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  2. Gaussian probability space - Wikipedia

    en.wikipedia.org/wiki/Gaussian_probability_space

    In probability theory particularly in the Malliavin calculus, a Gaussian probability space is a probability space together with a Hilbert space of mean zero, real-valued Gaussian random variables. Important examples include the classical or abstract Wiener space with some suitable collection of Gaussian random variables.

  3. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    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 known.

  4. Gaussian random field - Wikipedia

    en.wikipedia.org/wiki/Gaussian_random_field

    In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is also called a Gaussian process . An important special case of a GRF is the Gaussian free field .

  5. Matrix normal distribution - Wikipedia

    en.wikipedia.org/wiki/Matrix_normal_distribution

    The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ⁡ ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...

  6. Q-function - Wikipedia

    en.wikipedia.org/wiki/Q-function

    [1] [2] In other words, () is the probability that a normal (Gaussian) random variable will obtain a value larger than standard deviations. Equivalently, () is the probability that a standard normal random variable takes a value larger than .

  7. Complex normal distribution - Wikipedia

    en.wikipedia.org/wiki/Complex_normal_distribution

    The standard complex normal random variable or standard complex Gaussian random variable is a complex random variable whose real and imaginary parts are independent normally distributed random variables with mean zero and variance /. [3]: p. 494 [4]: pp. 501 Formally,

  8. Gaussian function - Wikipedia

    en.wikipedia.org/wiki/Gaussian_function

    Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value μ = b and variance σ 2 = c 2. In this case, the Gaussian is of the form [1]

  9. Random variable - Wikipedia

    en.wikipedia.org/wiki/Random_variable

    A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. [1] The term 'random variable' in its mathematical definition refers to neither randomness nor variability [ 2 ] but instead is a mathematical function in which