Tag Archives: maximum likelihood

Maximum likelihood, moments, and the mean of a Poisson

If we observe data coming from a distribution with known form but unknown parameters, estimating those parameters is our primary aim. If the distribution is uniform on $[0,\theta]$ with $\theta$ unknown, we already looked at two methods to estimate $\theta$ given $n$ i.i.d. observations $x_1,\dots,x_n$: Maximum likelihood, which maximizes the likelihood function and gives $\max\{ […]

Maximum likelihood, moments, and the uniform distribution

Suppose we have observations from a known probability distribution whose parameters are unknown. How should we estimate the parameters from our observations? Throughout we'll focus on a concrete example. Suppose we observe a random variable drawn from the uniform distribution on $[0,\theta]$, but we don't know what $\theta$ is. Our one observation is the number […]