In Auburngrads/teachingApps: Apps for Teaching Statistics, R Programming, and Shiny App Development

Functional relationships for $Y \sim LEV(\mu,\sigma),\;\;Y\in(-\infty,\infty)$

$$ \begin{aligned} f(t|\mu,\sigma)&=\frac{1}{\sigma}\phi_{lev}\left(\frac{y-\mu}{\sigma}\right)=\frac{1}{\sigma}e^{\left(-\frac{y-\mu}{\sigma}\right)}e^{-e^{\left(-\frac{y-\mu}{\sigma}\right)}}\\\\ F(t|\mu,\sigma)&=\Phi_{lev}\left(\frac{y-\mu}{\sigma}\right)=e^{-e^{\left(-\frac{y-\mu}{\sigma}\right)}}\\\\ h(t|\mu,\sigma)&=\frac{\exp\left(-\frac{y-\mu}{\sigma}\right)}{\sigma \left(\exp\left[\exp\left(-\frac{y-\mu}{\sigma}\right)\right]-1\right)}\\\\ t_{p}&=\exp\left[\mu+\Phi^{-1}_{sev}(p)\sigma\right]\\\\ E[T]&=\mu+\sigma\gamma\\\\ Var[T]&=\sigma^2\pi^2/6 \end{aligned} $$

Auburngrads/teachingApps documentation built on June 17, 2020, 4:57 a.m.