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

The Log-Location-Scale Family of Distributions

• A random variable $T$ belongs to the log-location scale family if $Y= \log(T)$ is a member of the location scale family $$P(T\le t)=F(t|\mu, \sigma)=\Phi\left(\frac{\log(y)-\mu}{\sigma}\right)$$

• where

  • $\mu$ represents the location parameter, $\; \mu \in (-\infty,\infty)$

  • $\sigma$ represents the scale parameter, $\; \sigma \in [0,\infty)$

  • $\Phi$ represents the "standard" form of the cdf i.e. $\; (\mu, \sigma)=(0,1)$

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