Wilks lambda statistic, Independence test, Sphericity test, Generalized Integer Gamma distribution, Generalized Near-Integer Gamma distribution, Mixtures, 62H10, 62E20, 62H05, 62H15,

No abstract

The distribution of linear combinations of independent Gumbel random variables is of great interest for modeling risk and extremes in the most different areas of application. In this paper we develop near-exact approximations for the distribution of linear combination of independent Gumbel random variables based on a shifted Generalized NearInteger Gamma distribution and on the distribution of the difference of two independent Generalized Integer Gamma distributions. These near-exact distributions are computationally appealing and numerical studies confirm their accuracy, as assessed by a proximity measure used in related studies. We illustrate the proposed approximations on applied problems in networks engineering, computational biology, and flood risk management.

No abstract

This paper introduces the nonparametric predictive inference approach for reproducibility of likelihood ratio tests. The general idea of this approach is outlined for tests between two simple hypotheses, followed by an investigation of reproducibility for tests between two Beta distributions. The paper reports on the first steps of a wider research programme towards tests involving composite hypotheses and substantial computational challenges.