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High Precision Numerical Computation of Principal Points for Univariate Distributions

Santanu Chakraborty (), Mrinal Kanti Roychowdhury () and Josef Sifuentes ()
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Santanu Chakraborty: University of Texas Rio Grande Valley
Mrinal Kanti Roychowdhury: University of Texas Rio Grande Valley
Josef Sifuentes: University of Texas Rio Grande Valley

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 14, 558-584

Abstract: Abstract Principal points were first introduced in 1990: for a positive integer n, n principal points of a random variable are the n points that minimize the mean squared distance between the random variable and the nearest of the n points. In this paper, we give a high precision numerical method for calculating the n principal points and the n th quantization errors for all positive integers n. For some absolutely continuous univariate distributions, we calculate the n principal points for different n using Newton’s method. Additionally, we also provide the corresponding values of mean squared distances.

Keywords: Probability distribution; Principal points; Quantization error; Newton’s method; Primary 60E05; 60E07; Secondary 60-08 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-020-00239-6

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