Inhaltszusammenfassung

Invited Lecture at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS, Berlin), June 27, 2012 Abstract: In this lecture the exact distribution of Greenwood's statistic - the square sum of spacings - is obtained as a special case among several distributions derived from independent gamma random variables. The exact distributions of the "basic-statistics", i.e. sum of squares, sample variance and sample coefficient of variation are represented by different methods as powe...Invited Lecture at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS, Berlin), June 27, 2012 Abstract: In this lecture the exact distribution of Greenwood's statistic - the square sum of spacings - is obtained as a special case among several distributions derived from independent gamma random variables. The exact distributions of the "basic-statistics", i.e. sum of squares, sample variance and sample coefficient of variation are represented by different methods as power series, convex combinations of cumulative gamma distributions, several orthogonal series and univariate integrals over well known transcendental functions. Some results are extended to some positive definite quadratic forms of not identically distributed gamma random variables. These methods have been used to compute a table with nine 8-digit percentage points of Greenwood's statistic for sample sizes up to n = 100. Furthermore, an exact test for the shape parameter of a gamma distribution with unknown scale is provided.» weiterlesen» einklappen

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Klassifikation

DFG Fachgebiet:
Mathematik

DDC Sachgruppe:
Statistik