Statistic Maximum Likelihood Bayesian Expectation Values Symbol Value Symbol Value Limit $n\to \infty$ location m $\stackrel{^}{m}$ $\overline{Y}$ $\overline{m}={〈m〉|}_{\left(2\right)}^{\left(n\right)}$ $\overline{Y}$ scale s $\stackrel{^}{s}$ $S\equiv \sqrt{\overline{{Y}^{2}}-{\overline{Y}}^{2}}$ $\overline{s}={〈s〉|}_{\left(2\right)}^{\left(n\right)}$ ${\left(\frac{n}{2}\right)}^{\frac{1}{2}}\frac{\Gamma \left(\left(n-1\right)/2\right)}{\Gamma \left(n/2\right)}S$ S $\mathrm{var}\left(m\right)$ ${\stackrel{^}{\sigma }}_{m}^{2}$ ${S}^{2}/n$ $\Delta {m}^{2}={〈{\left(m-\overline{m}\right)}^{2}〉|}_{\left(2\right)}^{\left(n\right)}$ $\frac{{S}^{2}}{n-2}$ ${S}^{2}/n$ $\mathrm{var}\left(s\right)$ ${\stackrel{^}{\sigma }}_{s}^{2}$ ${S}^{2}/2n$ $\Delta {s}^{2}={〈{\left(s-\overline{s}\right)}^{2}〉|}_{\left(2\right)}^{\left(n\right)}$ $\left[\frac{n}{n-2}-\frac{n\Gamma {\left(\left(n-1\right)/2\right)}^{2}}{2\Gamma {\left(n/2\right)}^{2}}\right]{S}^{2}$ ${S}^{2}/2n$ Sample Statistics: $\overline{Y}=\frac{1}{n}\sum _{k=1}^{n}\mathrm{ln}\left({z}_{k}\right)$ $\overline{{Y}^{2}}=\frac{1}{n}\sum _{k=1}^{n}\mathrm{ln}{\left({z}_{k}\right)}^{2}$