High-Accuracy Confidence Regions for Distribution Parameters

With the help of today’s computers, it is always relatively easy to find maximum-likelihood estimators one or more parameters any specific statistical distribution, and use these construct corresponding approximate confidence interval/region, facilitated by well-known asymptotic properties likelihood function. The purpose this article make approximation substantially accurate extending Taylor expansion probability density function include quadratic cubic terms in several centralized sample means, thus finding -proportional correction original algorithm. We then demonstrate new procedure’s usage, both for constructing regions testing hypotheses, emphasizing that incorporating carries minimal computational programming cost. In our final chapter, we present two examples indicate how significantly improves accuracy.