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:<math> \int_{-1}^1 f(x) (1 - x)^\alpha (1 + x)^\beta \,dx </math> :<math> \int_{-1}^1 f(x) (1 - x)^\alpha (1 + x)^\beta \,dx \approx \lambda_1 f(x_1) + \lambda_2 f(x_2) + \ldots + \lambda_n f(x_n ...

...alpha>0</math> [[shape parameter|shape]] ([[real number|real]])<br/><math>\beta>0</math> [[shape parameter|shape]] ([[real number|real]])<br/><math>\sigma> ...\beta\left[\log{\frac{x}{\sigma}}\right]^2} \left(\frac{\alpha}{x}+\frac{2\beta\log{\frac{x}{\sigma}}}{x}\right) </math>| ...

...>\frac{(x-a)^{\alpha-1}(c-x)^{\beta-1}} {\Beta(\alpha,\beta)(c-a)^{\alpha+\beta-1}} </math> <math>\beta = \frac{5c-a-4b} {c-a} = 1 + 4 \frac{c-b}{c-a}</math> ...

...primitive]] which would allow a [[computer program]] to be [[obfuscation (software)|obfuscated]] in a way such that it was impossible to determine anything ab ...{Cite web|date=2014-02-21|title=Cryptographic obfuscation and 'unhackable' software|url=https://blog.cryptographyengineering.com/2014/02/21/cryptographic-obfus ...

{{about|the software|other uses|conquest (disambiguation)}} ...sum_{i\alpha j\beta} \phi_{i\alpha}(\mathbf{r}) K_{i\alpha j\beta} \phi_{j\beta}(\mathbf{r}^\prime)</math>, ...

multiply the weights of all experts who predicted wrongly by <math>\beta</math> ...generalizing to multiplying the weights of the incorrect experts by <math>\beta < 1</math> instead of strictly <math>\frac{1}{2}</math> allows us to trade ...

{{Infobox software \text{width multiplier: } w &= \beta^{\phi} \\ ...

p(V) = - \beta \left(\frac{V}{V_0}\right)^n \ln\left(\frac{V}{V_0}\right) E(V) = \frac{\beta V_0}{n+1} \left(\frac{V}{V_0}\right)^{n+1} \left[\ln\left(\frac{V}{V_0}\rig ...

..._{n,\beta}} \prod_{1 \leq k < j \leq n} |e^{i \theta_k} - e^{i \theta_j}|^\beta~</math> : <math> Z_{n,\beta} = (2\pi)^n \frac{\Gamma(\beta n/2 + 1)}{\left(\Gamma(\beta/2 + 1)\right)^n}~,</math> ...

...derset {\alpha \ne 0,\beta,LAT(\alpha,\beta) \ne 0} {\min} (W(\alpha) + W(\beta))</math>.<ref>{{cite web |last1=SAGE |title=S-Boxes and Their Algebraic Rep ...Liu | first2=Siang Meng | last2 = Sim | date = 25 July 2016 | title = Fast Software Encryption: 23rd International Conference, FSE 2016, Bochum, Germany, March ...

...2n \pi/\beta</math> for [[Boson|bosonic]] ones and <math display="inline">\beta=1/ T</math> is the inverse temperature. This relation is an example of [[Kr ...mega_n) = \int_{-\infty}^{\infty} \frac{d\omega}{2\pi} A(\omega) \frac{1}{\beta}\sum_{\omega_n} \frac{e^{-i\omega_n \tau} }{i\omega_n - \omega}</math> ...

The size of the [[Workspace#Technology and software|workspace]] of a [[robot]] is, in general, proportional to the mass of the {{NumBlk|:|<math>\beta=\frac{W}{m}</math>|{{EquationRef|1}}}} ...

...ype I error]] level (<math>\alpha</math>), [[statistical power]] (<math>1-\beta</math>), and sample sizes (<math>n_1</math> and <math>n_2</math>). It is co ...rtions, incorporating critical values for <math>\alpha</math> and <math>1-\beta</math>, and the standard errors of the proportions:<ref>COOLSerdash (https: ...

...he gamma distribution with parameters <math>\alpha = d/p</math> and <math>\beta = 1</math>. The quantile function is then given by inverting <math>F</math> ...the quantile function for a gamma distribution with <math>\alpha = d/p,\, \beta = 1</math>. ...

{{Infobox software ...ath>. This can also be expressed as <math>y_n \sim \text{normal}(\alpha + \beta X_n, \sigma)</math>. The latter form can be written in Stan as the followin ...

| entropy =<math>1+\frac{1}{\alpha}-\log\frac{\alpha}{\beta}</math> .../pdf/ebookdistributions.pdf A Compendium of Distributions]'' [ebook]. Vose Software, Ghent, Belgium. Available at www.vosesoftware.com.</ref> ...

:<math>\|\beta\|_1 = \textstyle \sum_{j=1}^p |\beta_j|.</math> ...vercome these limitations, the elastic net adds a quadratic part (<math>\|\beta\|^2</math>) to the penalty, which when used alone is [[ridge regression]] ( ...

...ty} I(\boldsymbol x + \beta \cdot \boldsymbol \alpha)\varphi (\beta ) \, d\beta ...ty function of a [[Normal_distribution|Gaussian distribution]] (and <math>\beta</math>&nbsp; is a real number). In practice the roots of a nonlinear functi ...

...\ldots,\, n</math>. That is, <math>\boldsymbol{y} = \mathbf{X}\boldsymbol{\beta}+\boldsymbol{\varepsilon}</math>, where, <math>\mathbf{X}</math> is the <ma ...s equal to the number of parameters <math>(p)</math> in <math>\boldsymbol{\beta}</math> (including the intercept).<br>'''Proof:''' <math> \sum_{i=1}^n h_{i ...

== Software libraries == ...Operating System and the Free Software Movement | url=https://www.gnu.org/software/gsl/doc/html/randist.html | access-date=2022-08-18}}</ref> ...