This work studies the behavior of certain test criteria in multivariate analysis of variance, under the existence of multiplicity in the sample eigenvalues of the matrix S_E⁻¹S_H; where S_H is the matrix of sum of squares and sum of products due to the hypothesis and S_E is the matrix of sum of squares and sum of products due to the error.

For the first time, we derive explicit closed-form expressions for moments of some beta generalized distributions including the beta gamma, beta normal, beta beta, beta Student t and beta F distributions. These expressions are given as infinite weighted sums of well-known special functions for which numerical routines for computation are available.

Let {X_n, k, 1 ≤ k ≤ m_n, n ≥ 1} be independent random variables from the Pareto distribution. Let X_n(k) be the kth largest order statistic from the nth row of our array, where X_n(1) denotes the largest order statistic from the nth row. Then set R_{n, in, jn} = X_n(jn) / X_n(in) where j_n < i_n. This paper establishes limit theorems involving weighted sums from the sequence {R_{n, in, jn}, n ≥ 1}, where for the first time we allow j_n → ∞, but only at a slow rate.

A special type of the stochastic STOPBREAK process, which behaves properly when applied to time series data with emphatic permanent fluctuations, is presented. A good dynamic behavior is induced by the threshold regime and named the Split-BREAK process. General properties of this threshold STOPBREAK process are investigated, as well as some estimation procedures for the parameters of the process presented. A Monte Carlo simulation of the process is given and its application to the share trading on the Belgrade Stock Exchange illustrated.

For the first time, we introduce the log-generalized modified Weibull regression model based on the modified Weibull distribution [Carrasco, Ortega and Cordeiro Comput. Statist. Data Anal. 53 (2008) 450–462]. This distribution can accommodate increasing, decreasing, bathtub and unimodal shaped hazard functions. A second advantage is that it includes classical distributions reported in lifetime literature as special cases. We also show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as submodels several widely known regression models and therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. In addition, we define martingale and deviance residuals to detect outliers and evaluate the model assumptions. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.

The covariance structure among other properties of the square of the purely diagonal bilinear time series model is obtained. The time series properties of these squares are compared with those of the linear moving average time series model. It was discovered that the square of a linear moving average process is also identified as a moving average process whereas, while the nonlinear purely diagonal bilinear process is identified as a linear moving average process, its square is identified as an autoregressive moving average process.

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. More than 10 practical situations where the truncated distribution could be applied are discussed. Explicit expressions are derived for the moments, L moments, mean deviations, moment generating function, characteristic function, convolution properties, Bonferroni curve, Lorenz curve, entropies, order statistics and the asymptotic distribution of the extreme order statistics. Estimation procedures are detailed by the method of moments and the method of maximum likelihood and expressions derived for the associated Fisher information matrix. Simulation issues are discussed. Finally, an application is illustrated for consumer price indices from the six major economics.