Linear Approximations of Probability Density Functions

We develop a method for approximating the PDF of a continuous random variable with a piecewise-linear function. Four algorithms for choosing the endpoints of the linear segments are compared. The approximation is applied to estimating the convolution of two independent random variables.

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Bibliographic Details
Published inComputational Probability Applications pp. 119 - 132
Main Authors McDaniel, Lee S., Glen, Andrew G., Leemis, Lawrence M.
Format Book Chapter
LanguageEnglish
Published Cham Springer International Publishing 01.01.2017
SeriesInternational Series in Operations Research & Management Science
Subjects
Convolutions
Optimization
Online AccessGet full text
ISBN3319433156
9783319433158
ISSN0884-8289
2214-7934
DOI10.1007/978-3-319-43317-2_10

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Summary:We develop a method for approximating the PDF of a continuous random variable with a piecewise-linear function. Four algorithms for choosing the endpoints of the linear segments are compared. The approximation is applied to estimating the convolution of two independent random variables.
Bibliography:This original paper uses many aspects of APPL in order to make approximations to certain random variable algebra operations that do not have closed-form solutions. By making linear approximations of PDFs, APPL can then do operations such a Convolution, Product, and Transform in order to approximate probability distribution of the new random variable. APPL’s ability to define piecewise functions allows simpler linear piecewise functions to be used to approximate the true PDFs. Furthermore, the optimal placement of the segments can be embedded in the APPL explorations.
ISBN:3319433156
9783319433158
ISSN:0884-8289
2214-7934
DOI:10.1007/978-3-319-43317-2_10