This paper presents the distribution of the number of customers served during a busy period for special cases of the Geo/G/1 queue when initiated with m customers. We analyze the system under the assumptions of a late arrival system with delayed access and early arrival system policies. It is not easy to invert the functional equation for the number of customers served during a busy period except for the simple case Geo/Geo/1 queue, as stated by several researchers. Using the Lagrange inversion theorem, we give an elegant solution to this equation. We find the distribution of the number of customers served during a busy period for various service-time distributions such as geometric, deterministic, binomial, negative binomial, uniform, Delaporte, discrete phase-type and interrupted Bernoulli process. We compute the mean and variance of these distributions and also give numerical results. Due to the clarity of the expressions, the computations are very fast and robust. We also show that in the limiting case, the results tend to the analogous continuous-time counterparts.

Reliability theory and survival analysis, the residual entropy is known as a measure suitable to describe the dynamic information content in stochastic systems conditional on survival. Aiming to analyze the variability of such information content, in this paper we introduce the variance of the residual lifetimes, “residual varentropy” in short. After a theoretical investigation of some properties of the residual varentropy, we illustrate certain applications related to the proportional hazards model and the first-passage times of an Ornstein–Uhlenbeck jump-diffusion process.

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence (SP) order that is defined for two random variables to the case n > 2. All conventional stochastic orders are transitive, whereas the SP order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.

Varicella is an acute respiratory infectious diseases, with high transmissibility and quick dissemination. In this study, an SEIR (susceptible-exposed-infected-recovered) dynamic model was established to explore the optimal prevention and control measures according to the epidemiological characteristics about varicella outbreak in a school in a central city of China. Berkeley Madonna 8.3.18 and Microsoft Office Excel 2010 software were employed for the model simulation and data management, respectively. The result showed that the simulated result of SEIR model agreed well with the reported data when β (infected rate) equal to 0.067. Models showed that the cumulative number of cases was only 13 when isolation adopted when the infected individuals were identified (assuming isolation rate was up to 100%); the cumulative number of cases was only two and the TAR (total attack rate) was 0.56% when the vaccination coefficient reached 50%. The cumulative number of cases did not change significantly with the change of efficiency of ventilation and disinfection, but the peak time was delayed; when δ (vaccination coefficient) = 0.1, m (ventilation efficiency) = 0.7 or δ = 0.2, m = 0.5 or δ = 0.3, m = 0.1 or δ = 0.4 and above, the cumulative number of cases would reduce to one case and TAR would reduce to 0.28% with combined interventions. Varicella outbreak in school could be controlled through strict isolation or vaccination singly; combined interventions have been adopted when the vaccination coefficient was low.

We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. We give conditions for consistency and asymptotic normality of the Exponential Quasi-Maximum Likelihood Estimator of the conditional mean parameters. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in this paper.

Chlamydia trachomatis (CT) infection has been a major public health threat globally. Monitoring and prediction of CT epidemic status and trends are important for programme planning, allocating resources and assessing impact; however, such activities are limited in China. In this study, we aimed to apply a seasonal autoregressive integrated moving average (SARIMA) model to predict the incidence of CT infection in Shenzhen city, China. The monthly incidence of CT between January 2008 and June 2019 in Shenzhen was used to fit and validate the SARIMA model. A seasonal fluctuation and a slightly increasing pattern of a long-term trend were revealed in the time series of CT incidence. The monthly CT incidence ranged from 4.80/100 000 to 21.56/100 000. The mean absolute percentage error value of the optimal model was 8.08%. The SARIMA model could be applied to effectively predict the short-term CT incidence in Shenzhen and provide support for the development of interventions for disease control and prevention.

The literature on regression kink designs develops identification results for average effects of continuous treatments (Nielsen et al., 2010, American Economic Journal: Economic Policy 2, 185–215; Card et al., 2015, Econometrica 83, 2453–2483), average effects of binary treatments (Dong, 2018, Jump or Kink? Identifying Education Effects by Regression Discontinuity Design without the Discontinuity), and quantile-wise effects of continuous treatments (Chiang and Sasaki, 2019, Journal of Econometrics 210, 405–433), but there has been no identification result for quantile-wise effects of binary treatments to date. In this article, we fill this void in the literature by providing an identification of quantile treatment effects in regression kink designs with binary treatment variables. For completeness, we also develop large sample theories for statistical inference, present a practical guideline on estimation and inference, conduct simulation studies, and provide an empirical illustration.

A prevalence study was conducted on German sheep flocks including goats if they cohabitated with sheep. In addition, a novel approach was applied to identify an infection at the herd-level before lambing season with preputial swabs, suspecting venereal transmission and ensuing colonisation of preputial mucosa with Coxiella (C.) burnetii. Blood samples and genital swabs were collected from breeding males and females after the mating season and were analysed by enzyme-linked immunosorbent assay (ELISA) and quantitative polymerase chain reaction (qPCR) respectively. In total, 3367 animals were sampled across 71 flocks. The true herd-level prevalence adjusted for misclassification probabilities of the applied diagnostic tests using the Rogan-Gladen estimator for the prevalence estimate and a formula by Lang and Reiczigel (2014) for the confidence limits, ranged between 31.3% and 33% (95% confidence interval [95% CI] 17.3–45.5) detected by the ELISA and/or qPCR. Overall 26–36.6% (95% CI 13–56.8) were detected by ELISA, 13.9% (95% CI 4.5–23.2) by the qPCR and 7.9–11.2% (95% CI 0.08–22.3) by both tests simultaneously. The range of results is due to data obtained from literature with different specifications for test quality for ELISA. Among eight farms with females shedding C. burnetii, three farms (37.5%) could also be identified by preputial swabs from breeding sires. This indicates less reliability of preputial swabs if used as a single diagnostic tool to detect C. burnetii infection at the herd-level.

Models of mortality often require constraints in order that parameters may be estimated uniquely. It is not difficult to find references in the literature to the “identifiability problem”, and papers often give arguments to justify the choice of particular constraint systems designed to deal with this problem. Many of these models are generalised linear models, and it is known that the fitted values (of mortality) in such models are identifiable, i.e., invariant with respect to the choice of constraint systems. We show that for a wide class of forecasting models, namely ARIMA$(p,\delta, q)$ models with a fitted mean and $\delta = 1$ or 2, identifiability extends to the forecast values of mortality; this extended identifiability continues to hold when some model terms are smoothed. The results are illustrated with data on UK males from the Office for National Statistics for the age-period model, the age-period-cohort model, the age-period-cohort-improvements model of the Continuous Mortality Investigation and the Lee–Carter model.

Prospective, population-based surveillance to systematically ascertain exposures to food production animals or their environments among Minnesota residents with sporadic, domestically acquired, laboratory-confirmed enteric zoonotic pathogen infections was conducted from 2012 through 2016. Twenty-three percent (n = 1708) of the 7560 enteric disease cases in the study reported an animal agriculture exposure in their incubation period, including 60% (344/571) of Cryptosporidium parvum cases, 28% (934/3391) of Campylobacter cases, 22% (85/383) of Shiga toxin-producing Escherichia coli (STEC) O157 cases, 16% (83/521) of non-O157 STEC cases, 10% (253/2575) of non-typhoidal Salmonella enterica cases and 8% (9/119) of Yersinia enterocolitica cases. Living and/or working on a farm accounted for 61% of cases with an agricultural exposure, followed by visiting a private farm (29% of cases) and visiting a public animal agriculture venue (10% of cases). Cattle were the most common animal type in agricultural exposures, reported by 72% of cases. The estimated cumulative incidence of zoonotic enteric infections for people who live and/or work on farms with food production animals in Minnesota during 2012–2016 was 147 per 10 000 population, vs. 18.5 per 10 000 for other Minnesotans. The burden of enteric zoonoses among people with animal agriculture exposures appears to be far greater than previously appreciated.

Since the incursion of influenza A(H1N1)pdm09 virus in 2009, serosurveillance every year of the Norwegian pig population revealed the herd prevalence for influenza A(H1N1)pdm09 (HIN1pdm09) has stabilised between 40% and 50%. Between 30 September 2009 and 14 September 2017, the Norwegian Veterinary Institute and Norwegian Food Safety Authority screened 35,551 pigs for antibodies to influenza A viruses (IAVs) from 8,636 herds and found 26% or 8,819 pigs' sera ELISA positive (titre ≥40). Subtyping these IAV antibodies from 8,214 pigs in 3,629 herds, by a routine haemagglutination inhibition test (HAIT) against four standard antigens produced 13,771 positive results (HAIT titre ≥40) of binding antibodies. The four antigen subtypes eliciting positive HAIT titre in descending frequencies were immunogen H1N1pdm09 (n = 8,200 or 99.8%), swine influenza A virus (SIVs) subtypes swH1N1 (n = 5,164 or 62%), swH1N2 (n = 395 or 5%) and swH3N2 (n = 12 or 0.1%). Of these 8,214 pig pigs sera, 3,039 produced homologous HAIT subtyping, almost exclusively immunogen H1N1pdm09 (n = 3,026 or 99.6%). Using HAIT titre of pig and herd geometric mean titre (GMT) as two continuous outcome variables, and with the data already structured hierarchically, we used mixed effects linear regression analysis to investigate the impact of predictors of interests had on the outcomes. For the full data, the predictors in the regression model include categorical predictors antigen subtype (H1N1pdm09, swH1N1, swH1N2 & swH3N2), and production type (sow herd or fattening herd), ordinal predictors year (longitudinally from 2009 to 2017) and number of antigens in heterologous reactions (1, 2, 3, 4) in the same pig serum. The last predictor, the proportion of HAIT positive (antigen specific) in tested pigs within the herd, was a continuous predictor, which served as a proxy for days post-infection (dpi) or humoral response time in the pig or herd. Regression analysis on individual pig HAIT titres showed that antigen as a predictor, the coefficient for immunogen H1N1pdm09 was at least fourfold higher (P < 0.001) than the three SIVs antigen subtypes, whose much lower coefficients were statistically no different between the three SIVs antigen subtypes. Correspondingly, for herd GMT, immunogen H1N1pdm09 was 28–40-fold higher than the three SIVs antigen subtypes. Excluding the HAIT data of the three SIVs antigen subtypes, regression analysis focusing only on immunogen H1N1pdm09 increased greatly the coefficients of the predictors in the models. Homologous reactions (99.6% H1N1pdm09) have lower HAIT titres while the likelihood of the number of antigens involved in HAIT heterologous reactions in a single pig serum increased with higher HAIT titres of immunogen H1N1pdm09. For predictor ‘production’, sows and sow herds had higher HAIT titres and GMT compared to fattening pigs and fattening herds respectively. Herds with ‘higher proportion of pigs tested positive’ also had higher HAIT titre in the pig and herd GMT.