Probability Densities

  • Igor Grabec
  • Wolfgang Sachse
Part of the Springer Series in Synergetics book series (SSSYN, volume 68)


It was mentioned in Chap. 2 that a proper analytical description of empirical data is one of the primary tasks of empirical science. A basic related problem is the estimation of the probability density function (PDF) f(x) of a continuous, random variable X from a set of N independent, identically distributed sample values {x 1,…, x N }. Hereafter we assume that only continuity of the random variable and no other a priori information about its properties is known, therefore a non-parametric estimation is considered. Among various non-parametric techniques the presentation of the PDF by a kernel estimator is most common [4, 3, 6, 5] and this is also the focus of our treatment.


Probability Density Probability Density Function Probability Density Function Window Width Window Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Igor Grabec
    • 1
  • Wolfgang Sachse
    • 2
  1. 1.Faculty of Mechanical EngineeringUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Theoretical and Applied MechanicsCornell UniversityIthacaUSA

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