One final concern is that many times even the distribution
is incorrectly estimated because it is assumed
arbitrarily to belong to a family of distributions. For example, it
is often very easy to work with Gaussian densities. Therefore, it is
tempting to assume that
is Gaussian. Experiments can be
performed to estimate the mean and variance parameters. Even though
some best fit will be found, it does not necessarily imply that a
Gaussian is a good representation. Conclusions based on this model
may be incorrect, especially if the true distribution has a different
shape, such as having a larger tail or being multimodal. In many
cases, *nonparametric* methods may be
needed to avoid such biases. Such methods do not assume a particular
family of distributions. For example, imagine estimating a
probability distribution by making a histogram that records the
frequency of occurrences for a fixed value of . The
histogram can then be normalized to contain a representation of the
probability distribution without assuming an initial form.

Steven M LaValle 2012-04-20