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  2. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...

  3. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables. It is a special case of the Gamma distribution, and it is used in goodness-of-fit tests in statistics. The inverse-chi-squared distribution; The noncentral chi-squared distribution; The scaled inverse chi-squared distribution; The Dagum ...

  4. List of integrals of Gaussian functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    Download as PDF; Printable version; ... is the corresponding cumulative distribution function ... has an extensive list of Gaussian-type integrals; ...

  5. Cumulative distribution function - Wikipedia

    en.wikipedia.org/wiki/Cumulative_distribution...

    Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .

  6. Gaussian function - Wikipedia

    en.wikipedia.org/wiki/Gaussian_function

    Mathematically, the derivatives of the Gaussian function can be represented using Hermite functions. For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial, up to scale. Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory.

  7. Multivariate normal distribution - Wikipedia

    en.wikipedia.org/wiki/Multivariate_normal...

    If () is a general scalar-valued function of a normal vector, its probability density function, cumulative distribution function, and inverse cumulative distribution function can be computed with the numerical method of ray-tracing (Matlab code). [17]

  8. Q-function - Wikipedia

    en.wikipedia.org/wiki/Q-function

    In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.

  9. Exponentially modified Gaussian distribution - Wikipedia

    en.wikipedia.org/wiki/Exponentially_modified...

    In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean μ and variance σ 2, and Y is ...