Examining Distributions

Adding Density Estimates

A cumulative distribution function gives the proportion of the data less than each possible value. A density function is the derivative of the cumulative distribution function. Density estimation is the construction of an estimate of the density function from the observed data.

Histograms are one type of density estimation. You can also plot the density function to construct density curves. Density curves are sometimes preferred because they do not contain the discontinuous steps present in histograms.

Distribution ( Y ) provides two types of density estimation: parametric and kernel. In parametric estimation, the data are assumed to be from a known parametric family of distributions. The normal distribution is one of the most commonly used parametric distributions. Others include lognormal, exponential, and Weibull.

In kernel estimation, little is assumed about the functional form of the data. The data more completely determine the shape of the density curve. Kernel estimation is a type of nonparametric estimation.

Normal Density Curve

Kernel Density Curve

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