Kernel density estimation

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

${\displaystyle \rho (x)={\frac {1}{N}}\sum _{i=1}^{N}W(x-x_{i})}$

where W is some kernel. Quite often W is taken to be a Gaussian with mean zero.

Parzen window density estimate ρ(x) (blue); the Gaussians in the sum (red). Six sample points were considered. The variance of the Gaussians was set to 0.5. Note that where the points are denser, the density estimate has higher values.

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