We introduce new estimates and tests of independence in copula models with unknown margins using -divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of -divergence has good properties in terms of efficiency-robustness.
Some properties of the "new better than used in failure rate" (NBUFR) and the "new better than used in expectation" (NBUE) classes of life distributions are given. These properties include moment inequalities and moment generating functions behaviors. In addition, nonparametric estimation and testing of the survival functions of these classes are discussed.
Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.
The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].