The method of moments can be generalised to estimate two parameters by setting the distribution's mean and variance equal to those of a random sample.
Maximum likelihood can be used to estimate any number of unknown parameters. The estimates are usually where the partial derivatives of the log-likelihood are zero.
Maximum likelihood estimates of the normal distribution's two parameters are derived.
When the maximum likelihood estimators cannot be found algebraically, a grid search can be used to maximise the log-likelihood.
If an estimator's distribution is approximately normal, a confidence interval can be found as the estimate ± a multiple of its standard error.
A pivot for a parameter is a function of the data and parameter whose distribution is fully known. A confidence interval can be based on quantiles of this distribution.
A pivot is defined from the sum of values in an exponential random sample. The pivot has a gamma distribution so a confidence interval for the rate parameter, λ, can be based on quantiles of this distribution.
An approximate pivot is found for a binomial probability. A confidence interval from it has better properties than the conventional Wald-type confidence interval.