The Comparative Study Of Probability Density Function Estimation Based On The Different Kernel Functions

In probability theory and statistics, the probability density function estimation is the technology of estimation for the unknown probability density function based on the observed data that can make the mean integrated square error (MISE) between the true density and the estimated density reach the minimum. The classical non-parameter estimation method is Parzen Window method, also known as the kernel probability density function estimation method.The key point of kernel probability density function estimation method is the selection of kernel function and the determination of bandwidth. In this paper, we compare the performance of seven different kernel functions. For every different kernel function, the solve-the-equation method is used to derive the optimal bandwidth and the iterative algorithm is designed to calaulate the optimal bandwidth.In the experimental part, we estimate the probability density functions based on the three artificial data sets which respectively meet the Gaussian distribution, the Rayleigh distribution and exponential distribution. And, the theoretical analysis is carried out based on the performance of these seven kinds of kernel functions. The experimental results show that under the premise of minimum of MISE, compared with other kernel functions, the Epanechnikov kernel function and the Quartic kernel functions have the better estimation effect.