View source for Shape of a probability distribution

{{Short description|Concept in statistics}}
In [[Statistics|statistics]], the concept of the '''shape of a probability distribution''' arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population. The shape of a distribution may be considered either descriptively, using terms such as "J-shaped", or numerically, using quantitative measures such as [[Skewness|skewness]] and [[Kurtosis|kurtosis]].

Considerations of the shape of a distribution arise in statistical [[Data analysis|data analysis]], where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modelling purposes.

[[File:Standard deviation diagram.svg|right|thumb|350px|The [[Normal distribution|normal distribution]], often called the "bell curve"]]

[[File:Exponential pdf.svg|thumb|[[Exponential distribution|Exponential distribution]]]]

==Descriptions of shape==

The shape of a distribution will fall somewhere in a continuum where a flat distribution  might be considered central and where types of departure from this include: mounded (or unimodal), U-shaped, J-shaped, reverse-J shaped and multi-modal.<ref>Yule & Kendall (1950): Chapter 4 &mdash; Frequency Distributions</ref> A bimodal distribution would have two high points rather than one. The shape of a distribution is sometimes characterised by the behaviours of the tails (as in a long or short tail). For example, a flat distribution can be said either to have no tails, or to have short tails. A [[Normal distribution|normal distribution]] is usually regarded as having short tails, while an [[Exponential distribution|exponential distribution]] has exponential tails and a [[Pareto distribution]] has long tails.

==See also==
*[[Shape parameter]]
*[[List of probability distributions]]

==Notes==
{{Reflist}}

==References==
:*Yule, G.U., Kendall, M.G. (1950) ''An Introduction to the Theory of Statistics'', 14th Edition (5th Impression, 1968), Griffin, London. 
:*den Dekker A. J., Sijbers J., (2014) "[https://www.academia.edu/download/35303854/pm2014.pdf Data distributions in magnetic resonance images: a review]{{dead link|date=July 2022|bot=medic}}{{cbignore|bot=medic}}", ''Physica Medica''

{{Statistics|descriptive}}

[[Category:Theory of probability distributions]]

{{Sourceattribution|Shape of a probability distribution}}