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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 ...
Such a parameter must affect the shape of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does). For example, "peakedness" refers to how round the main peak is. [3] Probability density functions for selected distributions with mean 0 and variance 1.
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance , standard deviation , and interquartile range .
a measure of the shape of the distribution like skewness or kurtosis; if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient; A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
In the case where a parametrized family has a location parameter, a slightly different definition is often used as follows.If we denote the location parameter by , and the scale parameter by , then we require that (;,,) = (() /;,,) where (,,,) is the cmd for the parametrized family. [1]
The mean of gamma distribution is given by the product of its shape and scale parameters: = = / The variance is: = = / The square root of the inverse shape parameter gives the coefficient of variation: / = = /
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.