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The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
The gamma distribution is a two-parameter exponential family with natural parameters α − 1 and −1/θ (equivalently, α − 1 and −λ), and natural statistics X and ln X. If the shape parameter α is held fixed, the resulting one-parameter family of distributions is a natural exponential family.
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 ...
A histogram is a visual representation of the distribution of quantitative data. To construct a histogram, the first step is to "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval.
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
In probability theory and statistics, a shape parameter (also known as form parameter) [1] is a kind of numerical parameter of a parametric family of probability distributions [2] that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).
Figure 1. A simple bimodal distribution, in this case a mixture of two normal distributions with the same variance but different means. The figure shows the probability density function (p.d.f.), which is an equally-weighted average of the bell-shaped p.d.f.s of the two normal distributions.
This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]