A common assumption in the previous chapters has been that the sampled data comes from a continuous distribution. This chapter examines methods of estimating the distribution of the population from which the data is sampled in such cases. If an estimate of the density of a continuous population is available, one can find estimates of population statistics such as the mode, range, and quantiles and estimate probabilities associated with the population, as well as make subjective determinations of whether data appears to have a symmetric distribution or not, or whether two distributions appear to be of the same general form.
The methods of estimating densities are typically computationally intensive and require the use of software for even small sets of data. Accordingly, this chapter will rely on the use of software for examples. Section 12.1 provides an introduction to the density functions and gives a popular, commonly used estimate, the histogram. In Section 12.2, the idea of kernel estimation is introduced and several kernels are examined, and Section 12.3 discusses bandwidth selection methods.