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NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
The moment generating function of a real random variable is the expected value of , as a function of the real parameter . For a normal distribution with density f {\textstyle f} , mean μ {\textstyle \mu } and variance σ 2 {\textstyle \sigma ^{2}} , the moment generating function exists and is equal to
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.
A comprehensive step-by-step tutorial with an explanation of the theoretical foundations of Approximate Entropy is available. [8] The algorithm is: Step 1 Assume a time series of data (), (), …, (). These are raw data values from measurements equally spaced in time. Step 2
The noncentral F-distribution is implemented in the R language (e.g., pf function), in MATLAB (ncfcdf, ncfinv, ncfpdf, ncfrnd and ncfstat functions in the statistics toolbox) in Mathematica (NoncentralFRatioDistribution function), in NumPy (random.noncentral_f), and in Boost C++ Libraries.
The Marsaglia polar method [1] is a pseudo-random number sampling method for generating a pair of independent standard normal random variables. [2] Standard normal random variables are frequently used in computer science, computational statistics, and in particular, in applications of the Monte Carlo method. The polar method works by choosing ...
A graphical tool for assessing normality is the normal probability plot, a quantile-quantile plot (QQ plot) of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal quantiles (a measure of the goodness of fit) measures how well the data are modeled by a normal distribution. For ...
Plot of probit function. In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution.It has applications in data analysis and machine learning, in particular exploratory statistical graphics and specialized regression modeling of binary response variables.