Pattern Recognition, 4th Edition

2.5. Estimation of Unknown Probability Density Functions

So far, we have assumed that the probability density functions are known. However, this is not the most common case. In many problems, the underlying pdf has to be estimated from the available data. There are various ways to approach the problem. Sometimes we may know the type of the pdf (e.g., Gaussian, Rayleigh), but we do not know certain parameters, such as the mean values or the variances. In contrast, in other cases we may not have information about the type of the pdf but we may know certain statistical parameters, such as the mean value and the variance. Depending on the available information, different approaches can be adopted. This will be our focus in the next subsections. ...