Parzen-window Density Estimation (PWDE)

1. Probability density function

In mathematics, the probability density function of a continuous random variable (which can be abbreviated as a density function if not confused) is a function that describes the probability of the output value of this random variable near a certain point of value. The probability that the value of a random variable falls within an area is the integral of the probability density function in this region. When the probability density function exists, the distribution function is the integral of the probability density function. The probability density function is generally marked with a lowercase "pdf" (probability Density function).

The common probability density function has uniform distribution, two-value distribution, Gaussian distribution and so on.

2. Probability density function estimation

In the real world, we may need such an application, based on certain observations, we want to introduce the distribution of the overall probability of a thing, and the probability distribution is determined by the probability density function. The probability density function estimation is such a kind of thought, has the sample launches the whole law. Specific can be divided into two categories

2.1 Parameter Estimation method: Pre-assumed that each category of probability density function of the form known, and the specific parameters are unknown;

Maximum likelihood estimation (MLE, Maximum likelihood estimation);

Bayesian estimation (Bayesian estimation).

2.2 Nonparametric Estimation method.

3.Parzen window Density estimation

Parzen window density estimation is a basic data interpolation technique, given some random sample X,pwde to estimate the PDF driven by these samples. The Pwde overlay is placed on the observation value on the kernel function, and each observation value contributes to the estimation of the PDF, based on this approach. The formula for estimating a PDF using Pwde is as follows, and P (x) is the contribution of the observed value to the window.

Where is the width of the window or the bandwidth parameter of the kernel function. , the kernel function is Tan Feng, and the Gaussian density function kernel is often used to estimate the PDF. If you use a Gaussian nucleus, the above becomes

。

Reference: Http://zh.wikipedia.org/wiki/%E6%A9%9F%E7%8E%87%E5%AF%86%E5%BA%A6%E5%87%BD%E6%95%B8;

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Parzen-window Density Estimation (PWDE)