Poisson Distribution

Abstract: Abstract: Abstract: The objective of this paper is to develop a reorder policy for a two-echelon supply chain with one central stock and multiple stores. The products under concern are high value imported watches, which exhibit high intermittent demand on the points of sale. The manager has centralized stock information over the entire chain and each store employs a base stock ordering policy. In spite of the lumpy demand on the stores, the monthly aggregate demand on the supply chain is significant and so, can be modeled using the continuous normal distribution approximation. The proposed model consists of an exponential smoothing forecasting model for the aggregate demand, a simple disaggregating method to derive the single items forecasts and a periodic reorder procedure. The order quantities of each item are determined according to the Poisson distribution and a desired service level. The purchased items are kept in the central stock and are shipped to stores on demand...

Research has demonstrated that adolescents who actively commute have higher levels of physical activity (PA), which have declined precipitously over the past 30 years. The purpose of this study was to describe the prevalence of active commuting to school; and to identify barriers associated with active commuting. A cross-sectional study was conducted with 1672 students (46.8% boys and 53.2% girls) from 11 to 17 years of age in Caxias do Sul/RS, Brazil. The students were asked to answer questionnaires about active transport, PA, and sedentary behaviors. They also completed a cardiovascular fitness test and body composition measurements. The study used a multivariate Poisson regression analysis. A total of 62.5% of students were observed to actively commute and the prevalence ratio (PR) of not actively commuting was associated with the type of school (Private: 2.41; 1.47, 3.95) and the time spent on commuting (>20 min: 1.93; 1.23, 3.03). The associated barriers to passive commuting...

Mixture modeling within the context of pharmacokinetic (PK)/pharmacodynamic (PD) mixed effects modeling is a useful tool to explore a population for the presence of two or more subpopulations, not explained by evaluated covariates. At present, statistical tests for the existence of mixed populations have not been developed. Therefore, a simulation study was undertaken to evaluate mixture modeling with NONMEM and explore the following questions. First, what is the probability of concluding that a mixed population exists when there truly is not a mixture (false positive significance level)? Second, what is the probability of concluding that a mixed population (two subpopulations) exists when there is truly a mixed population (power), and how well can the mixture be estimated, both in terms of the population parameters and the individual subject classification. Seizure count data were simulated using a Poisson distribution such that each subject's count could decrease from its baseline value, as a function of dose via an Emax model. The dosing design for the simulation was based on a trial with the investigational anti-epileptic drug pregabalin. Four hundred and forty seven subjects received pregabalin as add on therapy for partial seizures, each with a baseline seizure count and up to three subsequent seizure counts. For the mixtures, the two subpopulations were simulated to differ in their Emax values and relative proportions. One subpopulation always had its Emax set to unity (Emax hi), allowing the count to approach zero with increasing dose. The other subpopulation was allowed to vary in its Emax value (Emax lo=0.75, 0.5, 0.25, and 0) and in its relative proportion (pr) of the population (pr=0.05, 0.10, 0.25, and 0.50) giving a total of 4 ⋅ 4=16 different mixtures explored. Three hundred data sets were simulated for each scenario and estimations performed using NONMEM. Metrics used information about the parameter estimates, their standard errors (SE), the difference between minimum objective function (MOF) values for mixture and non-mixture models (MOF(δ)), the proportion of subjects classified correctly, and the estimated conditional probabilities of a subject being simulated as having Emax lo (Emax hi) given that they were estimated as having Emaxlo (Emax hi) and being estimated as having Emaxlo (Emax hi) given that they were simulated as having Emax lo (Emax hi). The false positive significance level was approximately 0.04 (using all 300 runs) or 0.078 (using only those runs with a successful covariance step), when there was no mixture. When simulating mixed data and for those characterizations with successful estimation and covariance steps, the median (range) percentage of 95% confidence intervals containing the true values for the parameters defining the mixture were 94% (89–96%), 89.5% (58–96%), and 95% (92–97%) for pr, Emax lo, and Emax hi, respectively. The median value of the estimated parameters pr, Emax lo (excluding the case when Emax lo was simulated to equal 0) and Emax hi within a scenario were within ±28% of the true values. The median proportion of subjects classified correctly ranged from 0.59 to 0.96. In conclusion, when no mixture was present the false positive probability was less than 0.078 and when mixtures were present they were characterized with varying degrees of success, depending on the nature of the mixture. When the difference between subpopulations was greater (as Emax lo approached zero or pr approached 0.5) the mixtures became easier to characterize.

Attention deficit hyperactivity disorder (ADHD) is a common mental disorder associated with factors that are likely to increase mortality, such as oppositional defiant disorder or conduct disorder, criminality, accidents, and substance misuse. However, whether ADHD itself is associated with increased mortality remains unknown. We aimed to assess ADHD-related mortality in a large cohort of Danish individuals. By use of the Danish national registers, we followed up 1·92 million individuals, including 32 061 with ADHD, from their first birthday through to 2013. We estimated mortality rate ratios (MRRs), adjusted for calendar year, age, sex, family history of psychiatric disorders, maternal and paternal age, and parental educational and employment status, by Poisson regression, to compare individuals with and without ADHD. During follow-up (24·9 million person-years), 5580 cohort members died. The mortality rate per 10 000 person-years was 5·85 among individuals with ADHD compared with ...

Purpose It has been suggested that subjective measures of oral health are influenced by both individual and contextual characteristics. This study assessed the relationship between neighborhood and individual social networks and child oral health-related quality of life (COHRQoL). Methods This study followed a cross-sectional design using a multistage sample of 478 children aged 1–5 years old. Caregivers completed the Brazilian version of the Early Childhood Oral Health Impact Scale (ECOHIS) and answered questions related to socioeconomic status and social network. The dental examination provided information on the prevalence of dental caries, dental trauma, and occlusion. Contextual social determinants included the presence of cultural community centers and of workers’ association in the neighborhood. Data analysis considered the total ECOHIS scores as the outcome and neighborhood/individual social networks as the independent variables. A multilevel Poisson regression model was used to investigate the association among individual and contextual characteristics and COHRQoL. Results Total ECOHIS scores ranged from 0 to 41 (possible range 0–52). The mean ECOHIS score was low (mean = 1.8, SD = 3.9), and the functional domain presented the highest mean impact on COHRQoL (mean = 0.5, SD = 1.4). Following adjusted analysis, low household income, visiting a neighbor less than once a month, the presence of anterior open bite, dental trauma, and dental caries were identified as individual determinants of negative impact on a child’s quality of life. These variables remained associated with the outcome even after adding the contextual-level variables in the model. At the contextual level, the presence of community cultural centers was associated with overall mean ECOHIS score; higher impacts on COHRQoL were observed in those living in neighborhoods without cultural community centers. Conclusion There is a significant association between individual and contextual social determinants and COHRQoL; unfavorable social conditions and poor socioeconomic status have a negative impact on caregiver reports of children’s oral health-related quality of life.

The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

In some real case problems, the relationship between a response variable and one or more explanatory variables called as profile should be monitored over time instead of the quality characteristic itself. Profile monitoring is used in such instances. Many researches have been done in the area of profile monitoring but in most of them it is assumed that the response variable follows normal distribution. In recent years Yeh et al.(2009) proposed 5 T 2 based methods for monitoring logistic profiles in which response variable is binary. In ...

Scuba diving injuries vary greatly in severity and prognosis. While decompression sickness (DCS) and arterial gas embolism can be tracked easily, other forms of diving injury remain unaccounted for. The purpose of this paper is to assess rates of overall self-reported scuba-diving-related injuries, self-reported DCS-like symptoms, and treated DCS and their association with diver certification level, diving experience and demographic factors. We analyzed self-reported data from a Divers Alert Network membership health survey conducted during the summer of 2011. Poisson regression models with scaled deviance were used to model the relative rates of reported injuries. Models were adjusted for sex, age, body mass index (BMI) and average annual dives, based on the bias-variance tradeoff. The overall rate of diving-related injury was 3.02 per 100 dives, self-reported DCS symptoms was 1.55 per 1,000 dives and treated DCS was 5.72 per 100,000 dives. Diving-related injury and self-reported D...

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is