This paper presented a two discrete family of life distributions called discrete complementary exponentiated-G Poisson family and discrete Zubair-G family as a special case from discrete complementary exponentiated-G Poisson family. Some basic distributional properties are derived. Such as hazard rate, moments, quantiles, order statistics and Rényi Entropy. A special sub-model of the discrete Zubair-G family, called the discrete Zubair Weibull distribution is considered in detail. Discrete Zubair exponential distribution and discrete Zubair Rayleigh distribution are obtained as two special cases from discrete Zubair Weibull distribution. Method of maximum likelihood is used under Type-II censored samples for estimating the unknown parameters, survival, hazard rate and alternative hazard rate functions. Confidence intervals for the parameters are obtained. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood estimation. Finally, the performance of the new distribution is compared with existing distributions using applications of three real data sets to show the suitability and flexibility of the proposed model.

This paper discussed the Bayesian estimation for the unknown parameters, survival, hazard rate, and alternative hazard rate functions of the discrete Zubair Weibull distribution. Informative priors (gamma and beta) for the parameters of the distribution are assumed. The Bayes estimators are derived under the squared error and linear-exponential loss functions based on Type-II censored sample. Credible intervals for the parameters, survival, hazard rate, and alternative hazard rate functions are obtained. The Bayes predictors (point and interval) for the future observation are obtained considering two-sample prediction. A simulation study is performed using the Markov Chain Monte Carlo algorithm for different sample sizes, and censoring rates to assess the performance of the estimators. Moreover, three real data sets were applied to investigate the flexibility and applicability of the distribution.

In this paper, Bayesian inference is used to estimate the parameters, survival, hazard and alternative hazard rate functions of discrete Gompertz distribution. The Bayes estimators are derived under squared error loss function as a symmetric loss function and linear exponential loss function as an asymmetric loss function. Credible intervals for the parameters, survival, hazard and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for future observations of discrete Gompertz distribution based on two-sample prediction are investigated. A numerical illustration is carried out to investigate the precision of the theoretical results of the Bayesian estimation and prediction on the basis of simulated and real data. Regarding the results of simulation seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear exponential loss function is better than the corresponding results under squared error loss function. Two real lifetime data sets are used to insure the simulated results.

Objective Saline vaginal douching prior to intravaginal prostaglandin application might increase the vaginal pH, leading to improvement of prostaglandin bioavailability, by which the outcomes of labor induction can be greatly improved. Thus, we aimed to evaluate the effect of vaginal washing with normal saline before insertion of vaginal prostaglandin for labor induction. Study Design A systematic search was done in PubMed, Cochrane Library, Scopus, and ISI Web of Science from inception to March 2022. We selected randomized controlled trials (RCTs) that compared vaginal washing using normal saline versus no vaginal washing in the control group before intravaginal prostaglandin insertion during labor induction. We used RevMan software for our meta-analysis. Our main outcomes were the duration of intravaginal prostaglandin application, duration from intravaginal prostaglandin insertion to active phase of labor, duration from intravaginal prostaglandin insertion till total cervical dilatation, labor induction failure rate, incidence of cesarean section (CS), and rates of neonatal intensive care unit (NICU) admission and fetal infection postdelivery. Results Five RCTs were retrieved with a total number of 842 patients. Duration of prostaglandin application, duration from prostaglandin insertion to active phase of labor, and time interval from prostaglandin insertion to total cervical dilatation were significantly shorter among vaginal washing group (p < 0.05). Vaginal douching prior to prostaglandin insertion significantly decreased the incidence of failed labor induction (p < 0.001). After the removal of reported heterogeneity, vaginal washing was linked to a significant decline in CS incidence (p = 0.04). In addition, the rates of NICU admission and fetal infection were significantly lower in the vaginal washing group (p < 0.001). Conclusion Vaginal washing with normal saline before intravaginal prostaglandin insertion is a useful and easily applicable method for labor induction with good outcomes. Key Points

In this paper, a new family of discrete alpha power distributions is introduced. Some properties including quantiles, mean residual life, mean time to failure, R nyi entropy, moments and order statistics are obtained. Discrete alpha power Weibull distribution, as a member from this family, is studied in detail. Discrete two-parameter Weibull distribution, discrete alpha power one parameter Weibull distribution, discrete alpha power exponential distribution, discrete one parameter Weibull distribution, discrete Rayleigh distribution, discrete exponential distribution, discrete alpha power Rayleigh distribution are sub models of discrete alpha power Weibull distribution. A simulation study is conducted to investigate the precision of the theoretical results based on simulated and real data through some measurements of accuracy. Three real data sets are analyzed to illustrate the suitability and applicability of the proposed model.