A method for the estimation of a probability density function. Suppose X is a continuous random variable with unknown probability density function f. A random sample of observations of X is taken. If the sample values are denoted by x1, x2,…, xn, the estimate (see estimator) of f is given by
where K is a kernel function and the constant A is chosen so that . The observation xj may be regarded as being spread out between xj−a and xj+b (usually with a=b). The result is that the naive estimate of f as being a function capable of taking values only at x1, x2,…, xn, is replaced by a continuous function having peaks where the data are densest. Examples of kernel functions are the Gaussian kernel,
and the Epanechikov kernel,
The constant h is the window width or bandwidth. The choice of h is critical: small values may retain the spikes of the naive estimate, and large values may oversmooth so that important aspects of f are lost .
Kernel method. In this case a sample of twenty observations have been generated randomly from a chi-squared distribution with twenty degrees of freedom and a Gaussian kernel with h=3 has been used to generate the kernel density estimate.
- thermal mass
- thermal metamorphism
- thermal neutrons
- thermal noise
- thermal oxidation process
- thermal pollution
- thermal printer
- thermal protection
- thermal radiation
- thermal reactor
- thermal resistance
- thermal resistivity
- thermal runaway
- thermal stress
- thermal tile
- thermal transfer printer
- thermal velocity
- thermal wind
- thermic
- thermionic cathode
- thermionic emission
- thermionic-field emission
- thermionics
- thermionic valve
- thermistor