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Quantile normalization. In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. To quantile-normalize a test distribution to a reference distribution of the same length, sort the test distribution and sort the reference distribution. The highest entry in the test distribution then ...
In probability theory and statistics, a standardized moment of a probability distribution is a moment (often a higher degree central moment) that is normalized, typically by a power of the standard deviation, rendering the moment scale invariant. The shape of different probability distributions can be compared using standardized moments.
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 ...
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when and , and it is described by this probability density function (or density): The variable has a mean of 0 and a variance and standard deviation of 1.
The multivariate normal distribution is said to be "non-degenerate" when the symmetric covariance matrix is positive definite. In this case the distribution has density [5] where is a real k -dimensional column vector and is the determinant of , also known as the generalized variance.
Pseudo-Voigt approximation. The pseudo-Voigt profile (or pseudo-Voigt function) is an approximation of the Voigt profile V (x) using a linear combination of a Gaussian curve G (x) and a Lorentzian curve L (x) instead of their convolution. The pseudo-Voigt function is often used for calculations of experimental spectral line shapes.
This method is widely used for normalization in many machine learning algorithms (e.g., support vector machines, logistic regression, and artificial neural networks). [4] [5] The general method of calculation is to determine the distribution mean and standard deviation for each feature. Next we subtract the mean from each feature.
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution. [2][3] Equivalently, if Y has a normal distribution, then the exponential ...