The Rasch model allows for a conditional likelihood ratio goodness of fit test. The speed of approximation of the test statistic to the limiting distribution as a function of sample size and test length has not been analyzed so far. Three bootstrap simulation methods are analyzed with respect to their performance in providing a proper distribution of the test statistic under the null- and the alternative hypothesis. We found a stable approximation to the limiting χ 2-distribution for sample sizes of at least 500 and 10 items. The three bootstrap algorithms rendered consistent results for the H 0-cases but not for the H 1-cases. A sequential probability sampling scheme proves sufficiently apt for generating samples under the alternative hypothesis. This superiority can be justified from a theoretical point of view.

The importance of identifying outliers in a data set is well known. Although various outlier detection methods have been proposed in order to enable reliable inferences regarding a data set, a simple but less known method has been proposed by Ueda (1996/2009). Since this new method, called Ueda’s method, has not been systematically analysed in previous research, a simulation study addressing its performance and robustness is presented. Although the method was derived assuming that the underlying data is normally distributed, its performance was analysed using data from various outlier-prone distributions commonly found in several research fields. The results obtained enable us to define the strengths and weaknesses of the method along with its limits of applicability. Furthermore, an unforeseen field of application of the method, which requires further studies was also identified.

We propose a new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub. It includes as a special case the widely known exponentiated-Weibull distribution. We present and discuss three special models in the family. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Renyi entropies and order statistics. For the first time, we obtain the generating function of the Frechet distribution. Two useful characterizations of the family are also proposed. The parameters of the new family are estimated by the method of maximum likelihood. Its usefulness is illustrated by means of two real lifetime data sets. AMS Subject Classification Primary 60E05; secondary 62N05; 62F10

Geometric and stochastic representations are derived for the big class of p-generalized elliptically contoured distributions, and (generalizing Cavalieri's and Torricelli's method of indivisibles in a non-Euclidean sense) a geometric disintegration method is established for deriving even more general star-shaped distributions. Applications to constructing non-concentric elliptically contoured and generalized von Mises distributions are presented.AMS subject classification Primary 60E05; 60D05; secondary 28A50; 28A75; 51F99

A new family of distributions called exponentiated Kumaraswamy-Dagum (EKD) distribution is proposed and studied. This family includes several well known sub-models, such as Dagum (D), Burr III (BIII), Fisk or Log-logistic (F or LLog), and new sub-models, namely, Kumaraswamy-Dagum (KD), Kumaraswamy-Burr III (KBIII), Kumaraswamy-Fisk or Kumaraswamy-Log-logistic (KF or KLLog), exponentiated Kumaraswamy-Burr III (EKBIII), and exponentiated Kumaraswamy-Fisk or exponentiated Kumaraswamy-Log-logistic (EKF or EKLLog) distributions. Statistical properties including series representation of the probability density function, hazard and reverse hazard functions, moments, mean and median deviations, reliability, Bonferroni and Lorenz curves, as well as entropy measures for this class of distributions and the sub-models are presented. Maximum likelihood estimates of the model parameters are obtained. Simulation studies are conducted. Examples and applications as well as comparisons of the EKD and its sub-distributions with other distributions are given.Mathematics Subject Classification (2000)62E10; 62F30

The Pareto distribution has long been recognized as a suitable model for many non-negative socio-economic variables. Univariate and multivariate variations abound. Some unification is possible by representing the Pareto variables in terms of independent gamma distributed components. Further unification is sometimes possible since some of the frequently used multivariate Pareto models share the same copula. In some cases, inference strategies can be developed to take advantage of the stochastic representations in terms of gamma components.