# Frequency distribution

*Statistics*

A description of the relative number of times that given outcomes have occurred, or are expected to occur, relative to the whole population.

Three important frequency distributions are the Normal distribution, Lognormal distribution, and Leptokurtic distribution, described below.

All three of these types of distribution are used in practice as approximations to model the distributions of financial variables.

1. *Normal distributions* are usually the simplest approximations to work with, and are assumed by - for example - many Value at Risk analysis models and measures. A theoretical shortcoming of using normal distributions as a model is that they assume an infinitely large downside potential including negative prices; whereas many financial variables - such as asset prices - cannot in practice fall so far as to become negative.

2. *Lognormal distributions* usually describe better the theoretical range of financial variables such as traded equity prices, which theoretically have no upside limit but which cannot fall below zero.

3. In practice, observed financial returns are usually more closely approximated by *leptokurtic distributions*, with a greater frequency both of very high and of very low returns, than predicted by the comparable normal or lognormal distribution. So in risk analysis, if a population distribution is assumed to be normal or lognormal, but is in reality leptokurtic, downside risk will be understated.

Other commonly used types of theoretical frequency distribution include Binomial distributions and Poisson distributions.