Concepts inComputation of the multivariate normal integral
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
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Carl Friedrich Gauss
Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.
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Multivariate normal distribution
In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional normal distribution to higher dimensions. One possible definition is that a random vector is said to be p-variate normally distributed if every linear combination of its p components has a univariate normal distribution. However, its importance derives mainly from the Multivariate central limit theorem.
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Normal distribution
In probability theory, the normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability density function, known as the Gaussian function or informally the bell curve: The parameter μ is the mean or expectation (location of the peak) and σ is the variance. σ is known as the standard deviation. The distribution with μ = 0 and σ = 1 is called the standard normal distribution or the unit normal distribution.
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Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, such that areas above the axis add to the total, and the area below the x axis subtract from the total.
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Fortran
Fortran (previously FORTRAN) is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing.
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Computer program
A computer program (also software, or just a program) is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute the instructions.
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