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This paper proposes a new estimation procedure called Event Count Estimator (ECE). The estimator is straightforward to implement and is robust against outliers, censoring and ‘excess zeros’ in the ...

Counting repressive events is difficult because state leaders have an incentive to conceal actions of their subordinates and destroy evidence of abuse. In this article, we extend existing latent variable modeling techniques in the study of repression to account for the uncertainty inherent in count data generated for this type of difficult-to-observe event. We demonstrate the utility of the model by focusing on a dataset that defines ‘one-sided-killing’ as government-caused deaths of non-combatants. In addition to generating more precise estimates of latent repression levels, the model also estimates the probability that a state engaged in one-sided-killing and the predictive distribution of deaths for each country-year in the dataset. These new event-based, count estimates will be useful for researchers interested in this type of data but skeptical of the comparability of such events across countries and over time. Our modeling framework also provides a principled method for inferring unobserved count variables based on conceptually related categorical information.

What explains U.S. media coverage of Americans kidnapped abroad? While some hostages receive national media attention, others hardly make the local news. Using an original, event count dataset of n...

Due to the complex geological conditions and special mining approach of the steeply dipping thick coal seam in the south mining area of the Wudong coal mine, dynamic hazards are frequently encountered during horizontal section top-coal caving. Identification of rock burst precursor information can help effectively avoid its occurrence, decrease unnecessary loss, and ensure personal safety of underground workers. The B3+6 coal seam working face of the south mining area of the Wudong coal mine at +475 m level and +450 m level is monitored using a microseismic (MS) monitoring system. The spatial and temporal evolution patterns of MS parameters before rock burst occurrence are investigated and compared with the evolution pattern of precursor characteristics in the gently inclined coal seam. The results show the following data: (1) The daily MS total energy and event count exhibited a sudden decrease and abnormal fluctuation before rock burst occurrence in the steeply dipping thick coal seam of the south mining area of the Wudong coal mine, which can be employed as an effective precursor signal for rock burst early warning. (2) The MS sources were mainly concentrated around the rock pillar, which created a high static stress condition for the occurrence of rock burst and served as the force source of rock burst. The rock pillar was also the main cause of rock burst in the B3+6 coal seam. (3) The MS event aggregation index is defined, which shows sudden fall and rise variation and reaches an extremely low value immediately before the rock burst occurrence. This phenomenon can be considered as a rock burst precursor in the steeply dipping thick coal seam of the south mining area of the Wudong coal mine. (4) For the steeply dipping thick coal seam, the sharp rise and fall of the daily MS average energy does not necessarily mean rock burst occurrence, while the abnormal fluctuation of the daily MS average energy is very likely the precursor of rock burst occurrence. (5) More attention should be paid to the floor (rock pillar) rather than the roof in the study of rock burst in the steeply dipping thick coal seam under similar conditions.

Catalytic reaction events occurring on the surface of a nanoparticle constitute a complex stochastic process. Although advances in modern single-molecule experiments enable direct measurements of individual catalytic turnover events occurring on a segment of a single nanoparticle, we do not yet know how to measure the number of catalytic sites in each segment or how the catalytic turnover counting statistics and the catalytic turnover time distribution are related to the microscopic dynamics of catalytic reactions. Here, we address these issues by presenting a stochastic kinetics for nanoparticle catalytic systems. We propose a new experimental measure of the number of catalytic sites in terms of the mean and variance of the catalytic event count. By considering three types of nanocatalytic systems, we investigate how the mean, the variance, and the distribution of the catalytic turnover time depend on the catalytic reaction dynamics, the heterogeneity of catalytic activity, and communication among catalytic sites. This work enables accurate quantitative analyses of single-molecule experiments for nanocatalytic systems and enzymes with multiple catalytic sites.

Background: In the heart data mining and machine learning, dimension reduction is needed to remove the multicollinearity. Meanwhile, it has been proven to improves the interpretation of the parameter model. In addition, dimension reduction is also can increase the time of computing in high dimensional data. Methods: In this paper, we perform high dimensional ordination towards event counts in intensive care hospital , following emergency department (ED 1), First Intensive Care Unit (ICU1), Second Intensive Care Unit (ICU2), Respiratory Care Intensive Care Unit (RICU), Surgical Intensive Care Unit (SICU), Subacute Respiratory Care Unit (RCC), Trauma and Neurosurgery Intensive Care Unit (TNCU), Neonatal Intensive Care Unit (NICU) which use the Generalized Linear Latent Variable Models (GLLVM’s). Results: During the analysis, we measure the performance and calculate the time computing of GLLVM with employing variational approximation and Laplace approximation, and compare the different distributions including Negative Binomial, Poisson, Gaussian, ZIP, and Tweedi, respectively. Conclusions: In a nutshell, GLLVM’s leads as best performance reaching the accuracy 98% comparing other methods. In line with this, we get the best model negative binomial and Variational approximation which provides the best accuracy by accruacy value of AIC, AICc, and BIC. In a nutshell, our best model is GLLVM-VA Negative Binomial with AIC 7144.07 and GLLVM-LA Negative Binomial with AIC 6955.922.

Early warning of a potential rockburst risk and its area of occurrence helps to take effective and targeted measures to mitigate rockburst hazards. This study investigates the microseismic (MS) spatial-temporal precursory characteristic parameters in a typical steeply inclined and extremely thick coal seam (SIETCS) with high rockburst risk and proposes three spatial/temporal quantification parameters and a spatial-temporal early warning method. Analysis results of temporal parameters show that the sharp-rise-sharp-drop variation in total daily energy and event count can be regarded as a precursor for high energy tremor. The appearance of peak values of both energy deviation (≥20) and event count deviation (≥1) can be regarded as precursors that indicate imminent rockburst danger. A laboratory acoustic emission (AE) experiment reveals that precursor characteristics obtained from the study can be feasibly used to warn the rockburst risk. The spatial evolution laws of spatial parameters show that the high energy density index of MS (EDIM), velocity, velocity anomaly regions correlate well with stress concentration and rockburst risk areas. The field application verifies that the temporal-spatial early warning method can identify the potential rockburst risk in a temporal sequence and rockburst risk areas during the temporal early warning period.

Rockburst hazards are frequently encountered in tunnels at the Jinping II hydropower station, which pose serious threats to the safety of personnel and equipment. Abnormal stress concentration caused by the rock mass interfaces and geological defects along the #3 headrace tunnel makes the rockburst difficult to predict using routine estimate and monitoring methods. A two-body interaction model was used to interpret the mechanism of the rockburst, which divided the evolution of a rockburst into three stages, i.e., the stress buildup period, early warning period, and rockburst occurrence period. The microseismic (MS) monitoring technique, which can capture the associated seismicity in the stress buildup period and early warning period, was employed to study and predict the rockburst hazards. An intense rockburst occurred at the right sidewall of the #3 headrace tunnel on September 21, 2011. The rockburst location was recognized by analyzing the spatial-temporal distribution and density contour plot of the recorded MS events from September 12, 2011 to September 21, 2011. Some seismic precursors to the rockburst were obtained based on quantitative interpretation of the source and statistical parameters of the 367 MS events, and they are a sharp increase in the daily event count and average energy level, the energy index remains at extremely high levels accompanied with a rapid increase in the cumulative apparent volume, a sharp decrease in the b value to an extremely low level, and a rapid increase in the seismicity index to an abnormally high level. The multi-parameter precursors to the rockburst should be comprehensively used to improve the prediction accuracy. The validity of using the MS method to predict the rockburst was verified by the preliminary achievement at the #3 headrace tunnel. This study may be valuable to improve the accuracy of rockburst prediction, and helpful for the safety assessment during construction of deep-buried tunnels.

Many atmospheric river detection tools (ARDTs) have now been developed. However, their relative performance is not well documented. This paper compares a diverse set of ARDTs by applying them to a single location where a unique 12-year-long time-series from an atmospheric river observatory at Bodega Bay, California is available. The study quantifies the sensitivity of the diagnosed number, duration, and intensity of ARs at this location to the choice of ARDT, and to the choice of reanalysis data set. The ARDTs compared here represent a range of methods that vary in their use of different variables, fixed vs. percentile-based thresholds, geometric shape requirements, Eulerian vs. Lagrangian approaches, and reanalyses. The ARDTs were evaluated first using the datasets documented in their initial publication, which found an average annual count of 19 ± 7. Applying the ARDTs to the same reanalysis dataset yields an average annual count of 19 ± 4. Applying a single ARDT to three reanalyses of varying grid sizes (0.5°, 1.0°–2.5°) showed little sensitivity to the choice of reanalysis. While the annual average AR event count varied by about a factor of two (10–25 per year) depending on the ARDT, average AR duration and maximum intensity varied by less than ± 10%, i.e., 24 ± 2 h duration; 458 ± 44 kg m− 1 s− 1 maximum IVT. ARDTs that use a much higher threshold for integrated vapor transport were compared separately, and yielded just 1–2 ARs annually on average. Generally, ARDTs that include either more stringent geometric criteria or higher thresholds identified the fewest AR events.

The investigation of relationships between traffic crashes and relevant factors is important in traffic safety management. Various methods have been developed for modeling crash data. In real world scenarios, crash data often display the characteristics of over-dispersion. However, on occasions, some crash datasets have exhibited under-dispersion, especially in cases where the data are conditioned upon the mean. The commonly used models (such as the Poisson and the NB regression models) have associated limitations to cope with various degrees of dispersion. In light of this, a generalized event count (GEC) model, which can be generally used to handle over-, equi-, and under-dispersed data, is proposed in this study. This model was first applied to case studies using data from Toronto, characterized by over-dispersion, and then to crash data from railway-highway crossings in Korea, characterized with under-dispersion. The results from the GEC model were compared with those from the Negative binomial and the hyper-Poisson models. The cases studies show that the proposed model provides good performance for crash data characterized with over- and under-dispersion. Moreover, the proposed model simplifies the modeling process and the prediction of crash data.

Why do some national governments in East and Southeast Asia receive more transnational scrutiny and pressure on their domestic human rights practices than others? This article argues that transnational human rights reporting is more likely to target states where domestic activists and victims are densely connected with human rights international nongovernmental organizations (INGOs) through a local membership base. Human rights INGOs increase social demands and opportunities for transnational human rights reporting by strengthening local actors’ capabilities to leverage human rights and international solidarity as an advocacy strategy, and by mobilizing them for monitoring and information collection on the ground. Event count analyses of 25 Asian states from 1977 to 2008 find robust support for the theory, using new data on Amnesty International's human rights reporting and human rights INGOs’ local membership base, and controlling for government respect for human rights, regime type, military power, and other factors.

Early warning of surrounding rock mass deformation and failure is of great significance for an underground powerhouse and remains a challenge in rock engineering. The microseismic (MS) monitoring technique was adopted for surrounding rock mass deformation forecasting in the underground powerhouse of the Houziyan hydropower station. By analysing the evolution laws of multiple MS parameters, including the MS event count, the energy release, the energy index, the apparent volume, the dominant frequency, the b value, and the fractal dimension, typical abnormal variations prior to a large deformation were obtained, and these MS parameters were found to behave differently. The MS event count appeared with escalating fluctuation as the energy demonstrated a gradually accelerating increase, while the energy index sharply increased with a stable increase of the cumulative apparent volume. Moreover, the dominant frequency, the b value, and the fractal dimension decreased. Accordingly, these MS abnormalities can be regarded as indicators prior to a large deformation of surrounding rock mass. A comprehensive analysis of these MS parameters could allow for better warning and risk assessment of surrounding rock mass deformation and failure in underground caverns.

Conventional practice monitors accumulating information about drug safety in terms of the numbers of adverse events reported from trials in a drug development program. Estimates of between-treatment adverse event risk differences can be obtained readily from unblinded trials with adjustment for differences among trials using conventional statistical methods. Recent regulatory guidelines require monitoring the cumulative frequency of adverse event reports to identify possible between-treatment adverse event risk differences without unblinding ongoing trials. Conventional statistical methods for assessing between-treatment adverse event risks cannot be applied when the trials are blinded. However, CUSUM charts can be used to monitor the accumulation of adverse event occurrences. CUSUM charts for monitoring adverse event occurrence in a Bayesian paradigm are based on assumptions about the process generating the adverse event counts in a trial as expressed by informative prior distributions. This article describes the construction of control charts for monitoring adverse event occurrence based on statistical models for the processes, characterizes their statistical properties, and describes how to construct useful prior distributions. Application of the approach to two adverse events of interest in a real trial gave nearly identical results for binomial and Poisson observed event count likelihoods. Copyright © 2016 John Wiley & Sons, Ltd.

New-onset atrial fibrillation (AF) after coronary artery bypass graft surgery (CABG) is associated with poor outcomes, but data on the effects of its characteristics are lacking and conflicting. We examined the effect number of post-CABG AF events has on long-term mortality risk, and whether this is sex dependent.Routinely collected Society of Thoracic Surgeons (STS) data were supplemented with details on new-onset post-CABG AF (detected in-hospital by continuous electrocardiogram/telemetry monitoring) and long-term survival for 9203 consecutive patients with isolated-CABG (2002-2010). With the use of Cox regression, we determined the propensity-adjusted (STS-recognized risk factors) effect of number of AF events on survival, testing for effect modification by sex and controlling for AF duration.AF occurred in 739 women (29.4%) and 2157 men (32.3%) (P.001). Adjusted results showed 2 or more AF events significantly (P.001) increased 5-year mortality risk, independently of total AF duration. However, mortality risk differed between the sexes (P .001): women with 2 AF episodes had the greatest increase (hazard ratio [HR] = 2.98; 95% confidence interval [CI], 1.43-4.83; versus women without AF), followed by women and men with 4 or more AF events (HR = 2.76 [95% CI, 1.27-4.55] and HR = 2.73 [95% CI, 2.30-3.19], respectively). A single post-CABG AF episode was not associated with increased mortality risk.Both men and women who experienced 2 or more post-CABG AF episodes showed increased risk of 5-year mortality, independent of total AF duration. Although men's risk increased as the number of AF events increased, women's risk peaked at 2 AF events. Future research needs to determine whether this divergence stems from differences in treatment/management or underlying biology.

Fracture networks in coalbed reservoirs serve as the primary gas pathway and thus determine the gas production potential for coalbed methane (CBM) recovery. However, the characterization of the fracture network is extremely challenging due to the complexity of both the induced and natural fracture system. A microseismic event analysis can be used to locate the fracturing, and determine the orientation, length, complexity, and temporal growth of the induced fracture by using the focal mechanism. In this study, the fracture system of a coal-bearing formation covering 1.2 km2 in the Luan mining area of China is probed via passive microseismic imaging. Focal mechanisms of individual events are used to characterize the gas production potential for the 10 CBM wells in this area. Fracture reactivation modes are of three types - strike slip, dip slip, and extensional modes – with strike slip the most common followed by dip slip and then extensional type as the least likely. In addition, the location of different types of fractures are different, which indicates the difference of the in-situ stress regime. The 10 CBM wells were hydraulically stimulated in December 2017 then dewatered and allowed to produce for 14 months. We show that the microseismic data have a general positive correlation with gas production with a few exceptions - the higher the event count, the higher the gas production. This result is a best embodiment of the mutual control of reservoir fractures, stress regime, permeable and gas production in CBM development. We suggest passive microseismic imaging as an effective technique in evaluating the potential for gas production.

Applies the GLM framework to modeling event count data. Discusses the common problem of overdispersion and the methods for extending the model to account for it.

This paper presents a technique to identify a developer based on their IDE event data. We exploited the KaVE data set which recorded IDE activities from 85 developers with 11M events. We found that using an SVM with a linear kernel on raw event count outperformed k-NN in identifying developers with an accuracy of 0.52. Moreover, after setting the optimal number of events and sessions to train the classifier, we achieved a higher accuracy of 0.69 and 0.71 respectively. The findings shows that we can identify developers based on their IDE event data. The technique can be expanded further to group similar developers for IDE feature recommendations.

Advances in the study of civil war have led to the proliferation of event count data, and to a corresponding increase in the use of (zero-inflated) count models for the quantitative analysis of civil conflict events. Our ability to effectively use these techniques is met with two current limitations. First, researchers do not yet have a definitive answer as to whether zero-inflated count models are a verifiably better approach to civil conflict modeling than are ‘less assuming’ approaches such as negative binomial count models. Second, the accurate analysis of conflict-event counts with count models – zero-inflated or otherwise – is severely limited by the absence of an effective framework for the evaluation of predictive accuracy, which is an empirical approach that is of increasing importance to conflict modelers. This article rectifies both of these deficiencies. Specifically, this study presents count forecasting techniques for the evaluation and comparison of count models' predictive accuracies. Usin...

It has a significant and practical meaning for warning precisely gas outburst to reveal microseismic (MS) and acoustic emission (AE) effect of gas outburst precursor. It was thoroughly investigated and discussed on MS and AE effect on an abnormal gas outburst triggered by a strong rockburst using MS- and AE-monitoring systems through spectral analysis technique. We obtained main conclusions are as: (1) MS amplitude prominently decreased prior to outburst, the spectrum significantly moved from extremely low-frequency to high-frequency band, and evolved from “single-peak type” (the center frequency was about 1.5–3.5 Hz) to “multi-peak type” (the peak frequencies were about 25, 50, 75 and 125 Hz, respectively). (2) During the initiative stage of outburst, MS spectrum manifested the broadband distribution, and the predominant frequency was about 20–35 Hz. The high-frequency portion was generated by micro-cracks, and the low-frequency part attributed to macro-fracture for gas outburst channel. (3) The rockburst stimulated micro-fissures formation for gas emission channels, and maintained the event count of MS and AE signals in a relatively higher level, which is a major discrepancy to the common belief that both the total energy and event count should simultaneously and suddenly reduce to the lowest value in a non-outburst coal seam.

Objective How do immigrants become politically active? While this process has been extensively studied, the role of ties to formal and informal institutions of society has been understudied. We test whether informal (political discussion) and formal (connections to community organizations) ties encourage immigrant voters to participate in other campaign activities. Methods Data were collected through a 2008 exit poll of Miami-Dade County, Florida, USA voters. Along with assessing the bivariate relationship between social ties and campaign participation, we use a Poisson event count regression model to control for alternative explanations. Results The positive relationship between social ties and campaign participation among immigrant voters disappears once we control for alternative explanations. There is, however, a positive relationship among the native born (including second-generation immigrants). Conclusion Voters need to acquire personal resources, and become assimilated into American political culture, before social ties have an effect on campaign participation.

The hazard posed from large seismic events is often high enough to warrant the exclusion or evacuation of personnel from underground workings. A period of exclusion is often determined following blasts or large events due to the increased risk. The period of exclusion until re-entry occurs is a decision for site geotechnical engineers and mine management that must balance the potential risk to personnel with lost production time and associated costs. There is currently no widely accepted method for determining reentry times and mine sites typically develop their own rules for exclusions after blasts and large events. A systematic and evidence based approach to the development of re-entry protocols could potentially reduce the risk to personnel from an early re-entry or reduce the lost production from an unnecessary exclusion. Four methods of re-entry assessment have been considered in this paper. The seismic responses at three mines have been modelled and used to optimise each assessment method and gauge the relative success through back-analysis. These same techniques are available for other mines to review their own data and potentially improve their current re-entry protocols. The results of this research indicate that a realtime reentry assessment method can offer improved outcomes compared to blanket re-entry rules by reducing the average exclusion time while still capturing the same number of large events. The incorporation of event size in the assessment can result in better results than the event count. Vallejos and McKinnon (2009) developed a probabilistic framework for re-entry assessment but this method was found to be less efficient than the blanket rule in the majority of cases in this study. The method would also result in more administration and uncertainty for mine planning and scheduling. Several potential improvements to the analysis techniques, and avenues for further research, have been discussed.

Health, fitness, and overall wellbeing of college students depend on a variety of factors and a greater understanding of these factors will ensure that health and wellness interventions directed at students are effective. The widespread use of smartphones provides an opportunity to continuously track students and assess their behaviors and habits, such as mobility trends, social interactions, and academic activities. In this work, we analyze data collected from almost 200 students over three semesters and examine how health and mobility habits differ between Spring semester and Fall semester and how they are impacted by academic and social events. Our analysis shows that social events such as football games increase the students' mobility, but also decrease their usage of athletic facilities. In our study, students are significantly less mobile during the Spring semester compared to the Fall semester and their visits to athletic and spiritual places reduce significantly during exam times. Students' mobility is positively correlated with social event count; however, visits to athletic places are negatively correlated with event count and evening events have the strongest correlation with both mobility and visits to athletic places. These findings will provide useful guidelines for the design of interventions that aim to increase students' mobility and healthy choices during times when attention to health and wellness may suffer otherwise.

Knowledge of the in-situ stresses is essential for underground excavation design, particularly in evaluating stability of excavation. Acoustic Emission method, which utilizes the Kaiser effect, is one of the simple methods for measuring in-situ stresses. Experiments on the Kaiser effect has been carried out under uniaxial compression and triaxial compression (σ1 > σ2 = σ3), but has not been carried out under the three different principal stresses (σ1 > σ2 > σ3). In this study, we performed two experiments on the Kaiser effect under multiaxial loading, using a hollow cylindrical granite specimen. The rapidly increasing point of cumulative AE event count was determined as the peak point of AE event count rate increment (AERI). The main results are summarized as follows. (1) In the case of the cyclic incremental σ1 loading under σ2≠σ3, the large peak point of AERI appeared just before the pre-stress level. And as more stresses prior to just before the peak point were estimated, the estimated error showed a tendency to increase. (2) In the case of re-loading under the lower σ2 and σ3 more than pre-loading, the estimated stresses using the three peak points of AERI corresponded to the pre-differential stresses (σ1-σ2), (σ1-σ3) and pre-axial stress σ1. The magnitudes of the three principal stresses were estimated under multiaxial loading from the Kaiser effect, using only one specimen.

Data from a small air shower array were used to examine the cosmic ray shadow of the Moon at energies more than 100 TeV. A simple technique has been used for the analysis of this data. In this technique the number of EAS events with arrival directions falling in error circles centered about the moving moon is compared to the mean number of events falling in error circles with centers randomly chosen in the sky. For any assumed angular radius of the error circle the deficit in EAS event count in the direction of moon which is a moon-related effect is interpreted as the shadow of the moon. A simple theoretical model has been developed to relate the mean number of EAS events, N sky , to the angular radius of the error circle and has been applied to the counts from the moon’s direction in order to extract the physical parameters of the shadow of the moon. The technique and the theoretical model has been used on 1.7 × 10 5 EAS events recorded by a small air shower array.

While the number of charter schools has increased rapidly in the United States, few studies have examined whether charter schools are implemented in response to real and perceived educational needs or to political and institutional factors in the education policy arena. Unlike traditional policy adoption and diffusion studies that focus on the state level and use a dichotomous dependent variable—adoption or not—this article focuses on local school districts and uses the number of operating charter schools as the dependent variable. Accordingly, instead of applying event history analysis, this article conducts generalized event count regression to estimate models. Based on a data set that consists of Florida's 67 school districts across a six-year time period, the results suggest that charter school diffusion is more heavily driven by political and institutional factors than by educational needs. The results also demonstrate a dynamic trend of charter school diffusion over time.

Correct analysis and interpretation of longitudinal (cohort) studies with partially censored time-to-event data requires that the cumulative count of events and censored observations as well as the number at risk be calculated at appropriate time points (for example, every year), by baseline group or stratum. We present here a simple SAS program, for use in situations in which competing risks do not need to be accounted for, that calculates, by baseline group or stratum, the cumulative event count, cumulative event probability (with upper and lower 95% confidence limits), and number at risk at selected time points that can be chosen by the user. We demonstrate the use of the program in the analysis of longitudinal time-to-event data from a prospective study, the Atherosclerosis Risk In Communities (ARIC) Study, for four groups and a 10-year follow-up. The SAS code presented here is easy to follow and modify and can be incorporated quickly by the user for immediate use. It provides an especially valuable tool for less experienced SAS users.

No abstract available.

Motor activity of humans displays complex temporal fluctuations which can be characterized by scale-invariant statistics, thus documenting that structure and fluctuations of such kinetics remain similar over a broad range of time scales. Former studies on humans regularly deprived of sleep or suffering from sleep disorders predicted change in the invariant scale parameters with respect to those representative for healthy subjects. In this study we investigate the signal patterns from actigraphy recordings by means of characteristic measures of fractional point processes. We analyse spontaneous locomotor activity of healthy individuals recorded during a week of regular sleep and a week of chronic partial sleep deprivation. Behavioural symptoms of lack of sleep can be evaluated by analysing statistics of duration times during active and resting states, and alteration of behavioural organization can be assessed by analysis of power laws detected in the event count distribution, distribution of waiting times between consecutive movements and detrended fluctuation analysis of recorded time series. We claim that among different measures characterizing complexity of the actigraphy recordings and their variations implied by chronic sleep distress, the exponents characterizing slopes of survival functions in resting states are the most effective biomarkers distinguishing between healthy and sleep-deprived groups., Communicated at UPON2015, 14-17 July 2015, Barcelona. 21 pages, 11 figures; updated: figures 4-7, text revised, expanded Sec. 1,3,5

Discrete distributions derived from renewal processes, ie distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities for these distributions. We calculate the count probabilities by repeatedly convolving the discretized distribution, and then correct them using Richardson extrapolation. When just one probability is required, a second algorithm is described, an adaptation of De Pril's method, in which the computation time does not depend on the ordinality, so that even high-order probabilities can be rapidly found. Any survival distribution can be used to model the inter-arrival times, which gives a rich class of models with great flexibility for modelling both underdispersed and overdispersed data. This work could pave the way for the routine use of these distributions as an additional tool for modelling event count data. An empirical example using fertility data illustrates the use of the method and was fully implemented using an R package Countr developed by the authors and available from the Comprehensive R Archive Network., Comment: 20 pages, 6 figures