Gaussian Mixture Distribution Analysis as Estimation of Probability Density Function and it's the Periphery

Abstract

In statistics, Mixture distribution model is a stochastic model for a measured data set to express existence of the subpopulation in a population, without requiring that the subpopulation to whom each observational data belongs should be identified. Formally, Mixture distribution model is equivalent to expressing the probability distributions of observational data in a population. However, it is although it is related to the problem relevant to Mixture distribution pulling out a population's characteristic out of subpopulation. Mixture distribution model is used without subpopulation's identity information in order to make the statistical inference about the characteristic of the subpopulation who was able to give only the observational data about a population simultaneously. This paper considered these matters from the similarity of the linear combination of an element function with estimation problem of a density function which used the Kernel function, and estimation problem of the density function using a Spline function. How to take Translate in arrangement of knots of estimation problem of the density function using the method of Bandwidth picking in estimation problem of the density function using a Kernel function and a Spline function and Wavelets analysis and Scale has a related thing.