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

Functional relationships for $T \sim LOGNOR(\mu,\sigma),\;\;T\in[0,\infty)$

$$ \begin{aligned} f(t|\mu,\sigma)&=\frac{1}{\sigma}\phi_{nor}\left(\frac{\log(t)-\mu}{\sigma}\right)\\\\ F(t|\mu,\sigma)&=\Phi_{nor}\left(\frac{\log(t)-\mu}{\sigma}\right)\\\\ h(t|\mu,\sigma)&=\frac{f(t|\mu,\sigma)}{1-F(t|\mu,\sigma)}\\\\ t_{p}&=\exp\left[\mu+\Phi^{-1}{nor}(p)\sigma\right], \;\;\;\;\;\;\;\;\text{where}\;\Phi^{-1}{nor}(p)=z_p\\\\ E[T]&=\exp(\mu+0.5\sigma^2)\\\\ Var[T]&=\exp(2\mu+\sigma^2)(\exp(\sigma^2)-1) \end{aligned} $$

teachingApps documentation built on July 1, 2020, 5:58 p.m.