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A key mathematical property of the Pearson correlation coefficient is that it is invariant under separate changes in location and scale in the two variables. That is, we may transform X to a + bX and transform Y to c + dY, where a, b, c, and d are constants with b, d > 0, without changing the correlation coefficient.
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. , the value of the function's midpoint; , the supremum of the values of the function; , the logistic growth rate or steepness of the curve. [1] Standard logistic function where. For values of in the domain of real numbers from to , the S ...
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made ...
v. t. e. In quantum statistics, Bose–Einstein statistics ( B–E statistics) describes one of two possible ways in which a collection of non-interacting identical particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles ...
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean -valued outcome: success (with probability p) or failure (with probability ).
v. t. e. Given two random variables that are defined on the same probability space, [1] the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal ...
Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , , , or . [1]
In statistics and applications of statistics, normalization can have a range of meanings. [1] In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the ...