Abstract
We present a new method for reconstructing the density function underlying a given histogram. First we analyze the univariate case taking the approximating function in a class of quadratic-like splines with variable degrees. For the analogous bivariate problem we introduce a new scheme based on the Boolean sum of univariate B-splines and show that for a proper choice of the degrees, the splines are positive and satisfy local monotonicity constraints.
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Communicated by J. Carnicer and J.M. Peña
Dedicated to Prof. Mariano Gasca in occasion of his 60th birthday
Supported by Università di Siena, under P.A.R. 2002.
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Costantini, P., Pelosi, F. Shape preserving histogram approximation. Adv Comput Math 26, 205–230 (2007). https://doi.org/10.1007/s10444-004-8008-2
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DOI: https://doi.org/10.1007/s10444-004-8008-2