A distribution-free interval mathematical analysis of probability density functions

  • Rashid Ahmad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 29)


In many real problems, such as in physical, biological, socio-economic sciences, medicine and certain natural sciences, one is faced with probabilistic models. To completely specify these models one must know the form of either probability distribution or density function. In practice one does not know the exact forms, rather one has to approximate these functions from given data. A great number of researchers have investigated different aspects of this problem. In this paper we concentrate on two broad classes of density estimators, namely kernel and spline function based estimators. The approach adopted is interval analysis, oriented so that the end computations can be easily and economically performed on modern computers. In order to understand clearly and simply, the ideas involved are unified by using the Hilbert spaces.


Hilbert Space Probability Density Function Spline Function Reproduce Kernel Hilbert Space Probability Density Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Rashid Ahmad
    • 1
  1. 1.University of StrathclydeGlasgow

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