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Parzen Window




If ''x''1, ''x''2, ..., ''x''''N'' is a Sample of a random variable, then the Parzen window approximation of its probability density function is

: ho(x)= rac{1}{N}\sum_{i=1}^N W(x-x_i)

where ''W'' is some kernel, i.e., some probability density function. Quite often ''W'' is taken to be a Gaussian Function with Mean zero and Variance σ2:

:W(x) = {1 \over \sigma\sqrt{2\pi} }\,e^{-{x^2 / 2\sigma^2}}.


SEE ALSO



REFERENCES

  • Parzen E. (1962). ''On estimation of a probability density function and mode'', Ann. Math. Stat. 33, pp. 1065-1076.


  • Duda, R. and Hart, P. (1973). ''Pattern Classification and Scene Analysis''. John Wiley & Sons. ISBN 0471223611.