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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 ...
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 Weibull distribution (usually sufficient in reliability engineering) is a special case of the three parameter exponentiated Weibull distribution where the additional exponent equals 1. The exponentiated Weibull distribution accommodates unimodal, bathtub shaped [33] and monotone failure rates.
A stem-and-leaf plot of prime numbers under 100 shows that the most frequent tens digits are 0 and 1 while the least is 9. A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution.
The gamma distribution (;) (>) can be expressed as the product distribution of a Weibull distribution and a variant form of the stable count distribution. Its shape parameter can be regarded as the inverse of Lévy's stability parameter in the stable count distribution: (;) = [()], where () is a standard stable count distribution of shape , and ...
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.
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
Frequency distribution: a table that displays the frequency of various outcomes in a sample. Relative frequency distribution: a frequency distribution where each value has been divided (normalized) by a number of outcomes in a sample (i.e. sample size). Categorical distribution: for discrete random variables with a finite set of values.