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Probability density functions of the order statistics for a sample of size n = 5 from an exponential distribution with unit scale parameter. In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. [1]
High-order moments are moments beyond 4th-order moments. As with variance, skewness, and kurtosis, these are higher-order statistics, involving non-linear combinations of the data, and can be used for description or estimation of further shape parameters. The higher the moment, the harder it is to estimate, in the sense that larger samples are ...
In probability theory and statistics, a stochastic order quantifies the concept of one random variable being "bigger" than another. These are usually partial orders , so that one random variable A {\displaystyle A} may be neither stochastically greater than, less than, nor equal to another random variable B {\displaystyle B} .
L-moments are statistical quantities that are derived from probability weighted moments [11] (PWM) which were defined earlier (1979). [7] PWM are used to efficiently estimate the parameters of distributions expressable in inverse form such as the Gumbel , [ 8 ] the Tukey lambda , and the Wakeby distributions.
Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa. The first cumulant is the mean, the second cumulant is the variance, and the third cumulant is the same as the third central moment. But fourth and higher-order cumulants are not equal to central moments.
Linear interpolation of the expectations for the order statistics for the uniform distribution on [0,1]. That is, it is the linear interpolation between points (p h, x h), where p h = h/(N+1) is the probability that the last of (N+1) randomly drawn values will not exceed the h-th smallest of the first N randomly drawn values.