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The Shapiro–Wilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population. The test statistic is. where. with parentheses enclosing the subscript index i is the i th order statistic, i.e., the i th-smallest number in the sample (not to be confused with ). is the sample mean.
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Statement of the inequality. Suppose is a natural number and are positive numbers and: Then the Shapiro inequality states that. where and . For greater values of the inequality does not hold, and the strict lower bound is with . The initial proofs of the inequality in the pivotal cases [2] and [3] rely on numerical computations.
Irwin Ira Shapiro is an American astrophysicist and Timken University Professor at Harvard University. He has been a professor at Harvard since 1982. [2] He was the director of the Center for Astrophysics | Harvard & Smithsonian from 1982 to 2004.
According to Shapiro, there’s a straightforward reason the retirement age should be raised: average life expectancy has increased in the last few decades. Back in 1935, President Franklin ...
Samuel Sanford Shapiro (July 13, 1930 – November 5, 2023) was an American statistician and engineer. He was a professor emeritus of statistics at Florida International University . He was known for his co-authorship of the Shapiro–Wilk test and the Shapiro–Francia test .