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This paper proves the existence and uniqueness theorem for generalized (reflected) backward stochastic differential equations under stochastic Lipschitz and monotone condition. The result is shown by using Picard’s iteration, the Snell envelope theory and the penalization method.

Multivariate regression models and ANOVA are probably the most frequently applied methods of all statistical analyses. We study the case where the predictors are qualitative variables and the response variable is quantitative. In this case, we propose an alternative to the classic approaches that does not assume homoscedasticity but assumes that a Markov chain can describe the covariates’ correlations. This approach transforms the dependent covariates using a change of measure to independent covariates. The transformed estimates allow a pairwise comparison of the mean and variance of the contribution of different values of the covariates. We show that, under standard moment conditions, the estimators are asymptotically normally distributed. We test our method with data from simulations and apply it to several classic data sets.

In this paper, we develop a stochastic model to analyze how financial contagion may affect economic activity. In the deterministic case, we show that, according to specific parameter values, the economy may converge either to a stress-free equilibrium or to a stressed equilibrium: in the former situation, the level of economic growth is maximal, while in the latter, it is reduced by financial contagion. In the stochastic case, we compute a value around which the level of economic growth oscillates. Numerical simulations are performed to illustrate theoretical results obtained.

The main focus of this article is on the study of properties and characterizations of dynamic survival extropy and its scaled version. Its relation with other well-known measures is also discussed. A simple nonparametric estimator and a nonparametric estimator based on the kernel are proposed for survival extropy and scaled dynamic survival extropy respectively. These estimators could also be utilized to estimate the measures related to dynamic survival extropy, such as the Gini index. In addition, the performance of the suggested estimators is evaluated for the simulated data set.

We introduce a new test for exponentiality against decreasing (increasing) mean residual life alternatives based on a cumulative residual Renyi’s entropy of order α. The exact and asymptotic distributions of the test statistic are given. The performance of the proposed test statistic is compared with other constructed tests in the literature using a simulation study. Finally, some numerical examples illustrating the theory are given.

This article develops multiple dependent state (MDS) sampling inspection plans based on the mean of lifetime quality characteristic that follows non-normal distributions viz., exponential and Lindley distribution. In this plan, the lot quality is measured by the lot mean (𝜇). We have estimated the optimal plan parameters of the proposed technique by non-linear optimization approaches considering acceptable quality level and rejection quality level. We have compared the sample size between the MDS sampling inspection plan and the single sampling inspection plan for the variable. Finally, we have taken two examples to illustrate the proposed technique.

A nonparametric sequential probability ratio test control chart to monitor the process dispersion based on the sequential sign statistic is proposed. The statistical performance of this chart is evaluated by comparing it with that of the charts for dispersion based on sign statistic in the existing literature. It is found that the proposed chart outperforms all these charts uniformly in detecting a shift of any size over a wide range. An implementation of the chart is illustrated through an example.