Log‐normal example: 100 observations drawn from a log‐normal distribution. The top figure shows the data compared to two mixture models. The first, in red, was selected purely by eye as compared to the histogram, intended to indicate the mode and tail of the distribution. The second, in blue, was fit using the EM algorithm with the first mixture as a starting point. The bottom figure shows the two filtered kernel estimators using the two mixture models compared to a standard kernel estimator.
A probability density consisting of a mixture of two normals. We illustrate four estimators computed on 200 random variates drawn from this model: the filtered kernel estimator, using a two component mixture of normals fit to the data to define the filtering functions: a standard kernel estimator; the kernel estimator with the bandwidth inflated or reduced in order to match the two components.
