Kernel density estimation has number of applications in different fields such as Econometrics, Economics, Engineering, Agriculture, Signal processing and identifying accident hot spots etc. Kernel density estimation procedures need a number of decision such as choice between variable kernel density estimation (VKDE) and fixed kernel density estimation (FKDE). It has been proven that VKDE performs better than FKDE. However among the VKDE, one has to make choice of bandwidths selection algorithm and kernel functions. There are four general classes of bandwidth selection algorithm i.e. rule of thumb, Classical, Plug in and Bootstrap. The most popular algorithm one from each of these classes are Silverman rule of thumb (SRT), Least square cross validation (LSCV), Improve plug in (IPI), Exact bootstrap (EB) and one cannot find appropriate guideline for choice between these algorithms. In addition to bandwidth selection algorithm the VKDE also depend on kernel function. There are nine different type of kernel functions i.e. Epanechnikov, Bi-weight, Tri-weight, Gaussian, uniform, Triangular, Tri-cube, Cosine and Sigmoid. This study is aimed to help in the choice of kernel function and bandwidth selection algorithm. We compare four kernel function and four bandwidth selection algorithm via Monte Carlo simulation for ten different types of normal mixture distribution. Our results show that IPI bandwidth and epanechnikov kernel function is the best choice for Gaussian, kurtotic unimodal, tri-modal and double claw distribution. For the remaining six distributions the EB bandwidth performed well. Supervisor:- Dr. Atiq-ur-Rehman