In probability theory and statistics, a normal variance-mean mixture with mixing probability density g {\displaystyle g} is the continuous probability...

a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution...

normal variance-mean mixture where the mixing density is the gamma distribution. The tails of the distribution decrease more slowly than the normal distribution...

of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distribution as the number of samples...

(GH) is a continuous probability distribution defined as the normal variance-mean mixture where the mixing distribution is the generalized inverse Gaussian...

moment, μ k / σ k {\displaystyle \mu _{k}/\sigma ^{k}} Variance-to-mean ratio (or relative variance), σ 2 / μ {\displaystyle \sigma ^{2}/\mu } Fano factor...

components are Gaussian distributions, there will be a mean and variance for each component. If the mixture components are categorical distributions (e.g., when...

law). The log-normal distribution is the maximum entropy probability distribution for a random variate X—for which the mean and variance of ln X are specified...

α ~ β and α and β >> 1 is approximately normal with mean 1/2 and variance 1/(4(2α + 1)). If α ≥ β the normal approximation can be improved by taking the...

{X} } has a univariate normal distribution, where a univariate normal distribution with zero variance is a point mass on its mean. There is a k-vector μ...

prior for unknown mean and variance, but with a fixed, linear relationship between them, is found in the normal variance-mean mixture, with the generalized...

Normal curve equivalent Normal distribution Normal probability plot – see also rankit Normal score – see also rankit and Z score Normal variance-mean...

the mean of the i-th component. In the case of a mixture of one-dimensional distributions with weights wi, means μi and variances σi2, the total mean and...

off-diagonal element is less familiar but can be identified as a normal variance-mean mixture where the mixing density is a χ2 distribution. The corresponding...

total variance is a fundamental result in probability theory that expresses the variance of a random variable Y in terms of its conditional variances and...

parameters to estimate: the two means, the two variances and the mixing parameter. A mixture of two normal distributions with equal standard deviations...

population mean. The assumptions underlying a t-test in the simplest form above are that: X follows a normal distribution with mean μ and variance σ2/n. s2(n − 1)/σ2...

within-cluster variances (squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes...

data near the mean. Excess kurtosis, typically compared to a value of 0, characterizes the “tailedness” of a distribution. A univariate normal distribution...

harmonic mean is calculated as above. Both the mean and the variance may be infinite (if it includes at least one term of the form 1/0). The mean of the...

1/ κ {\displaystyle \kappa } are analogous to μ and σ2 (the mean and variance) in the normal distribution: μ is a measure of location (the distribution...

by utilizing the EM-algorithm. Gaussian scale mixtures: Compounding a normal distribution with variance distributed according to an inverse gamma distribution...

distribution is conjugate to the normal distribution when serving as the mixing distribution in a normal variance-mean mixture. Let the prior distribution...

converges to normal distribution with mean μ = αθ and variance σ2 = αθ2. The gamma distribution is the conjugate prior for the precision of the normal distribution...

Josephson et al. limited themselves to considering two normal mixtures with the same component variances and mixing proportions. As a consequence, their proposal...

minimum-variance mean (for large normal samples), which is to say the variance of the median will be ~50% greater than the variance of the mean. For any...

solutions that may be found by EM in a mixture model involves setting one of the components to have zero variance and the mean parameter for the same component...

practice, efficient estimators exist for: the mean μ of the normal distribution (but not the variance σ2), parameter λ of the Poisson distribution, the...

normal distribution with the exact variance – the normal distribution is a two-parameter model, with mean and variance. Thus, in the absence of an underlying...

distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the...