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In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. [1] Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference. Important special cases of the order statistics are the minimum and maximum value of a sample, and (with some ...
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant. [1] [2] References External links. k-Statistic on ...
For a population, of discrete values or for a continuous population density, the k-th q-quantile is the data value where the cumulative distribution function crosses k/q. That is, x is a k-th q-quantile for a variable X if Pr[X < x] ≤ k/q or, equivalently, Pr[X ≥ x] ≥ 1 − k/q. and Pr[X ≤ x] ≥ k/q.
The zeta distribution has uses in applied statistics and statistical mechanics, and perhaps may be of interest to number theorists. It is the Zipf distribution for an infinite number of elements. The Hardy distribution , which describes the probabilities of the hole scores for a given golf player.
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
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for k = 0, 1, 2, ..., n, where =!! ()! is the binomial coefficient. The formula can be understood as follows: p k q n−k is the probability of obtaining the sequence of n independent Bernoulli trials in which k trials are "successes" and the remaining n − k trials