Parameter estimation

• What Is the Fisher Information of a Normal Distribution?
  For n independent normal observations, the Fisher information is diagonal: n/σ² for the mean and n/(2σ⁴) for the variance.
• How to Estimate Uniform Distribution Parameters by Moments
  For a uniform model, match sample moments to population moments; see formulas for U(0, θ) and U(a, b), with a worked example.
• How to Use the Method of Moments for a Gamma Distribution
  Estimate a gamma distribution’s shape and scale by matching sample moments, with formulas, a worked example, and the rate-parameter alternative.
• How to Find the MLEs of a Negative Binomial Distribution
  For negative-binomial data, the MLE of p has a closed form when the size is fixed; estimate unknown size by solving a digamma score equation numerically.
• How to Find the MLE of a Uniform Distribution
  For an i.i.d. sample from Uniform(0, θ), the maximum-likelihood estimate is the sample maximum; endpoint estimates differ when both bounds are unknown.