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docs: fix README equations in stats/base/dists/negative-binomial #16226

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6 changes: 3 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/negative-binomial/kurtosis/README.md
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The [excess kurtosis][kurtosis] for a [negative binomial][negative-binomial-distribution] random variable is

<!-- <equation class="equation" label="eq:negative_binomial_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \frac{6}{r} + \frac{(1-p)^{2}}{pr}" alt="Excess kurtosis for a negative binomial distribution."> -->
<!-- <equation class="equation" label="eq:negative_binomial_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \frac{6}{r} + \frac{p^{2}}{r(1-p)}" alt="Excess kurtosis for a negative binomial distribution."> -->

```math
\mathop{\mathrm{Kurt}}\left( X \right) = \frac{6}{r} + \frac{(1-p)^{2}}{pr}
\mathop{\mathrm{Kurt}}\left( X \right) = \frac{6}{r} + \frac{p^{2}}{r(1-p)}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \frac{6}{r} + \frac{(1-p)^{2}}{pr}" data-equation="eq:negative_binomial_kurtosis">
<!-- <div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \frac{6}{r} + \frac{p^{2}}{r(1-p)}" data-equation="eq:negative_binomial_kurtosis">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/kurtosis/docs/img/equation_negative_binomial_kurtosis.svg" alt="Excess kurtosis for a negative binomial distribution.">
<br>
</div> -->
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6 changes: 3 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/negative-binomial/mean/README.md
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The [mean][expected-value] for a [negative binomial][negative-binomial-distribution] random variable is

<!-- <equation class="equation" label="eq:negative_binomial_mean" align="center" raw="\mathbb{E} \left[ X \right] = \frac{pr}{1-p}" alt="Mean for a negative binomial distribution."> -->
<!-- <equation class="equation" label="eq:negative_binomial_mean" align="center" raw="\mathbb{E} \left[ X \right] = \frac{r(1-p)}{p}" alt="Mean for a negative binomial distribution."> -->

```math
\mathbb{E} \left[ X \right] = \frac{pr}{1-p}
\mathbb{E} \left[ X \right] = \frac{r(1-p)}{p}
```

<!-- <div class="equation" align="center" data-raw-text="\mathbb{E} \left[ X \right] = \frac{pr}{1-p}" data-equation="eq:negative_binomial_mean">
<!-- <div class="equation" align="center" data-raw-text="\mathbb{E} \left[ X \right] = \frac{r(1-p)}{p}" data-equation="eq:negative_binomial_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/mean/docs/img/equation_negative_binomial_mean.svg" alt="Mean for a negative binomial distribution.">
<br>
</div> -->
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6 changes: 3 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/negative-binomial/mode/README.md
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Expand Up @@ -28,13 +28,13 @@ limitations under the License.

The [mode][mode] for a [negative-binomial][negative-binomial-distribution] random variable is

<!-- <equation class="equation" label="eq:negative_binomial_mode" align="center" raw="\operatorname{mode}\left( X \right) = \begin{cases}{\big \lfloor }{\frac{p(r-1)}{1-p}}{\big \rfloor } & \text{ if }\ r>1\\ 0 & \text{ if } \ r\leq 1\end{cases}" alt="Mode for a negative-binomial distribution."> -->
<!-- <equation class="equation" label="eq:negative_binomial_mode" align="center" raw="\operatorname{mode}\left( X \right) = \begin{cases}{\big \lfloor }{\frac{(1-p)(r-1)}{p}}{\big \rfloor } & \text{ if }\ r>1\\ 0 & \text{ if } \ r\leq 1\end{cases}" alt="Mode for a negative-binomial distribution."> -->

```math
\mathop{\mathrm{mode}}\left( X \right) = \begin{cases}{\big \lfloor }{\frac{p(r-1)}{1-p}}{\big \rfloor } & \text{ if }\ r>1\\ 0 & \text{ if } \ r\leq 1\end{cases}
\mathop{\mathrm{mode}}\left( X \right) = \begin{cases}{\big \lfloor }{\frac{(1-p)(r-1)}{p}}{\big \rfloor } & \text{ if }\ r>1\\ 0 & \text{ if } \ r\leq 1\end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{mode}\left( X \right) = \begin{cases}{\big \lfloor }{\frac{p(r-1)}{1-p}}{\big \rfloor } &amp; \text{ if }\ r&gt;1\\ 0 &amp; \text{ if } \ r\leq 1\end{cases}" data-equation="eq:negative_binomial_mode">
<!-- <div class="equation" align="center" data-raw-text="\operatorname{mode}\left( X \right) = \begin{cases}{\big \lfloor }{\frac{(1-p)(r-1)}{p}}{\big \rfloor } &amp; \text{ if }\ r&gt;1\\ 0 &amp; \text{ if } \ r\leq 1\end{cases}" data-equation="eq:negative_binomial_mode">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/mode/docs/img/equation_negative_binomial_mode.svg" alt="Mode for a negative-binomial distribution.">
<br>
</div> -->
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6 changes: 3 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/negative-binomial/skewness/README.md
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The [skewness][skewness] for a [negative binomial][negative-binomial-distribution] random variable is

<!-- <equation class="equation" label="eq:negative_binomial_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{1+p}{\sqrt{pr}}" alt="Skewness for a negative binomial distribution."> -->
<!-- <equation class="equation" label="eq:negative_binomial_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{2-p}{\sqrt{r(1-p)}}" alt="Skewness for a negative binomial distribution."> -->

```math
\mathop{\mathrm{skew}}\left( X \right) = \frac{1+p}{\sqrt{pr}}
\mathop{\mathrm{skew}}\left( X \right) = \frac{2-p}{\sqrt{r(1-p)}}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{1+p}{\sqrt{pr}}" data-equation="eq:negative_binomial_skewness">
<!-- <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{2-p}{\sqrt{r(1-p)}}" data-equation="eq:negative_binomial_skewness">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/skewness/docs/img/equation_negative_binomial_skewness.svg" alt="Skewness for a negative binomial distribution.">
<br>
</div> -->
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6 changes: 3 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/negative-binomial/variance/README.md
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The [variance][variance] for a [negative binomial][negative-binomial-distribution] random variable is

<!-- <equation class="equation" label="eq:negative_binomial_variance" align="center" raw="\operatorname{Var}\left( X \right) = \frac{pr}{(1-p)^{2}}" alt="Variance for a negative binomial distribution."> -->
<!-- <equation class="equation" label="eq:negative_binomial_variance" align="center" raw="\operatorname{Var}\left( X \right) = \frac{r(1-p)}{p^{2}}" alt="Variance for a negative binomial distribution."> -->

```math
\mathop{\mathrm{Var}}\left( X \right) = \frac{pr}{(1-p)^{2}}
\mathop{\mathrm{Var}}\left( X \right) = \frac{r(1-p)}{p^{2}}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Var}\left( X \right) = \frac{pr}{(1-p)^{2}}" data-equation="eq:negative_binomial_variance">
<!-- <div class="equation" align="center" data-raw-text="\operatorname{Var}\left( X \right) = \frac{r(1-p)}{p^{2}}" data-equation="eq:negative_binomial_variance">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/variance/docs/img/equation_negative_binomial_variance.svg" alt="Variance for a negative binomial distribution.">
<br>
</div> -->
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