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### 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. $\; (\mu, \sigma)=(0,1)$
