Poisson Distribution MLE Applet
$X \sim Pois(\lambda)$


This applet computes probabilities for the Poisson distribution: $$X \sim Pois(\lambda)$$ It also can plot the likelihood, log-likelihood, asymptotic CI for $\lambda$, and determine the MLE and observed Fisher information.

Probability Mass Function (PMF) mode


To compute a probability, select $P(X = x)$ from the drop-down box, enter a numeric $x$ value, and press "Tab" or "Enter" on your keyboard. The probability $P(X = x)$ will appear in the pink box. Select $P(X \le x)$ from the drop-down box for a left-tail probability (i.e. the cdf).

Maximum Likelihood (MLE) mode


Note that the green line is drawn at $$max(log(likelihood))-\frac{3.84}{2}$$ The resulting asymptotic 95% CI is shown in green on the horizontal axis. The asymptotic CI is based on large sample theory; it is shown in this applet for all sample sizes, however.