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Examples of platykurtic distributions include the continuous and discrete uniform distributions, and the raised cosine distribution. The most platykurtic distribution of all is the Bernoulli distribution with p = 1/2 (for example the number of times one obtains "heads" when flipping a coin once, a coin toss ), for which the excess kurtosis is −2.
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. [1] It results from a system of one or more inter-related Poisson processes occurring in sequence , or phases.
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. [1] A bimodal distribution would have two high points rather than one. The shape of a distribution is ...
Thus for platykurtic distributions, which can often be thought of as between a uniform distribution and a normal distribution, the informativeness of the middle sample points versus the extrema values varies from "equal" for normal to "uninformative" for uniform, and for different distributions, one or the other (or some combination thereof ...
This is a sample of size 50 from a normal distribution, plotted as both a histogram, and a normal probability plot. Normal probability plot of a sample from a normal distribution – it looks fairly straight, at least when the few large and small values are ignored.
The kurtosis of a frequency distribution is a measure of the proportion of extreme values (outliers), which appear at either end of the histogram. If the distribution is more outlier-prone than the normal distribution it is said to be leptokurtic; if less outlier-prone it is said to be platykurtic.
In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.