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Estimation of the Parameters of a Probability Distribution Using Kernel Density Estimators Abstract The probability density function (pdf) plays an important role in the field of Statistics. In particular, the pdf is used with every random variable in determining the distribution of the possible values of the variable, the values of the parameters of the distribution, and every probability statement concerning a random variable. Typically, in applied data analysis the underlying pdf associated with the observed data will be unknown. Moreover, it can be difficult to determine the parametric form of a pdf that generated the observed data. It is often important to estimate the pdf through a method known as density estimation. A mathematical approach to density estimation is Non-Parametric Density Estimators (NPDE’s). NPDE’s are differentiable and produce smooth estimates of the pdf. The NPDE’s that are under consideration in this research project are the Normal and Epanechnikov kernel estimators. The goal of this project are to study estimators of parameters based on the Normal and Epanechnikov kernels. The estimators based on the kernel estimates will be compared the standard estimators. Biography
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