The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) one-tailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at small and moderate sample sizes. We introduce a new confidence interval notion, called fuzzy conf...

Ranked Set Sampling (RSS) is a statistical method for data collection that leads to more efficient estimators than competitors based on Simple Random Sampling (SRS). We consider testing the correlation coefficient of bivariate normal distribution based on Bivariate RSS (BVRSS). Under one-sided and two-sided alternatives, we show that the new tests based on BVRSS are more powerful than the usua...

The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) one-tailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at small and moderate sample sizes. We introduce a new confidence interval notion, called fuzzy conf...

The problem of hypothesis testing of the location parameter of the two-parameter exponential distribution and scale parameter of the pareto and uniform distribution are considered. We construct the test statistics based on Ranked Set Sampling (RSS) and Extreme RSS (ERSS) and compared their powers to the power of Uniformly Most Powerful (UMP) test by numerical computation. The results show that ...

Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null among all corresponding data-based of given size. When underlying data distributions known, likelihood ratio principle can be applied to conduct tests. Reversing this notion, we consider following questions. (a) Assuming test statistic, say T, is given, how trans...