In regression problems where covariates are subject to errors (albeit small) it often happens that maximum likelihood estimators (MLE) of relevant parameters have infinite moments. We study here circular and elliptic regression, that is, the problem of fitting circles and ellipses to observed points whose both coordinates are measured with errors. We prove that several popular circle fits due to Pratt, Taubin, and others return estimates of the center and radius that have infinite moments. We also argue that estimators of the ellipse parameters (center and semiaxes) should have infinite moments, too.

This paper deals with a computational aspect of the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC methods cannot be applied. We propose here a general approach to sample from such posterior distributions that bypasses the computation of the normalizing constant. Our method can be thought as a Bayesian version of the MCMC-MLE approach of Geyer and Thompson [J. Roy. Statist. Soc. Ser. B 54 (1992) 657–699]. We illustrate our approach on examples from image segmentation and social network modeling. We study as well the asymptotic behavior of the algorithm and obtain a strong law of large numbers for empirical averages.

We study sample path deviations of the Wiener process from three different representations of its bridge: anticipative version, integral representation and space–time transform. Although these representations of the Wiener bridge are equal in law, their sample path behavior is quite different. Our results nicely demonstrate this fact. We calculate and compare the expected absolute, quadratic and conditional quadratic path deviations of the different representations of the Wiener bridge from the original Wiener process. It is further shown that the presented qualitative behavior of sample path deviations is not restricted only to the Wiener process and its bridges. Sample path deviations of the Ornstein–Uhlenbeck process from its bridge versions are also considered and we give some quantitative answers also in this case.

We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given score. We use these findings to investigate the dependence of these quantities on the different parameters involved (number of points needed to win a set, number of consecutive serves, etc.), with particular focus on the rule change imposed in 2001 by the International Table Tennis Federation (ITTF). Finally, we briefly indicate how our results can lead to more efficient estimation techniques of individual players’ abilities.

In this paper, we derive some recurrence relations satisfied by single and product moments of generalized upper record values arising from the Makeham distribution. We obtain similar results for the inverse Makeham distribution using generalized lower record values. Further, we have identified some of these recurrence relations and other properties of generalized record values which characterize Makeham and inverse Makeham distributions.

For the first time, the beta Burr III distribution is introduced as an important model for problems in several areas such as actuarial sciences, meteorology, economics, finance, environmental studies, survival analysis and reliability. The new distribution can be expressed as a linear combination of Burr III distributions and then it has tractable properties for the moments, generating and quantile functions, mean deviations, reliability and entropies. The density of its order statistics can be given in terms of an infinite linear combination of Burr III densities. The beta Burr III model is modified for the possibility of long-term survivors. We define a log-beta Burr III regression model to analyze censored data. The estimation of parameters is approached by maximum likelihood and the observed information matrix is derived. The proposed models are applied to three real data sets.

Edward Nelson derived Brownian motion from the Ornstein–Uhlenbeck theory by a scaling limit. Previously we extended the scaling limit to an Ornstein–Uhlenbeck process driven by an $\alpha$-stable Lévy process. In this paper we extend the scaling result to $\alpha$-stable Lévy processes in the presence of a nonlinear drift, an external field of force in physical terms.

Determining the acceptability of any product, reliability sampling plans are used. In this paper, reliability sampling plans for truncated life test are developed when the lifetimes of a test follow an alpha distribution. The sampling plan proposed here can save the test time in practical situations. Sampling plans are established through an algorithm. Moreover, some tables are provided for the proposed sampling plans so that proposed method can be used conveniently for the practitioner. Operating characteristic values of the sampling plans are also presented. Examples are provided to illustrate its use.

In this paper, we introduce the complementary exponential power series distributions, with failure rate increasing, which is complementary to the exponential power series model proposed by Chahkandi and Ganjali [Comput. Statist. Data Anal. 53 (2009) 4433–4440]. The new class of distribution arises on latent complementary risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the maximum lifetime value among all risks. This new class contains several distributions as a particular case. The properties of the proposed distribution class are discussed, such as quantiles, moments and order statistics. Estimation is carried out via maximum likelihood. Simulation results on maximum likelihood estimation are presented. A real application illustrates the usefulness of the new distribution class.

In this paper, we propose a new cure rate survival model under a flexible family of distributions. Our approach enables different underlying activation mechanisms that lead to the event of interest. The number of competing causes of the event of interest follows a power series distribution. This model includes the standard mixture cure model and the promotion time cure model. The model is parametrized in terms of the cured fraction, which is then linked to covariates. We carried out a simulation study to assess some properties of our proposal. An illustrative example with a real data set is provided to illustrate the models.

This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of such transformations of normal variables which produces non-infinitely divisible distributions. We relate our result with some known skewing mechanisms.

Towards the search for improving the randomized response models used to estimate a population proportion bearing a sensitive characteristic, a new model, based on the use of a two-stage randomized response procedure, is proposed. The condition under which the proposed estimator is more efficient than the Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimator has been obtained. An empirical study has also been performed to examine the relative efficiency of the proposed estimator with respect to the Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimator. Moreover, the proposed estimator can be easily adjusted to be more efficient than the Warner [J. Amer. Statist. Assoc. 60 (1965) 63–69], Mangat and Singh [Biometrika 77 (1990) 439–442], Mangat [J. R. Stat. Soc. Ser. B Stat. Methodol. 56 (1994) 93–95] and Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimators.