 (2014), DOI: https://doi.org/10.3103/S875669901402006X.
A. V. Lapko and V. A. Lapko, “Regression estimate of multidimensional probability density and its properties,” Avtometriya, 50, No. 2, 50–56 (2014).
I. Heinhold and K. Gaede, Ingeniur Statistic, Springer Verlag, München, Vienna (1964).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izmeritel’naya Tekhnika, No. 1, pp. 16–20, January, 2019.
Rights and permissions
About this article
Cite this article
Lapko, A.V., Lapko, V.A. Discretization Method for the Range of Values of a Multi-Dimensional Random Variable. Meas Tech 62, 16–22 (2019). https://doi.org/10.1007/s11018-019-01579-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11018-019-01579-0