Probability Distribution Of Time Research Articles

Duration Diabetes Survival Times Modelling Using Some Extended Lomax Distribution

The precise modeling of survival time in diabetes is essential for accurately estimating the potential lifespan of individuals diagnosed with diabetes. One of the key factors in assessing the potential survival times of diabetes patients in a specific region is the probability distribution of diabetes survival times. Therefore, data on diabetes survival times are necessary to conduct statistical modeling, particularly in determining the most suitable probability distribution. Statistical models are developed to draw conclusions about the probability distribution of diabetic patients at the Mandau Regional General Hospital (RSUD) in Bengkalis Regency, Riau Province. To achieve this, six distributions will be utilized and evaluated to identify the best model for describing diabetes survival times. The primary objective of this research is to identify the most appropriate distribution to represent the survival times of diabetes patients from 50 individuals in the Bengkalis region, using the Lomax (LM) distribution, three parameters modified Lomax distributions (Rayleigh Lomax (RL), Logistics Lomax (LL), New Rayleigh Lomax (NRL)) and four parameters modified Lomax Distribution (Odd Lomax Log Logistics (OL), Novel Extended Power Lomax (PL)). The maximum likelihood method will be employed to estimate the parameter values of the distributions used in this study. Additionally, graphical assessments (density-density plot) and numerical criteria (Akaike’s Information Criterion (AIC), -log likelihood (-l)) will be utilized to determine the best-fitting model. In most instances, the results obtained from graphical assessments were consistent but differed from the numerical criteria. The model with the lowest values of AIC and -l was selected as the best fit. Overall, the RL and OL distributions was identified as the most suitable model.

Field Driven Polymer Translocation Through a Nanochannel

In this paper, we used Monte Carlo simulations in two dimension (2D) to investigate field driven polymer translocation through a nanochannel with Bond Fluctuation Method. Accordingly, we studied the static properties of a polymer chain by calculating the mean-squared end-to-end distance 〈 R 2 〉 and the average squared radius of gyration 〈 R g 2 〉 of the polymer. In addition, the scaling behavior of radius of gyration and end-to-end distance with respect to chain length N has been investigated. And we got non-universal and non-monotonic scaling behavior. Moreover, we investigated the probability distribution of the escape time of the chain in the presence of an external field, and the most probable escape times were calculated.The influences of the external force F and the chain length N on the escape time has been also studied in terms of the scaling exponent α and δ ( τ ∼ F − δ and τ ∼ N α ). We found that the scaling exponents α = 2.1 for weak force and 1.80 for strong force; while δ = 0.97 for N = 31 and 0.74 for N = 71. Finally, the effect of the channel size on the translocation time of the polymer has been investigated. Our result indicates that escape times decreases rapidly with increasing channel width and the escape time τ increases with increasing channel length.

Inspiral time probability distribution for two black holes captured by emitting gravitational radiation

Inspiral time probability distribution for two black holes captured by emitting gravitational radiation

Integrated optimization of vessel dispatching and empty container repositioning considering turnover time uncertainty

The global trade disproportion results in the accumulation of containers in import-dominated ports and shortages in export-dominated ports, causing congestion and high freight costs, thus hindering maritime shipping economy development. To address these issues, this study develops a stochastic programming model considering uncertain container turnover times. The model integrates decisions for vessel deployment and empty container repositioning over multiple planning periods through a two-stage decision process, aiming to minimize the total cost, including vessel deployment, container leasing, and penalty costs for unfulfilled demand. By formulating the scenario selection problem as a p-median problem, we effectively reduce the model size. We propose an accelerated Benders decomposition algorithm which leverages the independence of sub-problems in the second stage to enable parallel computation. Numerical experiments show that our Benders decomposition algorithm improves solution speed by over 63% compared to the Gurobi optimization solver. Furthermore, our integrated optimization approach proves to be more cost-effective than the reactive method used by shipping lines, achieving an average cost savings of 0.72%. Additionally, our method of constructing turnover time scenarios to address uncertainty saves approximately 0.45% in costs compared to using the probability distribution of container turnover time.

Arrival Times Versus Detection Times

How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a straightforward way the distribution of the time at which the particle actually does arrive at a given surface in 3-space in the absence of detectors. However, as we discuss here, since the presence of detectors can change the evolution of the wave function and thus the particle trajectories, it cannot be taken for granted that the arrival time of the Bohmian trajectories in the absence of detectors agrees with the one in the presence of detectors, and even less with the detection time. In particular, we explain why certain distributions that Das and Dürr (Sci. Rep. 9: 2242, 2019) presented as the distribution of the detection time in a case with spin, based on assuming that all three times mentioned coincide, are actually not what Bohmian mechanics predicts.

Voyage charterparty arrangement for river tramp shipping: Green and traditional vessels comparison

Voyage charterparty arrangement (VCA) for river shipping is a common agreement between a shipowner and a charterer regarding the transportation of specific cargoes from one port to another via a tramp vessel. Optimizing VCA with the essential terms such as laytime and sailing speed of the vessel, is a crucial task for both parties to reduce potential disputes and achieve win-win outcomes. This paper models the problem from two perspectives: the VCA negotiation stage and execution stage. Firstly, according to the given probability distribution of port time, the theoretically optimal laytime is obtained by using textbook formulation of newsvendor problems (NVP). On this basis, considering the concerns about the inaccuracy of the given probability distribution and the adjustment measures taken by charterers and shipowners in reality, an integrated adjustment model is constructed to determine the optimal laytime in the VCA negotiation stage. Secondly, taking into account the vessel's uncertain lock crossing time, an operations coordination model with information sharing of the berth plan is established to obtain the optimal sailing speed under a certain confidence level in the VCA execution stage. Finally, a case study of chartering tramp vessels on the Yangtze River validates the applicability and effectiveness of the models proposed in this paper, and some important management insights are derived. The results show that establishing lower optimal speed limits and relatively shorter laytime when signing a contract with the shipowner of green river vessels is reasonable for the charterer. By notifying the shipowner of the berth plan after the green river vessel crosses through the lock, the charterer can avoid higher demurrage costs due to speeding-up. Operations coordination would be mutually beneficial without abusing the contract terms. Compared to traditional river vessels, it's more reasonable to reduce the benefits allocated to charterers from the deceleration of green river vessels by shipowners.

An asset management modelling framework for wind turbine blades considering monitoring system reliability

By incorporating information about asset condition from a monitoring system, engineers can utilize asset management models to manage maintenance activities on wind turbine blades throughout their lifespan. This can lower operating and maintenance costs and increase the life of the blades. The asset management model relies on the monitoring system as a source of information, however, commonly the reliability of the monitoring system is not considered. This paper presents a wind turbine blade asset management Petri net (PN) model that covers the blade asset management process, including degradation, inspection, condition monitoring (CM), and maintenance processes. The paper proposes two contributions. Firstly, while taking into account detailed industry guidelines, the developed model can forecast the future blade condition for a given asset management strategy. Secondly, it investigates the impact of the reliability of the monitoring system on the asset management modelling results. With the aid of the developed model, the number of repair actions and probability distributions of blade condition discovery time are obtained. In addition, the PN gives an indication of how misreporting (underestimation and overestimation) occurs and the extent of the misreporting. The simulation results illustrate the degree of uncertainty introduced into the monitoring results by the reliability of the monitoring system and, consequently, the extent to which this factor influences the maintenance strategies. The proposed model can be used to support asset management decisions when monitoring system performance degrades.

Uncertainty modeling and propagation for groundwater flow: a comparative study of surrogates

We compare sparse grid stochastic collocation and Gaussian process emulation as surrogates for the parameter-to-observation map of a groundwater flow problem related to the Waste Isolation Pilot Plant in Carlsbad, NM. The goal is the computation of the probability distribution of a contaminant particle travel time resulting from uncertain knowledge about the transmissivity field. The latter is modelled as a lognormal random field which is fitted by restricted maximum likelihood estimation and universal kriging to observational data as well as geological information including site-specific trend regression functions obtained from technical documentation. The resulting random transmissivity field leads to a random groundwater flow and particle transport problem which is solved realization-wise using a mixed finite element discretization. Computational surrogates, once constructed, allow sampling the quantities of interest in the uncertainty analysis at substantially reduced computational cost. Special emphasis is placed on explaining the differences between the two surrogates in terms of computational realization and interpretation of the results. Numerical experiments are given for illustration.

An analytical approach to evaluate life-cycle cost of deteriorating pipelines

Optimal inspection and maintenance planning for deteriorating pipelines is important for cost-effective risk management decisions. The objective of this study is to develop an analytical approach for determining the expected value and standard deviation of life-cycle cost (LCC) for deteriorating pipelines, which can incorporate imperfect repair and inspection actions without making independent assumptions of failure and repair events. The framework is developed based on a decision tree model by using analytical methods to evaluate events and considers the impact of the inspection schedules and possible repair actions on the probability distributions of failure times. To illustrate the proposed framework, a steel transmission pipeline with a corrosion defect is used, where a stochastic model of corrosion growth is assumed and burst failure is considered as the pipeline failure mode. The case study indicates that the failure cost due to two or more failure occurrences can be ignored; and the inspection interval, repair threshold and type, the length of lifetime considered, and unit failure cost all play important roles in the expected value of the total cost. The variation in the LCC estimation is found to be significant, and it has a great impact on determination of optimal decision variables.

Reduced human fecundity attributable to ambient fine particles in low- and middle-income countries

BackgroundExposure to ambient fine particulate matter (PM2.5) has been associated with reduced human fecundity. However, the attributable burden has not been estimated for low- and middle-income countries (LMICs), where the exposure–response function between PM2.5 and the infertility rate has been insufficiently studied. ObjectiveThis study examined the associations between long-term exposure to PM2.5 and human fecundity indicators, namely the expected time to pregnancy (TTP) and 12-month infertility rate (IR), and then estimated PM2.5-attributable burden of infertility in LMICs. MethodsWe analyzed 164,593 eligible women from 100 Demographic and Health Surveys conducted in 49 LMICs between 1999 and 2021. We assessed PM2.5 exposures during the 12 months before a pregnancy attempt using the global satellite-derived PM2.5 estimates produced by Atmospheric Composition Analysis Group (ACAG). First, we created a series of pseudo-populations with balanced covariates, given different levels of PM2.5 exposure, using a matching approach based on the generalized propensity score. For each pseudo-population, we used 2-stage generalized Gamma models to derive TTP or IR from the probability distribution of the questionnaire-based duration time for the pregnancy attempt before the interview. Second, we used spline regressions to generate nonlinear PM2.5 exposure–response functions for each of the two fecundity indicators. Finally, we applied the exposure–response functions to estimate number of infertile couples attributable to PM2.5 exposure in 118 LMICs. ResultsBased on the Gamma models, each 10 µg/m3 increment in PM2.5 exposure was associated with a TTP increase by 1.7 % (95 % confidence interval [CI]: -2.3 %–6.0 %) and an IR increase by 2.3 % (95 %CI: 0.6 %–3.9 %). The nonlinear exposure–response function suggested a robust effect of an increased IR for high-concentration PM2.5 exposure (>75 µg/m3). Based on the PM2.5-IR function, across the 118 LMICs, the number of infertile couples attributable to PM2.5 exposure exceeding 35 µg/m3 (the first-stage interim target recommended by the World Health Organization global air quality guidelines) was 0.66 million (95 %CI: 0.061–1.43), accounting for 2.25 % (95 %CI: 0.20 %–4.84 %) of all couples affected by infertility. Among the 0.66 million, 66.5 % were within the top 10 % high-exposure infertile couples, mainly from South Asia, East Asia, and West Africa. ConclusionPM2.5 contributes significantly to human infertility in places with high levels of air pollution. PM2.5-pollution control is imperative to protect human fecundity in LMICs.

An essay on semiclassical analysis for microlocal singularities, turbulence intensity and integration of singularities by Schrödinger equation in probabilistic behavior

The Schrödinger equation governs the probabilistic behavior of quantum particles through the wave function. Microlocal singularities denote regions with significantly high probability density or abrupt changes therein. By visualizing the probability distribution in time and space, we discern regions with higher probability density, indicative of potential microlocal singularities. These regions probably correspond to areas with a greater probability of particle presence. Such analysis aligns with Theorem 1, predicting characteristics of microlocal singularities of wave functions. Furthermore, Theorem 2 postulates that semiclassical path integrals along these singularities contribute significantly to solving the Schrödinger equation. Interpreting the temporal evolution of the probability density in the probability distribution visualization reveals the propagation of the particle over time. Regions of high density mean likely presence of particles at specific times, aligning with the predictions of Theorem 2. Consequently, the analysis of the contribution of high-density regions to the temporal evolution of the wave function resembles semi-classical path integral calculations. Thus, our findings demonstrate that visualization of probability distributions obtained from the numerical resolution of the Schrödinger equation allows a comprehensive interpretation of the behavior of quantum particles, consistent with the theorems.

Prediction of hourly wind speed time series at unsampled locations using machine learning

Various models for wind speed mapping have been developed, with increasing attention on models focusing on mapping wind speed distribution. This study extends these models to predict hourly wind speed time series at unsampled locations. A model based on the quantile mapping (QM) procedure was compared to a traditional and machine-learning model to interpolate wind speed spatially. These proposed models were also used with inputs from the ERA5 reanalysis dataset, enabling them to consider local variation in orography and large-scale wind fields. A widely used procedure for mean bias correction of reanalysis based on the Global Wind Atlas (GWA) was implemented and compared to the proposed models. It was found that the QM and machine learning model, both using input from ERA5, significantly outperformed GWA bias correction in terms of time series correlation and probability distribution. Despite being more computationally intensive than GWA bias correction, both models are recommended due to their significantly (in a statistical sense) superior performance.

Occupation time of a system of Brownian particles on the line with steplike initial condition.

We consider a system of noninteracting Brownian particles on the line with steplike initial condition and study the statistics of the occupation time on the positive half-line. We demonstrate that even at large times, the behavior of the occupation time exhibits long-lasting memory effects of the initialization. Specifically, we calculate the mean and the variance of the occupation time, demonstrating that the memory effects in the variance are determined by a generalized compressibility (or Fano factor), associated with the initial condition. In the particular case of the uncorrelated uniform initial condition we conduct a detailed study of two probability distributions of the occupation time: annealed (averaged over all possible initial configurations) and quenched (for a typical configuration). We show that at large times both the annealed and the quenched distributions admit large deviation form and we compute analytically the associated rate functions. We verify our analytical predictions via numerical simulations using importance sampling Monte Carlo strategy.

Response times are affected by mispredictions in a stochastic game

Acting as a goalkeeper in a video-game, a participant is asked to predict the successive choices of the penalty taker. The sequence of choices of the penalty taker is generated by a stochastic chain with memory of variable length. It has been conjectured that the probability distribution of the response times is a function of the specific sequence of past choices governing the algorithm used by the penalty taker to make his choice at each step. We found empirical evidence that besides this dependence, the distribution of the response times depends also on the success or failure of the previous prediction made by the participant. Moreover, we found statistical evidence that this dependence propagates up to two steps forward after the prediction failure.

First passage time and peak size probability distributions for a complex epidemic model

First passage time and peak size probability distributions for a complex epidemic model

Calculation of Epidemic First Passage and Peak Time Probability Distributions

Calculation of Epidemic First Passage and Peak Time Probability Distributions

Spatiotemporal variability of streamflow in the Pearl River Basin: Controls of land surface processes and atmospheric impacts

AbstractTo advance understanding of the spatiotemporal variability of the streamflow in the Pearl River Basin (PRB), we used the Soil and Water Assessment Tool model to simulate the water fluxes from 2010 to 2020 and to identify the underlying controlling mechanisms. The streamflow in the PRB is highly variable and controlled by complex land surface processes and atmospheric impacts over the heterogeneous terrain. Two key factors primarily govern the streamflow: (1) the location of the active precipitation zone, which is determined by the interaction between the monsoon path and uplifting effect of the terrain, and (2) the redistributions resulting from land use and soil characteristics. We observe distinct patterns in the different water fluxes across the different regions. Specifically, surface flow exhibits the highest activity within the precipitation zone. Lateral flow and actual evapotranspiration (AET) have the greatest intensity in the forests and in agricultural regions, respectively, and the aquifer flow is more active in areas with coarse soil textures. The land surface processes of the AET and aquifer retention significantly govern the temporal variability of the streamflow, contributing to the precipitation and streamflow being out of phase in the PRB. Based on the underlying mechanisms driving streamflow variability, we classify the PRB into three substreams: a drought‐prone upstream, a hydrologically active midstream, and a typhoon‐affected downstream, and each substream exhibits distinct spatiotemporal characteristics of streamflow. We find that the time series and probability distributions of the streamflow at different tributaries within each substream are similar. Each probability distribution is multimodal and can be decomposed into three unimodal distributions representing dry, transitional, and wet conditions. Specifically, the PRB features a large and steep dry mode, a flat transitional mode, and a short wet mode.

Survey of Lactating Anesthesiologists Using Wearable Breast Milk Pumps While Working in Operating Rooms and Other Clinical Settings.

We performed a prospective Internet survey study of anesthesiologists lactating in 2022 or 2023. Approximately half (48%, 75 of 156) lacked convenient dedicated lactation space and approximately half (55%, 86 of 155) used a wearable breast pump. The vast majority using a wearable pump did so in clinical settings, including operating rooms (88%, 76 of 86). When using during cases, approximately half reported that milk production was sufficient to substitute for lactation pumping sessions (52%, 39 of 75). Based on probability distributions of surgical times, future research can evaluate the usefulness of wearable pumps based on the objective of reducing anesthesiologists' durations of lactation sessions to <15 minutes.

Optimal ordering based on shortage scenarios under presence of a low-quality substitute and supply uncertainty

Global trade has shifted from short-distance supply chains within countries to long-distance supply chains between countries. As a result, delivery lead time has become a key operational factor, and uncertainty causes stock-outs, resulting in massive losses. An important solution for shortages is product substitutes, but they can affect the quality of the end products. Moreover, even when demand is expected and planned for, unexpected last-minute demand makes operational conditions challenging. This paper considers a single-period problem of replenishing a high-quality product under both lead time and demand-related uncertainty. Stock-outs during and at the end of the replenishment period can be handled only by providing a low-quality substitute product that requires repeated replacements, therefore affecting pending demand. We provide detailed modeling of possible stock-out scenarios and show that, in presence of these two types of uncertainty, the optimal order quantity of a high-quality product can be determined using an upper and lower threshold and a base stock level equal to anticipated (planned) demand over the replenishment period. In particular, we derive a closed-form solution for the optimal order quantity under general probability distributions of lead time and demand and explicit solutions for uniform distributions. We also show the conditions under which optimal order quantities can be insensitive to the cost of the high-quality product.

Observed trends in timing and severity of streamflow droughts across global tropics

Drought is a recurrent climatic hazard impacting natural and built environmental systems, including human lives. Although several studies have assessed streamflow droughts and their multivariate characterization, very few studies have focused on understanding spatiotemporal changes in drought attributes, such as drought seasonality, severity and duration across global tropics. Further, the nonlinear response between onset time and severity of streamflow droughts at a large scale are unknown. Leveraging ground-based streamflow observations, this study for the first time investigate changes in streamflow drought characteristics across global tropics using two 30 year climate normal periods: 1961–1990 and 1991–2020. Our analyses of changes in probability distributions of onset time and severity (deficit volume) of streamflow droughts over the two time windows show significant shifts towards higher values for Northeast and South American Monsoon region, Western Africa, eastern South Africa, north and eastern Australia. Around 55% of the sites show an increase in drought frequency in recent times. We found that in the recent times, only 27% of sites depict an increase in deficit volume accompanied by delayed onset. Further, we identify a few regional hotspots, such as Northeast and South American monsoon region, and eastern coast of Australia show an increased frequency of droughts with an upward trend in deficit volume in recent years. As expected, the individual changes in drought attributes have translated into changes in joint occurrences of their interdependent attributes, assuming the correlation between onset time and deficit volume. Our analyses show robust dependence strengths between onset time and deficit volume, which strengthen further in the recent time window over 50% of catchments. The nonstationary changes identified here in individual drought attributes and their joint dependence can alter the hazard potential of extreme droughts, which has consequences in risk management, climate adaptation and water resources planning.