This applet computes probabilities and percentiles for log-normal random variables:
$$X \sim LogN(\mu, \sigma)$$
Directions
- Enter $\mu$ and $\sigma$.
- To compute a left-tail probability, select $P(X \lt x)$ from the drop-down box,
enter a numeric $x$ value in the blue
box and press "Tab" or "Enter" on your keyboard. The probability $P(X \lt x)$ will appear in the
pink box.
Select $P(X \gt x)$ from the drop-down box for a right-tail probability.
- To determine a percentile, enter the percentile (e.g. use 0.8 for the 80th percentile) in the
pink
box, select $P(X \lt x)$ from the drop-down box, and press "Tab" or "Enter" on your keyboard.
The percentile $x$ will appear in the blue box.
On the graph, the $x$ value appears in
blue
while the probability is shaded in
pink.
Details
- Probability density function
$$f(x)=\frac{1}{x\sqrt{2\pi \sigma^2}} e^{-\frac{1}{2\sigma^2}(\ln(x)-\mu)^2}$$
where $x > 0$, $-\infty < \mu < \infty$, and $\sigma > 0$
- $E(X)=e^{\mu+\sigma^2/2}$
- $Var(X)=(e^{\sigma^2}-1)e^{2\mu+\sigma^2}$
- $SD(X)=\sqrt{(e^{\sigma^2}-1)e^{2\mu+\sigma^2}}$