diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/skewness/README.md b/lib/node_modules/@stdlib/stats/base/dists/anglit/skewness/README.md index ec5280e1efce..b42c67345056 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/anglit/skewness/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/skewness/README.md @@ -34,6 +34,11 @@ The [skewness][skewness] for an [anglit][anglit-distribution] random variable wi \mathop{\mathrm{skew}}\left( X \right) = 0 ``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/skewness/docs/img/equation_anglit_skewness.svg b/lib/node_modules/@stdlib/stats/base/dists/anglit/skewness/docs/img/equation_anglit_skewness.svg new file mode 100644 index 000000000000..5b4c9de86bf9 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/skewness/docs/img/equation_anglit_skewness.svg @@ -0,0 +1,27 @@ + +s k e w left-parenthesis upper X right-parenthesis equals 0 + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/README.md b/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/README.md index b86652d9bf39..d7f2acd9a677 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/README.md @@ -32,6 +32,11 @@ The [cumulative distribution function][cdf] for a [Burr (type III)][burr-distrib F(x; c, d) = (1 + x^{-c})^{-d} ``` + + where `c > 0` is the first shape parameter and `d > 0` is the second shape parameter. diff --git a/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/docs/img/equation_burr_type3_cdf.svg b/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/docs/img/equation_burr_type3_cdf.svg new file mode 100644 index 000000000000..d08b56cf49c4 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/docs/img/equation_burr_type3_cdf.svg @@ -0,0 +1,45 @@ + +upper F left-parenthesis x semicolon c comma d right-parenthesis equals left-parenthesis 1 plus x Superscript negative c Baseline right-parenthesis Superscript negative d + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/README.md index f5bbc02c1ed7..c188c8177587 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/README.md @@ -29,9 +29,14 @@ The [variance][variance] for a [log-logistic][log-logistic-distribution] random ```math -\operatorname{Var}\left[ X \right] = \alpha^2 \left( \frac{2b}{\sin 2b} - \frac{b^2}{\sin^2 b} \right), \quad b = \frac{\pi}{\beta} +\mathop{\mathrm{Var}}\left[ X \right] = \alpha^2 \left( \frac{2b}{\sin 2b} - \frac{b^2}{\sin^2 b} \right), \quad b = \frac{\pi}{\beta} ``` + + where `b = π/β`. diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/img/equation_log_logistic_variance.svg b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/img/equation_log_logistic_variance.svg new file mode 100644 index 000000000000..3109cbcb2133 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/img/equation_log_logistic_variance.svg @@ -0,0 +1,88 @@ + +upper V a r left-bracket upper X right-bracket equals alpha squared left-parenthesis StartFraction 2 b Over sine 2 b EndFraction minus StartFraction b squared Over sine squared b EndFraction right-parenthesis comma b equals StartFraction pi Over beta EndFraction + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/base/dists/wald/cdf/README.md b/lib/node_modules/@stdlib/stats/base/dists/wald/cdf/README.md index acda82d27642..6871101902dd 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/wald/cdf/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/wald/cdf/README.md @@ -29,9 +29,14 @@ The [cumulative distribution function][cdf] for a [Wald][wald-distribution] rand ```math -F(x;\mu,\lambda) = \Phi\!\left(\sqrt{\frac{\lambda}{x}}\left(\frac{x}{\mu}-1\right)\right) + \exp\!\left(\frac{2\lambda}{\mu}\right)\,\Phi\!\left(-\sqrt{\frac{\lambda}{x}}\left(\frac{x}{\mu}+1\right)\right) +F(x;\mu,\lambda)=\Phi(\sqrt{\lambda/x}((x/\mu)-1))+\exp(2\lambda/\mu)\Phi(-\sqrt{\lambda/x}((x/\mu)+1)) ``` + + where `μ > 0` is the mean and `λ > 0` is the shape parameter. diff --git a/lib/node_modules/@stdlib/stats/base/dists/wald/cdf/docs/img/equation_wald_cdf.svg b/lib/node_modules/@stdlib/stats/base/dists/wald/cdf/docs/img/equation_wald_cdf.svg new file mode 100644 index 000000000000..7dcf12855411 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/wald/cdf/docs/img/equation_wald_cdf.svg @@ -0,0 +1,90 @@ + +upper F left-parenthesis x semicolon mu comma lamda right-parenthesis equals normal upper Phi left-parenthesis StartRoot lamda slash x EndRoot left-parenthesis left-parenthesis x slash mu right-parenthesis minus 1 right-parenthesis right-parenthesis plus exp left-parenthesis 2 lamda slash mu right-parenthesis normal upper Phi left-parenthesis minus StartRoot lamda slash x EndRoot left-parenthesis left-parenthesis x slash mu right-parenthesis plus 1 right-parenthesis right-parenthesis + + + \ No newline at end of file