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In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value.
Inline the sin and operator+ function calls. Fuse the loops into a single loop. Remove the unused stores into the temporary arrays (can use a register or stack variable instead). Remove the unused allocation and free. All of these steps are individually possible.
Standard deviation may be abbreviated SD or Std Dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
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
Functionality similar to MATLAB and Octave. LAPACK++, a C++ wrapper library for LAPACK and BLAS; MFEM is a free, lightweight, scalable C++ library for finite element methods. Intel MKL, Intel Math Kernel Library (in C and C++), a library of optimized math routines for science, engineering, and financial applications, written in C/C++ and ...
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
An approximation for the exact correction factor for the normal distribution is given by using n − 1.5 in the formula: the bias decays quadratically (rather than linearly, as in the uncorrected form and Bessel's corrected form).