Two-sample sequential test of normal distributions when one of the sample sizes is fixed

Assessing when a sample is mostly normal

The use of trimming procedures constitutes a natural approach to robustifying statistical methods. This is the case of goodness-of-fit tests based on a distance, which can be modified by choosing trimmed versions of the distributions minimizing that distance. In this paper we consider the L2-Wasserstein distance and introduce the trimming methodology for assessing when a data sample can be cons...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

The Two Sample T-test with One Variance Unknown

We consider the situation in two sample testing when one variance is assumed to be known while the other variance is considered unknown. This situation arises, for example, when one is interested in comparing a standard treatment with a new treatment. Although this situation occurs relatively infrequently, our example discusses the important tool of moment matching and makes the classic two sam...

One-Sample Hypothesis Test Examples

Sample Sizes to Compare Two Poisson Rates

In this note, procedures for determining the sample sizes needed to compare the rates of two Poisson populations to achieve a pre-specifi ed power at a given ratio of the rates are proposed. The fi rst method relies on a conditional uniformly most powerful test (CUMPT) which leads to sample sizes that will guarantee the desired power, but at the cost of using more units than necessary. The seco...