Skew-symmetric distributions are defined based on the reflected gamma, reflected Weibull and the reflected Pareto distributions. Expressions are derived for the probability density function, cumulative distribution functions, moments and the shape. Estimation procedures by the methods of moments and maximum likelihood and Fisher information matrices are provided. Evidence of flexibility of the distributions is shown. An application is illustrated using the Old Faithful Geyser data. Some of the attractive properties of the distributions include multimodality and polynomial tails.

An optimal alternative bivariate ranked set sample designs for the matched pairs sign test are obtained. Our investigation revealed that the optimal bivariate ranked set sample designs for matched pairs sign test are those with quantifying order statistics with labels {((r+1)/2, (r+1)/2)} when the set size r is odd and {(r/2, r/2), (r/2 + 1, r/2 + 1)} when the set size r is even. The exact null distributions, asymptotic distributions and Pitman efficiencies of those designs are derived. Numerical analysis of the power of the proposed optimal designs is included. An illustration using real data with a bootstrap algorithm for P-value estimation is used.

Decision making based on censored data is a problem of serious concern as such data can provide only limited information compared to the corresponding uncensored data. In this article we describe a very general method of estimating the distribution of type I and II singly censored data. We derive single unified expressions for the probability weighted moments and L-moments of all univariate continuous distributions using a four-parameter family of distributions known as the Generalised Lambda Distribution (GLD) and use them to estimate the density of complete and censored data.

The aim of this paper is to introduce an approximation approach to fractional stochastic integration. Based on our obtained result, we find explicit solution of some fractional stochastic differential equations and study the ruin probability in the asset liability management (ALM) model.

In this paper a Bayesian approach is applied to the correlated binomial model, CB(n, p, ρ), proposed by Luceño (Comput. Statist. Data Anal. 20 (1995) 511–520). The data augmentation scheme is used in order to overcome the complexity of the mixture likelihood. MCMC methods, including Gibbs sampling and Metropolis within Gibbs, are applied to estimate the posterior marginal for the probability of success p and for the correlation coefficient ρ. The sensitivity of the posterior is studied taking into account several reference priors and it is shown that the posterior characteristics appear not to be influenced by these prior distributions. The article is motivated by a study of plant selection.

Different measures of inequality such as the Lorenz curve, the generalised Lorenz curve (GLC) and the cumulated mean income curve (COMIC) are obtained for any univariate continuous distribution. GLC and COMIC are used to identify the best income distribution on welfare grounds when the ordinary Lorenz curves fail to work. Explicit expressions for the moments of a given Lorenz curve are also derived. The proposed method selects the appropriate generalised lambda distribution (GLD) representation corresponding to a given distribution under consideration and computes the different measures of inequality. A numerical illustration of the results, using per capita domestic product at current prices for various states/union territories of India for two periods 1994–95 and 2000–01, is also provided.

In this article we propose a generalized negative binomial distribution, which is constructed based on an extended Poisson process (a generalization of the homogeneous Poisson process). This distribution is intended to model discrete data with presence of zero-inflation and over-dispersion. For a dataset on animal abundance which presents over-dispersion and a high frequency of zeros, a comparison between our extended distribution and other common distributions used for modeling this kind of data is addressed, supporting the fitting of the proposed model.

Yin and Ibrahim [Canad. J. Statist. 33 (2005) 559–570] presented a unified class of cure rate models based on a Box–Cox type transformation of the population survival function. Our work provides a probabilistic justification to this transformation by means of the negative binomial distribution.