Skip to content
Merged
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
6 changes: 3 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/beta/mgf/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,14 +28,14 @@ limitations under the License.

The [moment-generating function][mgf] for a [beta][beta-distribution] random variable is

<!-- <equation class="equation" label="eq:beta_beta_mgf" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r} \right) \frac{t^k}{k!}" alt="Moment-generating function (MGF) for a beta distribution."> -->
<!-- <equation class="equation" label="eq:beta_mgf" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r} \right) \frac{t^k}{k!}" alt="Moment-generating function (MGF) for a beta distribution."> -->

```math
M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r} \right) \frac{t^k}{k!}
```

<!-- <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r} \right) \frac{t^k}{k!}" data-equation="eq:beta_beta_mgf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/beta/mgf/docs/img/equation_beta_beta_mgf.svg" alt="Moment-generating function (MGF) for a beta distribution.">
<!-- <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r} \right) \frac{t^k}{k!}" data-equation="eq:beta_mgf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/beta/mgf/docs/img/equation_beta_mgf.svg" alt="Moment-generating function (MGF) for a beta distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [probability density function][pdf] (PDF) for a [Cauchy][cauchy-distribution] random variable is

<!-- <equation class="equation" label="eq:cauchy_cauchy_pdf" align="center" raw="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" alt="Probability density function (PDF) for a Cauchy distribution."> -->
<!-- <equation class="equation" label="eq:cauchy_pdf" align="center" raw="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" alt="Probability density function (PDF) for a Cauchy distribution."> -->

```math
f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!
```

<!-- <div class="equation" align="center" data-raw-text="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" data-equation="eq:cauchy_cauchy_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cauchy/logpdf/docs/img/equation_cauchy_cauchy_pdf.svg" alt="Probability density function (PDF) for a Cauchy distribution.">
<!-- <div class="equation" align="center" data-raw-text="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" data-equation="eq:cauchy_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cauchy/logpdf/docs/img/equation_cauchy_pdf.svg" alt="Probability density function (PDF) for a Cauchy distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [probability density function][pdf] (PDF) for a [Cauchy][cauchy-distribution] random variable is

<!-- <equation class="equation" label="eq:cauchy_cauchy_pdf" align="center" raw="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" alt="Probability density function (PDF) for a Cauchy distribution."> -->
<!-- <equation class="equation" label="eq:cauchy_pdf" align="center" raw="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" alt="Probability density function (PDF) for a Cauchy distribution."> -->

```math
f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!
```

<!-- <div class="equation" align="center" data-raw-text="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" data-equation="eq:cauchy_cauchy_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cauchy/pdf/docs/img/equation_cauchy_cauchy_pdf.svg" alt="Probability density function (PDF) for a Cauchy distribution.">
<!-- <div class="equation" align="center" data-raw-text="f(x;\gamma,x_0)=\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!" data-equation="eq:cauchy_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cauchy/pdf/docs/img/equation_cauchy_pdf.svg" alt="Probability density function (PDF) for a Cauchy distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [quantile function][quantile-function] for a [Cauchy][cauchy-distribution] random variable is

<!-- <equation class="equation" label="eq:cauchy_cauchy_quantile_function" align="center" raw="Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right]" alt="Quantile function for a Cauchy distribution."> -->
<!-- <equation class="equation" label="eq:cauchy_quantile_function" align="center" raw="Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right]" alt="Quantile function for a Cauchy distribution."> -->

```math
Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right]
```

<!-- <div class="equation" align="center" data-raw-text="Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right]" data-equation="eq:cauchy_cauchy_quantile_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/docs/img/equation_cauchy_cauchy_quantile_function.svg" alt="Quantile function for a Cauchy distribution.">
<!-- <div class="equation" align="center" data-raw-text="Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right]" data-equation="eq:cauchy_quantile_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/docs/img/equation_cauchy_quantile_function.svg" alt="Quantile function for a Cauchy distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [quantile function][quantile-function] for a [chi][chi-distribution] random variable is

<!-- <equation class="equation" label="eq:chi_chi_quantile_function" align="center" raw="Q(p; k) = 2 \cdot P^{-1}( p, k/2 )" alt="Quantile function for a chi distribution."> -->
<!-- <equation class="equation" label="eq:chi_quantile_function" align="center" raw="Q(p; k) = 2 \cdot P^{-1}( p, k/2 )" alt="Quantile function for a chi distribution."> -->

```math
Q(p; k) = 2 \cdot P^{-1}( p, k/2 )
```

<!-- <div class="equation" align="center" data-raw-text="Q(p; k) = 2 \cdot P^{-1}( p, k/2 )" data-equation="eq:chi_chi_quantile_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chi/quantile/docs/img/equation_chi_chi_quantile_function.svg" alt="Quantile function for a chi distribution.">
<!-- <div class="equation" align="center" data-raw-text="Q(p; k) = 2 \cdot P^{-1}( p, k/2 )" data-equation="eq:chi_quantile_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chi/quantile/docs/img/equation_chi_quantile_function.svg" alt="Quantile function for a chi distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [probability density function][pdf] (PDF) for a [normal][normal-distribution] random variable is

<!-- <equation class="equation" label="eq:normal_normal_pdf" align="center" raw="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" alt="Probability density function (PDF) for a normal distribution."> -->
<!-- <equation class="equation" label="eq:normal_pdf" align="center" raw="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" alt="Probability density function (PDF) for a normal distribution."> -->

```math
f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}
```

<!-- <div class="equation" align="center" data-raw-text="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" data-equation="eq:normal_normal_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/normal/logpdf/docs/img/equation_normal_normal_pdf.svg" alt="Probability density function (PDF) for a normal distribution.">
<!-- <div class="equation" align="center" data-raw-text="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" data-equation="eq:normal_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/normal/logpdf/docs/img/equation_normal_pdf.svg" alt="Probability density function (PDF) for a normal distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [probability density function][pdf] (PDF) for a [normal][normal-distribution] random variable is

<!-- <equation class="equation" label="eq:normal_normal_pdf" align="center" raw="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" alt="Probability density function (PDF) for a normal distribution."> -->
<!-- <equation class="equation" label="eq:normal_pdf" align="center" raw="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" alt="Probability density function (PDF) for a normal distribution."> -->

```math
f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}
```

<!-- <div class="equation" align="center" data-raw-text="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" data-equation="eq:normal_normal_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/normal/pdf/docs/img/equation_normal_normal_pdf.svg" alt="Probability density function (PDF) for a normal distribution.">
<!-- <div class="equation" align="center" data-raw-text="f(x;\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}" data-equation="eq:normal_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/normal/pdf/docs/img/equation_normal_pdf.svg" alt="Probability density function (PDF) for a normal distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [probability density function][pdf] (PDF) for a [Weibull][weibull-distribution] random variable is

<!-- <equation class="equation" label="eq:weibull_weibull_pdf" align="center" raw="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}" alt="Probability density function (PDF) for a Weibull distribution."> -->
<!-- <equation class="equation" label="eq:weibull_pdf" align="center" raw="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}" alt="Probability density function (PDF) for a Weibull distribution."> -->

```math
f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} &amp; x \geq 0 \\ 0 &amp; x &lt; 0\end{cases}" data-equation="eq:weibull_weibull_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/logpdf/docs/img/equation_weibull_weibull_pdf.svg" alt="Probability density function (PDF) for a Weibull distribution.">
<!-- <div class="equation" align="center" data-raw-text="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} &amp; x \geq 0 \\ 0 &amp; x &lt; 0\end{cases}" data-equation="eq:weibull_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/logpdf/docs/img/equation_weibull_pdf.svg" alt="Probability density function (PDF) for a Weibull distribution.">
<br>
</div> -->

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -26,14 +26,14 @@ limitations under the License.

The [probability density function][pdf] (PDF) for a [Weibull][weibull-distribution] random variable is

<!-- <equation class="equation" label="eq:weibull_weibull_pdf" align="center" raw="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}" alt="Probability density function (PDF) for a Weibull distribution."> -->
<!-- <equation class="equation" label="eq:weibull_pdf" align="center" raw="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}" alt="Probability density function (PDF) for a Weibull distribution."> -->

```math
f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} &amp; x \geq 0 \\ 0 &amp; x &lt; 0\end{cases}" data-equation="eq:weibull_weibull_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/pdf/docs/img/equation_weibull_weibull_pdf.svg" alt="Probability density function (PDF) for a Weibull distribution.">
<!-- <div class="equation" align="center" data-raw-text="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} &amp; x \geq 0 \\ 0 &amp; x &lt; 0\end{cases}" data-equation="eq:weibull_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/pdf/docs/img/equation_weibull_pdf.svg" alt="Probability density function (PDF) for a Weibull distribution.">
<br>
</div> -->

Expand Down