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Median of medians finds an approximate median in linear time. Using this approximate median as an improved pivot, the worst-case complexity of quickselect reduces from quadratic to linear, which is also the asymptotically optimal worst-case complexity of any selection algorithm. In other words, the median of medians is an approximate median ...
The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter.
As a baseline algorithm, selection of the th smallest value in a collection of values can be performed by the following two steps: . Sort the collection; If the output of the sorting algorithm is an array, retrieve its th element; otherwise, scan the sorted sequence to find the th element.
The median is the value such that the fractions not exceeding it and not falling below it are each at least 1/2. It is not necessarily unique, but never infinite or totally undefined. For a data sample it is the "halfway" value when the list of values is ordered in increasing value, where usually for a list of even length the numerical average ...
The following pseudocode rearranges the elements between left and right, such that for some value k, where left ≤ k ≤ right, the kth element in the list will contain the (k − left + 1)th smallest value, with the ith element being less than or equal to the kth for all left ≤ i ≤ k and the jth element being larger or equal to for k ≤ j ≤ right:
In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter.For populations that are symmetric about one median, such as the Gaussian or normal distribution or the Student t-distribution, the Hodges–Lehmann estimator is a consistent and median-unbiased estimate of the population median.
In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator has a breakdown point of 50%. [ 1 ] Although it is equivariant under scaling, or under linear transformations of either its explanatory variable or its response variable, it is not under affine ...
Median test (also Mood’s median-test, Westenberg-Mood median test or Brown-Mood median test) is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical. The data in each sample are assigned to two groups ...