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Thus computing the gamma function becomes a matter of evaluating only a small number of elementary functions and multiplying by stored constants. The Lanczos approximation was popularized by Numerical Recipes , according to which computing the gamma function becomes "not much more difficult than other built-in functions that we take for granted ...
This spectrum was taken from a Uranium ore sample from Moab, Utah. Gamma-ray spectroscopy is the qualitative study of the energy spectra of gamma-ray sources, such as in the nuclear industry, geochemical investigation, and astrophysics. Gamma-ray spectrometry, on the other hand, is the method used to acquire a quantitative spectrum measurement. [1]
The gamma distribution is the conjugate prior for the precision of the normal distribution with known mean. The matrix gamma distribution and the Wishart distribution are multivariate generalizations of the gamma distribution (samples are positive-definite matrices rather than positive real numbers).
A gamma-ray spectrometer (GRS) is an instrument for measuring the distribution (or spectrum—see figure) of the intensity of gamma radiation versus the energy of each photon. The study and analysis of gamma-ray spectra for scientific and technical use is called gamma spectroscopy , and gamma-ray spectrometers are the instruments which observe ...
Generally, plots show the semivariogram values as a function of sample point separation . In the case of empirical semivariogram, separation distance bins h ± δ {\displaystyle h\pm \delta } are used rather than exact distances, and usually isotropic conditions are assumed (i.e., that γ {\displaystyle \gamma } is only a function of h ...
Prompt-gamma neutron activation analysis (PGAA) is a very widely applicable technique for determining the presence and amount of many elements simultaneously in samples ranging in size from micrograms to many grams. It is a non-destructive method, and the chemical form and shape of the sample are relatively unimportant.
The Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution. It occurs frequently in likelihood-ratio tests in multivariate statistical analysis. It also arises in the spectral theory of random matrices [citation needed] and in multidimensional Bayesian analysis. [5]
Gautschi's inequality is specific to a quotient of gamma functions evaluated at two real numbers having a small difference. However, there are extensions to other situations. If x {\displaystyle x} and y {\displaystyle y} are positive real numbers , then the convexity of ψ {\displaystyle \psi } leads to the inequality: [ 6 ]