###### **Normal** **distribution**

... and

**Distributions**modeled as**normal**- the**normal****distribution**being the**distribution**with maximum entropy for a given mean and ... The conjugate prior of the mean of a**normal****distribution**is another**normal****distribution**. Specifically, if x1, …, xn are iid N(μ ... Measurement errors in physical experiments are often modeled by a**normal****distribution**. This use of a**normal****distribution**does ... The generalized**normal****distribution**, also known as the exponential power**distribution**, allows for**distribution**tails with ...###### Folded **normal** **distribution**

The folded

**normal****distribution**is a probability**distribution**related to the**normal****distribution**. Given a normally distributed ... the**distribution**of Y is a half-**normal****distribution**. The random variable (Y/σ)2 has a noncentral chi-squared**distribution**with ... "The Folded**Normal****Distribution**". J Qual Technol. 12 (4): 236-238. Elandt RC (1961). "The folded**normal****distribution**: two ... "On multivariate folded**normal****distribution**". Sankhya B. 75 (1): 1-15. Virtual Laboratories: The Folded**Normal****Distribution**. ...###### Half-**normal** **distribution**

... follows a half-

**normal****distribution**. Thus, the half-**normal****distribution**is a fold at the mean of an ordinary**normal****distribution**... see truncated**normal****distribution**) If Y has a half-**normal****distribution**, then (Y/σ)2 has a chi square**distribution**with 1 degree ... The entropy of the half-**normal****distribution**is exactly one bit less the entropy of a zero-mean**normal****distribution**with the ... In probability theory and statistics, the half-**normal****distribution**is a special case of the folded**normal****distribution**. Let X ...###### Logit-**normal** **distribution**

... a logit-

**normal****distribution**is a probability**distribution**of a random variable whose logit has a**normal****distribution**. If Y is a ... The logistic**normal****distribution**is a generalization of the logit-**normal****distribution**to D-dimensional probability vectors by ... The logistic**normal****distribution**is a more flexible alternative to the Dirichlet**distribution**in that it can capture ... Beta**distribution**and Kumaraswamy**distribution**, other two-parameter**distributions**on a bounded interval with similar shapes ...###### Complex **normal** **distribution**

**Distribution**of the mean

**Normal**

**distribution**Multivariate

**normal**

**distribution**(a complex

**normal**

**distribution**is a bivariate ... The modulus of a complex

**normal**random variable follows a Hoyt

**distribution**. The 'circularly-symmetric

**normal**

**distribution**...

**normal**

**distribution**) Generalized chi-squared

**distribution**Wishart

**distribution**Complex random variable Goodman (1963) ... has the complex

**normal**

**distribution**. This

**distribution**can be described with 3 parameters: μ = E [ Z ] , Γ = E [ ( Z − μ ...

###### Generalized **normal** **distribution**

The Student-t

**distribution**, the Irwin-Hall**distribution**and the Bates**distribution**also extend the**normal****distribution**, and ... The t**distribution**, unlike this generalized**normal****distribution**, obtains heavier than**normal**tails without acquiring a cusp at ... Skew**normal****distribution**Nadarajah, Saralees (September 2005). "A generalized**normal****distribution**". Journal of Applied ... and Weibull**distributions**, but these do not include the**normal****distributions**as special cases. The two generalized**normal**...###### Matrix **normal** **distribution**

... the matrix

**normal****distribution**is a probability**distribution**that is a generalization of the multivariate**normal****distribution**... Multivariate**normal****distribution**. A K Gupta; D K Nagar (22 October 1999). "Chapter 2: MATRIX VARIATE**NORMAL****DISTRIBUTION**". ... Dawid (1981) provides a discussion of the relation of the matrix-valued**normal****distribution**to other**distributions**, including ... from the matrix**normal****distribution**is a special case of the sampling procedure for the multivariate**normal****distribution**. Let X ...###### Skew **normal** **distribution**

... the skew

**normal****distribution**is a continuous probability**distribution**that generalises the**normal****distribution**to allow for non ... skew multivariate t**distribution**and others. The**distribution**is a particular case of a general class of**distributions**with ... Then the probability density function (pdf) of the skew-**normal****distribution**with parameter α {\displaystyle \alpha } is given ... One can verify that the**normal****distribution**is recovered when α = 0 {\displaystyle \alpha =0} , and that the absolute value of ...###### Multivariate **normal** **distribution**

... has a joint

**normal****distribution**. A simple example is one in which X has a**normal****distribution**with expected value 0 and ... aTX has a univariate**normal****distribution**, where a univariate**normal****distribution**with zero variance is a point mass on its mean ... In probability theory and statistics, the multivariate**normal****distribution**or multivariate Gaussian**distribution**is a ... the**distribution**reduces to a univariate**normal****distribution**and the Mahalanobis distance reduces to the absolute value of the ...###### Wrapped **normal** **distribution**

... a wrapped

**normal****distribution**is a wrapped probability**distribution**that results from the "wrapping" of the**normal****distribution**... the circular moments of the wrapped**normal****distribution**are the characteristic function of the**normal****distribution**evaluated at ... e iθn drawn from a wrapped**normal****distribution**may be used to estimate certain parameters of the**distribution**. The average of ... which is a useful measure of dispersion for the wrapped**normal****distribution**and its close relative, the von Mises**distribution**...###### Truncated **normal** **distribution**

In probability and statistics, the truncated

**normal****distribution**is the probability**distribution**derived from that of a ... Suppose X ∼ N ( μ , σ 2 ) {\displaystyle X\sim N(\mu ,\sigma ^{2})} has a**normal****distribution**and lies within the interval X ... The truncated**normal****distribution**has wide applications in statistics and econometrics. For example, it is used to model the ...###### Split **normal** **distribution**

The split

**normal****distribution**results from merging two halves of**normal****distributions**. In a general case the 'parent'**normal**... In probability theory and statistics, the split**normal****distribution**also known as the two-piece**normal****distribution**results ... of**normal****distributions**in their common mode. The PDF of the split**normal****distribution**is given by f ( x ; μ , σ 1 , σ 2 ) = A ... the split**normal****distribution**reduces to**normal****distribution**with variance σ ∗ 2 {\displaystyle \sigma _{*}^{2}} . When σ2≠σ1 ...###### Log-**normal** **distribution**

Likewise, if Y has a

**normal****distribution**, then the exponential function of Y, X = exp(Y), has a log-**normal****distribution**. A ... The log-**normal****distribution**also has been associated with other names, such as McAlister, Gibrat and Cobb-Douglas. A log-**normal**... The log-**normal****distribution**is the maximum entropy probability**distribution**for a random variate X for which the mean and ... In fact, there is a whole family of**distributions**with the same moments as the log-**normal****distribution**.[citation needed] The ...###### **Normal**-Wishart **distribution**

The multivariate

**normal****distribution**and Wishart**distribution**are the component**distributions**out of which this**distribution**is ... In probability theory and statistics, the**normal**-Wishart**distribution**(or Gaussian-Wishart**distribution**) is a multivariate four ... is a multivariate**normal****distribution**. The marginal**distribution**over μ {\displaystyle {\boldsymbol {\mu }}} is a multivariate ... The**normal**-inverse Wishart**distribution**is essentially the same**distribution**parameterized by variance rather than precision. ...###### **Normal**-exponential-gamma **distribution**

As for the Laplace

**distribution**, the pdf of the NEG**distribution**can be expressed as a mixture of**normal****distributions**, f ( x ... In probability theory and statistics, the**normal**-exponential-gamma**distribution**(sometimes called the NEG**distribution**) is a ... the**distribution**-names should be interpreted as meaning the density functions of those**distributions**. The**distribution**has ... of the**normal**-exponential-gamma**distribution**is proportional to f ( x ; μ , k , θ ) ∝ exp ( ( x − μ ) 2 4 θ 2 ) D − 2 k − 1 ...###### **Normal**-inverse-gamma **distribution**

See the articles on

**normal**-gamma**distribution**and conjugate prior. See the articles on**normal**-gamma**distribution**and conjugate ... In probability theory and statistics, the**normal**-inverse-gamma**distribution**(or Gaussian-inverse-gamma**distribution**) is a four- ... The**normal**-gamma**distribution**is the same**distribution**parameterized by precision rather than variance A generalization of this ... has an inverse gamma**distribution**. Then ( x , σ 2 ) {\displaystyle (x,\sigma ^{2})} has a**normal**-inverse-gamma**distribution**, ...###### **Normal**-inverse-Wishart **distribution**

The multivariate

**normal****distribution**and inverse Wishart**distribution**are the component**distributions**out of which this ... In probability theory and statistics, the**normal**-inverse-Wishart**distribution**(or Gaussian-inverse-Wishart**distribution**) is a ... The**normal**-Wishart**distribution**is essentially the same**distribution**parameterized by precision rather than variance. If ( μ , ... is a multivariate t-**distribution**. Suppose the sampling density is a multivariate**normal****distribution**y i , μ , Σ ∼ N p ( μ , Σ ...###### **Normal**-inverse Gaussian **distribution**

The

**normal**-inverse Gaussian**distribution**(NIG) is a continuous probability**distribution**that is defined as the**normal**variance- ... The**normal**-inverse Gaussian**distribution**can also be seen as the marginal**distribution**of the**normal**-inverse Gaussian process ... Hyperbolic**Distributions**and**Distributions**on Hyperbolae, Scandinavian Journal of Statistics 1978 O. Barndorff-Nielsen,**Normal**... The class of**normal**-inverse Gaussian**distributions**is closed under convolution in the following sense: if X 1 {\displaystyle X ...###### Statistics education

Binomial

**Distribution**; Poisson**Distributions**; Continuous Probability**Distributions**; The**Normal****Distribution**; Estimation; ... The coverage of "Further Statistics" includes: Continuous Probability**Distributions**; Estimation; Hypothesis Testing; One Sample ... "variability is**normal**" and how "coincidences… are not uncommon because there are so many possibilities." Gal (2002) suggests ... approach of reasoning under the null and the restrictions of**normal**theory, they use comparative box plots and bootstrap to ...###### Normality test

The

**normal****distribution**has the highest entropy of any**distribution**for a given standard deviation. There are a number of ... The empirical**distribution**of the data (the histogram) should be bell-shaped and resemble the**normal****distribution**. This might ... measures how well the data are modeled by a**normal****distribution**. For**normal**data the points plotted in the QQ plot should fall ... of the standardized data against the standard**normal****distribution**. Here the correlation between the sample data and**normal**...###### Lisa Goldberg

"Don't Risk Using

**Normal****Distribution**?". Financial Times. Anderson, Robert M.; Bianchi, Stephen W.; Goldberg, Lisa R. (November- ...###### Student's t-**distribution**

This

**distribution**results from compounding a Gaussian**distribution**(**normal****distribution**) with mean μ {\displaystyle \mu } and ... Chi-squared**distribution**F-**distribution**Gamma**distribution**Folded-t and half-t**distributions**Hotelling's T-squared**distribution**... t-**distribution**arises as the marginal**distribution**of the unknown mean of a**normal****distribution**, when the dependence on an ... a t-**distribution**with infinitely many degrees of freedom is a**normal****distribution**. (See Related**distributions**above). The first ...###### Gaussian function

... s appear as the density function of the

**normal****distribution**, which is a limiting probability**distribution**of ... Also see multivariate**normal****distribution**. A more general formulation of a Gaussian function with a flat-top and Gaussian fall- ...**Normal****distribution**Lorentzian function Radial basis function kernel Using the logarithmic identity log x = − log ( 1 x ... Gaussian functions are widely used in statistics to describe the**normal****distributions**, in signal processing to define Gaussian ...###### Elżbieta Pleszczyńska

In most cases the real

**distribution**is skewed or discrete, which does not prevent people from using**normal****distribution**methods ... in practice multivariate**normal****distribution**is being assumed). Parametric statistical tests are derived from**distribution**... there is no**normal****distribution**in the real world, because every real variable is limited (for example people cannot be -170 cm ... and the**normal****distribution**implies positive probability density for every real number. ...###### Rachev ratio

"Beyond the

**Normal****Distribution**" (PDF). Frankfurter Allgemeine Zeitung. Retrieved 16 March 2006. Cheridito, P.; Kromer, E. (2013 ... Since the performance levels in the Rachev ratio are quantiles of the active return**distribution**, they are relative levels as ... In quantitative finance, non-Gaussian return**distributions**are common. The Rachev ratio, as a risk-adjusted performance ... they adjust according to the**distribution**. For example, if the scale is small, then the two performance levels will be closer ...