The Parzen window method is a way of estimating the probability density function of a random variable. As an illustration, given some data about a sample of a population, the Parzen window method makes it possible to extrapolate the data to the entire population.

If x₁, x₂, ..., x_N is a sample of a random variable, then the Parzen window approximation of its probability density function is

where W is some kernel. Quite often W is taken to be a Gaussian function with mean zero and variance σ²:

See also

• Density estimation.

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.

External links

• Parzen Window -- from MathWorld