Improving Kernel Methods for Density Estimation in Random Differential Equations Problems
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
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
▼
Show Figures
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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 StyleCortés 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
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.