Kernel probability density function estimation is a method to estimate unknown probability density function

and the key of kernel probability density function estimation method is the selection of kernel function and the determination of bandwidth. In this paper

the Solve-the-Equation method is used to derive the second deriva- tive of the bandwidth

and the iterative algorithm is designed to calaulate the optimal bandwidth. Under the premise of the determinate kernel method

cosine kernel is used to estimate unknown probability density function and make an improvement. Results show that the new kernel function improves the precision and gliding property of kernel density estimation.