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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.
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.
Jack Shapiro. Jack Emanuel "Soupy" Shapiro (March 22, 1907 – February 5, 2001) was an American gridiron football player who played in one game with the Staten Island Stapletons of the National Football League (NFL) in 1929. Shapiro is most famous for being the shortest player in NFL history at about 5 ft 1 in (1.55 m).
Running time. 88 minutes. Language. English. Budget. $1 million. Box office. $45,724. Safe Men is a 1998 American crime comedy film written and directed by John Hamburg (in his directorial debut ), and starring Sam Rockwell and Steve Zahn as a pair of aspiring lounge singers who are mistaken for ace safe crackers .
Shapiro's lemma. In mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the Eckmann–Shapiro lemma, relates extensions of modules over one ring to extensions over another, especially the group ring of a group and of a subgroup.
Karl Jay Shapiro (November 10, 1913 – May 14, 2000) was an American poet. He was awarded the Pulitzer Prize for Poetry in 1945 for his collection V-Letter and Other Poems . [1] He was appointed the fifth Poet Laureate Consultant in Poetry to the Library of Congress in 1946.