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Open AccessFeature PaperArticle

Improving Kernel Methods for Density Estimation in Random Differential Equations Problems

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
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Math. Comput. Appl. 2020, 25(2), 33; https://doi.org/10.3390/mca25020033
Received: 30 May 2020 / Revised: 16 June 2020 / Accepted: 18 June 2020 / Published: 18 June 2020
(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2019)
Kernel density estimation is a non-parametric method to estimate the probability density function of a random quantity from a finite data sample. The estimator consists of a kernel function and a smoothing parameter called the bandwidth. Despite its undeniable usefulness, the convergence rate may be slow with the number of realizations and the discontinuity and peaked points of the target density may not be correctly captured. In this work, we analyze the applicability of a parametric method based on Monte Carlo simulation for the density estimation of certain random variable transformations. This approach has important applications in the setting of differential equations with input random parameters. View Full-Text
Keywords: probability density estimation; Monte Carlo simulation; parametric method; random differential equation probability density estimation; Monte Carlo simulation; parametric method; random differential equation
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MDPI and ACS Style

Cortés López, J.C.; Jornet Sanz, M. Improving Kernel Methods for Density Estimation in Random Differential Equations Problems. Math. Comput. Appl. 2020, 25, 33. https://doi.org/10.3390/mca25020033

AMA Style

Cortés López JC, Jornet Sanz M. Improving Kernel Methods for Density Estimation in Random Differential Equations Problems. Mathematical and Computational Applications. 2020; 25(2):33. https://doi.org/10.3390/mca25020033

Chicago/Turabian Style

Cortés López, Juan C.; Jornet Sanz, Marc. 2020. "Improving Kernel Methods for Density Estimation in Random Differential Equations Problems" Math. Comput. Appl. 25, no. 2: 33. https://doi.org/10.3390/mca25020033

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