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Formalized by John Tukey, the Tukey lambda distribution is a continuous, symmetric probability distribution defined in terms of its quantile function.It is typically used to identify an appropriate distribution (see the comments below) and not used in statistical models directly.
Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, [1] is a single-step multiple comparison procedure and statistical test.
This function is plotted in the following figure for a = 1.645, b = 3 and r = 6.5. 2. Tukey's biweight or bisquare M estimators have Ψ functions for any positive k, which defined by: = ((/)); | | This function is plotted in the following figure for k = 5. 3.
On the right is Tukey's biweight function, which, as we will later see, is an example of what a "good" (in a sense defined later on) empirical influence function should look like. In mathematical terms, an influence function is defined as a vector in the space of the estimator, which is in turn defined for a sample which is a subset of the ...
A popular window function, the Hann window. Most popular window functions are similar bell-shaped curves. In signal processing and statistics, a window function (also known as an apodization function or tapering function [1]) is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are ...
In statistics and computational geometry, the Tukey depth [1] is a measure of the depth of a point in a fixed set of points. The concept is named after its inventor, John Tukey . Given a set of n points X n = { X 1 , … , X n } {\displaystyle {\mathcal {X}}_{n}=\{X_{1},\dots ,X_{n}\}} in d -dimensional space, Tukey's depth of a point x is the ...
Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.
Example of a bagplot created in R. A bagplot, or starburst plot, [1] [2] is a method in robust statistics for visualizing two-or three-dimensional statistical data, analogous to the one-dimensional box plot. Introduced in 1999 by Rousseuw et al., the bagplot allows one to visualize the location, spread, skewness, and outliers of a data set. [3]