In this paper, we introduce a family of bivariate generalized Gompertz-power series distributions. This new class of bivariate distributions contains several models such as: bivariate generalized Gompertz -geometric, -Poisson, - binomial, -logarithmic, -negative binomial and bivariate generalized exponental-power series distributions as special cases. We express the method of construction and derive different properties of the proposed class of distributions. The method of maximum likelihood and EM algorithm are used for estimating the model parameters. Finally, we illustrate the usefulness of the new distributions by means of application to real data sets.

In order to construct the asymmetric models and analyzing data set with asymmetric properties, an useful approach is the weighted model. In this paper, a new class of skew-Laplace distributions is introduced by considering a two-parameter weight function which is appropriate to asymmetric and multimodal data sets. Also, some properties of the new distribution namely skewness and kurtosis coefficients, moment generating function, etc are studied. Finally, The practical utility of the methodology is illustrated through a real data collection.

One of the most critical challenges in progressively Type-II censored data is determining the removal plan. It can be fixed or random so that is chosen according to a discrete probability distribution. Firstly, this paper introduces two discrete joint distributions for random removals, where the lifetimes follow the two-parameter Weibull distribution. The proposed scenarios are based on the normalized spacings of exponential progressively Type-II censored order statistics. The expected total test time has been obtained under the proposed approaches. The parameters estimation are derived using different estimation procedures as the maximum likelihood, maximum product spacing and least-squares methods. Next, the proposed random removal schemes are compared to the discrete uniform, the binomial, and fixed removal schemes via a Monte Carlo simulation study in terms of their biases; root means squared errors of estimators and their expected experiment times. The expected experiment time ratio is also discussed under progressive Type-II censoring to the complete sampling plan.