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Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value.
Inverted logistic S-curve to model the relation between wheat yield and soil salinity. Many natural processes, such as those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time.
A similar canonical set of sigma points can be generated in any number of dimensions by taking the zero vector and the points comprising the rows of the identity matrix, computing the mean of the set of points, subtracting the mean from each point so that the resulting set has a mean of zero, then computing the covariance of the zero-mean set ...
The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed , and is called a normal deviate . Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not ...
In the empirical sciences, the so-called three-sigma rule of thumb (or 3 σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.
Wolfgang Pauli (1900–1958), c. 1924. Pauli received the Nobel Prize in Physics in 1945, nominated by Albert Einstein, for the Pauli exclusion principle.. In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary.
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.
x erf x 1 − erf x; 0: 0: 1: 0.02: 0.022 564 575: 0.977 435 425: 0.04: 0.045 111 106: 0.954 888 894: 0.06: 0.067 621 594: 0.932 378 406: 0.08: 0.090 078 126: 0.909 ...