ABSTRACT
Several methods of density estimation are discussed in the literature. This chapter focuses on nonparametric density estimation. For problems that require a nonparametric approach, density estimation provides a flexible and powerful tool for visualization, exploration, and analysis of data. The chapter presents univariate density estimation methods, including the histogram, frequency polygon, average shifted histogram, and kernel density estimators. Orthogonal systems provide an alternate approach to density estimation. Introduced in elementary statistics courses, and available in all popular statistics packages, the probability histogram is the most widely used density estimate in descriptive statistics. To select an optimal smoothing parameter for density estimation, one needs to establish a criterion for comparing smoothing parameters. One approach aims to minimize the squared error in the estimate. The frequency polygon is constructed by computing the density estimate at the midpoint of each class interval, and using linear interpolation for the estimates between consecutive midpoints.
