In this article, acceptance sampling plans are developed for the Marshall–Olkin extended exponential distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer’s risk. The operating characteristic values (and curves) of the sampling plans as well as the producer’s risk are presented. Two examples with real data sets are also given as illustration.

In this paper, a new extension for the Birnbaum–Saunders distribution, which has been applied to the modeling of fatigue failure times and reliability studies, is introduced. The proposed model, called the Marshall–Olkin extended Birnbaum–Saunders distribution, arises based on the scheme introduced by Marshall and Olkin [Biometrika 84 (1997) 641–652]. The maximum likelihood estimators and statistical inference for the new distribution parameters and influence diagnostic for the new distribution are presented. Finally, the proposed new distribution is applied to model three real data sets.

A nonstandard saddlepoint approximation to the distribution of a sum of Markov dependent trials is introduced. The relative error of the approximation is studied, not only for the number of summands tending to infinity, but also for the parameter approaching the boundary of its definition range. A comparison is made with another recent study of Markov dependent trials.

In this article we consider a class of asymmetric distributions which belongs to one parameter regular exponential family. The Marshall–Olkin version of this family is also considered. Various properties are examined. Applications of these models in time series analysis are discussed. We also consider an application of Marshall–Olkin Esscher transformed Laplace distribution in financial modeling. A comparative study shows that Marshall–Olkin Esscher transformed Laplace distribution is a better fit to our data compared to asymmetric Laplace and Esscher transformed Laplace distributions.

For the first time, a four-parameter beta generalized logistic distribution is obtained by compounding the beta and generalized logistic distributions. The new model extends some well-known distributions and its shape is quite flexible, specially the skewness and the tail weights, due to the extra shape parameters. We obtain general expansions for the moment generating and quantile functions. The estimation of the parameters is investigated by maximum likelihood. An application to a real data set is given to show the flexibility and potentiality of our distribution.

We consider a stochastic model for species evolution. A new species is born at rate $\lambda$ and a species dies at rate $\mu$. A random number, sampled from a given distribution $F$, is associated with each new species and assumed as its fitness, at the time of birth. Every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time of a species with a given fitness $f$. We show that the survival time distribution depends crucially on whether $f<f_{c}$, $f=f_{c}$ or $f>f_{c}$ where $f_{c}$ is a critical fitness that is computed explicitly.

Statistical classification methods based on score statistics have received a considerable attention in recent years. The use of these methodologies requires that asymptotic properties relative to such measures are satisfied. In this context, the classification error rates generally present biased values to the nominal level when submitted to small or moderate sample sizes. However, Nelson, Turin and Hastie [Journal of Pattern Recognition and Artificial Intelligence 8 (1994) 749–770] proposed a successful classification method based on score statistic described asymptotically by a chi-square law. That proposal presented good results for several sample sizes. On the other hand, stochastic measures with exact distributions described by beta and Hotelling’s $\mathcal{T}^{2}$ laws have also been employed in such situations. This paper presents two Bartlett-type corrections for score statistics considering the method proposed by Cordeiro and Ferrari [J. Statist. Plann. Inference 71 (1998) 261–269]. Moreover, Monte Carlo experiments are performed in order to compare the corrected statistics to their respective noncorrected versions and to a classic classifier defined on the nonmodified score statistic. In a confirmatory sense, the proposed methodology is applied to actual signature data, obtained by the Electrical Engineering and Computer Department from the State University of Campinas (UNICAMP, Brazil).

We show that the total variational distance between a process of two particles interacting by exclusion and a process of two independent particles goes to $0$ as time goes to infinity, when the underlying one particle system is a symmetric random walk on $\mathbb{Z}^{d}$ with finite second moments. Upper bounds for the speed of convergence are given.

In this article we develop an estimation method based on the augmented data scheme and EM/SEM (Stochastic EM) algorithms for fitting one-parameter probit (Rasch) IRT (Item Response Theory) models. Instead of using the S steps of the SEM algorithm, that is, instead of simulating values for the unobserved variables (augmented data and the latent traits), we consider the conditional expectations of a set of unobserved variables on the other set of unobserved variables, the current estimates of the parameters and the observed data, based on the full conditional distributions from the Gibbs sampling algorithm. Our method, named the CADEM algorithm (conditional augmented data EM), presents straightforward E steps, which avoid the need to evaluate the usual integrals, also facilitating the M steps, without the need to use numerical methods of optimization. We use the CADEM algorithm to obtain both maximum likelihood estimates and maximum a posteriori estimates of the difficulty parameters for the one-parameter probit (Rasch) model. Also, we obtain estimates for the latent traits, based on conditional expectations. In addition, we show how to calculate the associated standard errors. Some directions are provided to extend our approach to other IRT models. In this respect, we perform a simulation study to compare the estimation methods. The results indicated that our approach is quite comparable to the usual marginal maximum likelihood (MML) and Gibbs sampling methods (GS) in terms of parameter recovery. However, CADEM is as fast as MML and as flexible as GS.