diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/entropy/README.md b/lib/node_modules/@stdlib/stats/base/dists/f/entropy/README.md index 58cc34117a0e..04688b164001 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/f/entropy/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/f/entropy/README.md @@ -28,13 +28,13 @@ limitations under the License. The [differential entropy][entropy] (in [nats][nats]) for a [F][f-distribution] random variable is - + ```math -h\left( X \right) = \ln\left( \tfrac{d_2}{d_1} \Gamma\left( \tfrac{d_1}{2} \right) \Gamma\left( \tfrac{d_2}{2} \right) \Gamma\left( \tfrac{d_1+d_2}{2} \right) \right) \\ + \left( 1-\tfrac{d_1}{2} \right) \Psi\left( \tfrac{d_1}{2} \right) + \left( 1-\tfrac{d_2}{2} \right) \Psi\left( \tfrac{d_2}{2} \right) + \tfrac{d_1+d_2}{2} \Psi\left( \tfrac{d_1+d_2}{2} \right) +h\left( X \right) = \ln\left( \tfrac{d_2}{d_1} \frac{\Gamma\left( \tfrac{d_1}{2} \right) \Gamma\left( \tfrac{d_2}{2} \right)}{\Gamma\left( \tfrac{d_1+d_2}{2} \right)} \right) \\ + \left( 1-\tfrac{d_1}{2} \right) \Psi\left( \tfrac{d_1}{2} \right) - \left( 1+\tfrac{d_2}{2} \right) \Psi\left( \tfrac{d_2}{2} \right) + \tfrac{d_1+d_2}{2} \Psi\left( \tfrac{d_1+d_2}{2} \right) ``` - diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/stdev/README.md b/lib/node_modules/@stdlib/stats/base/dists/f/stdev/README.md index b65256fc3fd0..7171245959c2 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/f/stdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/f/stdev/README.md @@ -28,13 +28,13 @@ limitations under the License. The [standard deviation][standard-deviation] for a [F][f-distribution] random variable is - + ```math -\sigma = \sqrt{2} \tfrac{d_1}{d_2-2} \sqrt{\tfrac{d_1+d_2-2}{d_1 \cdot (d_2-4)}} +\sigma = \sqrt{2} \tfrac{d_2}{d_2-2} \sqrt{\tfrac{d_1+d_2-2}{d_1 \cdot (d_2-4)}} ``` -