Calculate the first and third quartiles for the lognormal distribution

p-valueprobability distributionsquantilestatistics

I intend to calculate the first and third quartiles of a lognormal distribution with mu and sigma (two lognormal parameters) equal to -0.33217492 and 0.6065058. The expected value and the standard deviation gave me 0.8622153003153145 and 0.6191622375133721.

I intend to calculate the first and third quartiles and found this formula:
\begin{equation}
F^{-1}(p)=exp\big(\mu+\sigma\Phi^{-1}(p)\big) \text{ with } 0<p<1
\end{equation}

to calculate the quartiles but I didn't quite understand how to apply it and how to calculate the p-value. How can I find out the first and third quartiles of this distribution?

Best Answer

First quartile is the $25$th quantile, i.e., $p=0.25$, and the third quartile is $p=0.75$, so just plug in your values of $-0.33217492$ and $0.6065058$, for $\mu$ and $\sigma$, respectively, and find the correspoinding quantile of the standard normal distribution, i.e., $Z_p$ (for $p=0.25$ and $0.75$) from the normal distribution table or your preferred software.

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