Cumulative Probability Values Research Articles

Probabilistic Evaluation of Hydraulic Fracture Performance Using Ensemble Machine Learning

Evaluation of hydraulic fracture (HF) performances is critical to develop unconventional resources such as tight oil and gas. We present a probabilistic evaluation approach that integrates ensemble machine learning with Monte Carlo simulation. In the method, we employ the ensemble learning to develop a predictive model between well productivity and its influential factors including both geological properties and HF treatment parameters. Next, coupling the built prediction model with Monte Carlo simulation, an empirical cumulative probability distribution of the well productivity is generated. The well HF performance is assessed by estimating its cumulative probability value. The proposed method is applied to evaluate the HF performances in a developed block of the eastern Sulige region. The study shows that 19% of the wells were fractured with good quality and 55% of the wells were fractured with average quality, while the rest were stimulated with poor quality. The evaluations provide a guideline for optimization of HF designs of wells that have not been hydraulically stimulated in the region.

Health risks from multiroute exposure of potentially toxic elements in a coastal community: a probabilistic risk approach in Pangkep Regency, Indonesia

Populations in coastal areas are vulnerable to chronic exposure to potentially toxic elements (PTEs) from aquatic ecosystems. In this study, we estimated the health risks from Cd, Cr, Fe, and Pb exposure in river water, sediments, and edible aquatic biota (Anadara granosa and Chanos chanos). Human daily intake was determined by an interview process with 287 respondents that were selected by proportional cluster random sampling. The cumulative probability value for total risk exceeded the acceptable limit value, indicating that adverse health impacts from PTE exposure may occur in the Pangkep coastal population. The sensitivity analysis showed that exposure duration and Cr concentrations are the factors with the greatest influence in a recreational exposure scenario, whereas the frequency of exposure to shellfish and milkfish is the most influential factor for health risks in a residential scenario. Thus, reducing Cr concentrations in river water, restricting swimming duration, and limiting the frequency of shellfish and milkfish consumption are required to mitigate health risks in the future.

Multi-blockchain-based Privacy Access Control Technique for 5G IoT/IoB

5G 기술이 다양한 환경의 사용되면서 5G 기반의 다양한 알고리즘 및 암호 기법들이 제시되고 있다. 그러나, 현재까지 연구되고 있는 서비스들은 5G 환경을 완벽하게 지원되고 있지 못하는 문제점을 가지고 있다. 본 논문에서는 5G 환경에서 IoT/IoB 장치를 사용하는 사용자의 프라이버시 정보를 안전하게 보호하기 위한 다중 블록체인 기반의 접근 제어 기법을 제안한다. 제안 기법은 5G 정책에 따라 다양하게 액세스 처리가 이루어지고 있기 때문에 사용자의 프라이버시 정보가 제3자에게 노출될 수 있는 부분을 해결하기 위해서 다중 블록체인을 사용하여 사용자의 프라이버시를 보호한다. 특히, 제안 기법은 다중 블록체인을 사용하기 위해서 IoT/IoB 장치를 계층적으로 3계층(n-1, n, n+1)으로 구성한 후 쌍방향 인증이 가능하도록 임의의 랜덤키를 2개 사용하여 서로 중복되지 않도록 교차 사용하고 있다. 또한, 제안 기법은 다중 블록체인을 사용하기 때문에 IoT/IoB 프라이버시 정보에 가중치 정보와 누적 확률 값을 이용하여 IoT/IoB 프라이버시 정보의 무결성에 대한 정확도를 향상시키고 있다.As 5G technology is increasingly used in various environments, numerous 5G-based algorithms and encryption techniques are being proposed. However, any services being studied so far have a problem in that they are not fully supported in the 5G environment. This paper proposes a multi-blockchainbased access control technique to safely protect the privacy information of users using IoT/IoB devices in a 5G environment. Since various access processes are performed according to 5G policies, the proposed technique implements a multi-blockchain to protect the privacy of users in areas where user privacy information may be exposed to third parties. In particular, the proposed technique employs two random keys to enable interactive authentication after hierarchically configuring IoT/IoB devices into three layers (n-1, n, n+1) to use multiple blockchains. In addition, since the proposed technique uses multiple blockchains, the accuracy of the integrity of IoT/IoB privacy information is improved by including weight information and cumulative probability values in the IoT/IoB privacy information.

Internet of Medical Things-Based Multiple Data Processing Techniques Optimized for Healthcare Environments

As IT technology has recently been combined with portable device (smartphones, tablets, etc.), demands for state-of-the-art infrastructure are growing. Among them, there is a need for IoMT technology that combines big data and IoT technologies into healthcare. In this paper, we propose a distributed management technique that can efficiently manage the health care (monitoring and chronic disease management, etc.) information of remote patients by applying various artificial intelligence-related technologies (big data analysis, blockchain, deep learning, etc.) to IoMT technology. The proposed technique facilitates the collection and management of data by equating the basic management structure of the data with the existing patient model of the hospital. In particular, since the information collected from the IoMT sensor is composed of multiple blockchains, the task weight of the endpoints is minimized. Also, the proposed technique improved the accuracy of the IoMT information by using the stratified cumulative probability values of the IoMT sensor information. Proposed technique have improved the efficiency of data collection processing by 14.7% over conventional techniques by automating the linkage between IoMT equipment on the central server for all actions of the IoMT device.

Applicability of a reduced order model for a safety analysis code to statistical safety analysis

ABSTRACT A reduced order model (ROM) for a safety analysis code (RELAP/SCDAPSIM) is developed and is applied to the statistical safety analysis in order to reduce computational load. The ROM that reproduces output of the safety analysis code (e.g., the peak cladding temperature) is constructed using the singular value decomposition and the low-rank approximation for time-series data of a safety analysis code. A sampling method that incorporates dissimilarity among input data is tested to generate training data for the ROM. A loss of coolant accident with multiple failures of safety functions in a BWR is considered as an accident scenario. Statistical results such as the average, the standard deviation, and the 95% cumulative probability value of safety parameters obtained by the ROM and those obtained by the safety analysis code are compared. The reference results obtained by the direct random sampling method with the safety analysis code are within the 95% confidence interval of the results obtained by ROM. Thus the applicability and effectiveness of the ROM to the statistical safety analysis are confirmed through numerical analysis.

Utilizing Gompertz curve to calculate median, mean and sorting of grain-size distribution (GSD)

In traditional calculating median, mean and sorting of grain-size distribution (GSD) by Folk and Ward (1957), graphing cumulative probability curves and estimating grain-sizes are tedious and slow for vast samples. Taking 88 samples of cores in Well Y1 in Gasikule Oilfield, Qaidam Basin, as the primary material, a new approach to calculate these three parameters is proposed in this paper, which is based on sigmoidal Gompertz curve and Folk-Ward Formula. Establishing Gompertz curve to fit cumulative probability values is the first stage. Solving the coefficients of Gompertz curve using least-squares algorithm is the second stage. Calculating median, mean and sorting of GSD by Gompertz inverse function in Folk-Ward Formula is the third stage. Coefficient of determination between fitted and laboratorial cumulative probability values are ranged from 0.994 to 1, and that of frequency values are larger than 0.565. The coefficients of determination of calculated and laboratorial median, mean and sorting of 88 samples are 0.9960, 0.9943 and 0.5416 respectively. The results demonstrate that the proposed method is feasible and effective to fit the cumulative probability values of GSD, and calculate median and mean in Folk-Ward Formula.

Normal Information Diffusion Distribution and Its Application in Inferring the Optimal Probability Density Functions of the Event Coordinates From the Microseismic or Acoustic Emission Sources

To obtain optimal probability density functions (PDFs) or cumulative density functions (CDFs) of the event coordinates from the microseismic or acoustic emission sources, the normal information diffusion (NID) method based on the “ $3\sigma $ ” truncated interval is introduced. Six sets of different data of the event coordinates from the locating sources are used to illustrate the goodness-of-fit of the NID method, log-logistic (3P) method, lognormal method, and normal method. The results show that the Kolmogorov-Smirnov (K-S) and chi-square test values of the NID distributions (NIDDs) are always less than those of the log-logistic (3P) distributions (LLD3s), lognormal distributions (LNDs), and normal distributions (NDs); the cumulative probability values of the NIDDs are equal to 1, while those of the LLD3s, LNDs, and NDs are less than 1; the curves of the NIDDs have multimodal feature and can reflect the fluctuation of the event coordinates’ data. The conclusion can be drawn that the NIDDs are the optimal PDFs or CDFs of the event coordinates from the microseismic or acoustic emission sources. In the locating methods of the microseismic or acoustic emission sources, it is suggested that the NID method can be further used to improve the locating accuracy.

Inference of the optimal probability distribution model for geotechnical parameters by using Weibull and NID distributions

To obtain the optimal probability distribution models of geotechnical parameters, the goodness of fit of the normal information diffusion (NID) distribution and Weibull distribution were investigated and compared for actual engineering samples and Monte Carlo (MC) simulated samples. Two datasets from actual engineering parameters (the strength of a rock mass and the average wind speed) were used to test the fitting abilities of these two distributions. The results show that the parameters of the NID distribution are easily estimated, the Kolmogorov-Smirnov (K-S) test results of the NID distribution are smaller than those of the Weibull distribution, and the NID distribution curves can perfectly reflect the stochastic volatility of geotechnical parameters with small sample sizes. The sample size effects on the fitting accuracy of the NID distribution and Weibull distribution were also investigated in this paper. Eight simulated samples with different sample sizes, namely, 15, 20, 30, 50, 100, 200, 500, and 1000, were produced by using the MC method based on two known Weibull distributions. The results show that with an increase in the sample size, the K-S test results of the NID distribution gradually decrease and tend to converge, while the chi-square test results of the NID distribution remain low and are always lower than those of the Weibull distribution. The cumulative probability values of the NID distribution are larger than those of the Weibull distribution and are always equal to 1.0000. Finally, the comparison of the fitting accuracy between the NID distribution and normalized Weibull distribution was also analyzed.

Calculating heterogeneity of Majnoon Field/Hartha reservoir using Dykstra Parsons method

One of the principle concepts for understanding the hydrocarbon field is the heterogeneity scale; this becomes particularly challenging in supergiant oil fields with medium to low lateral connectivity in carbonate reservoir rocks.
 The main objective of this study is to quantify the value of the heterogeneity for any well, and propagate it to the full reservoir. This is quite useful specifically prior conducting detailed water flooding or full field development studies and work, in order to be prepared for a proper design and exploitation requirements, which fits with the level of heterogeneity of this formation.
 The main tool used for these purposes is the application of the famous Lorenz coefficient method, in conjunction with the Dykstra Parsons technique for calculating the degree of heterogeneity for any well. 
 The starting point for this kind of complicated studies needs to start from the basics. In order to understand the big picture and be able to plan properly for the scope to be delivered. Utilizing analytical tools like the ones mentioned above becomes quite necessary, if not crucial, to the success of full field modelling and choosing an optimum water flood pattern and design.
 This work covers the methodology for quantifying and calculating the level of heterogeneity in a given reservoir.
 The Dykstra-Parsons Coefficient or the variation of Dykstra Parsons (VDP) is commonly used in calculating permeability variation. The method of calculating begins by sorting the property of interest and make the other property fixed value (to calculate permeability you have to make porosity a fixed value for all calculations) and make permeability in order of decreasing magnitude.
 For each of the values calculate the percentage of values greater or the ‘cumulative probability’, so that the probability of X is P(x≤X). Then plot the original permeability values on a log probability graph with the cumulative probability values. The slope value and the intercept of the line of the best fit, for all data are used to calculate the 50th and 84th probability values or by variation layering system to calculate the variation of P10, P50 and P90, which are used to find VDP.
 This methodology has been tested successfully in the stated super giant oil field, in which the reservoir is a carbonate rock formation. The reservoir is areally extensive reservoir and not of a great thickness.
 The importance of this step is to conclude a utilizing heterogeneity calculation method before conducting any detailed reservoir simulation study. It can save a lot of time and effort by providing guidance to the path, which needs to be followed, and sheds light on the critical elements to be looked after. This also can help to uncover many insights on the reservoir itself, hence allowing the engineer to plan for the necessary voidage replacement and water injection rates to sustain the reservoir pressure and pattern development based on the magnitude of heterogeneity those results from this procedure.
 The suggested method, in combination with geological and petrophysical information available, can be applied to majority of the reservoirs. This combination is paramount to ensure optimum time and planning is followed for each reservoir development study that involves for example water flooding

Human-induced vibration serviceability assessment of the floor based on the full path of the source-path-receiver

The acceleration peak of the structure response is a common method to evaluate the vibration serviceability, while the perception (human) is the only perceptual body to judge whether it is comfortable or not, and the response of the structure to judge the comfort of the human is not comprehensive enough. In order to comprehensively evaluate the vibration serviceability of the floor, the framework of human-induced vibration serviceability assessment of the floor based on full path of the source-path-receiver is proposed. And the coupled vibration governing equation of source-path-receiver is established and dealt with differential quadrature-integral quadrature method (DQ-IQ) mixing method, and the acceleration response of the floor and the perceptron can be obtained by the Newmark method, and the vibration serviceability of the structure is evaluated by the probabilistic method. The CFS composite floor is selected as an example to calculate the acceleration responses of floor and perception under different frequencies respectively by mode decomposition method and DQ-IQ method. Comparing the calculation results of the two methods, the accuracy of the DQ-IQ method is verified. When pedestrians pass through the floor at slow, medium speed and fast pace of step frequency, the probability value corresponding to the specific acceleration peak and and the cumulative probability value less than or equal to a specific acceleration peak are obtained of floor and perception. The peak acceleration of the perception is compared with the peak acceleration of the floor at the same cumulative probability value, which is based on the cumulative probability value of the peak acceleration less than or equal to 0.05 m/s2 by assuming that the perception and structure have the same serviceability limits. The results show that increasing the damping ratio of the floor can increase the serviceability probability, and the peak acceleration of the perception is greater than the acceleration peak of the floor under the same conditions, so it is necessary to consider increasing the peak acceleration of the perception as a reference for evaluation of vibration serviceability.

Most effective pain-control procedure for open liver surgery: a network meta-analysis.

To determine the most effective pain-control procedure for open liver surgery through a network meta-analysis and provide a best developing direction in this field. PubMed, Embase and Cochrane Library database were searched for randomized controlled trials up to 1 July 2016. We extracted data on post-operative pain score at the 4th-8th hour and 24th hour from studies that compared various pain-control strategies. Network meta-analysis was conducted in Aggregate Data Drug Information System software by evaluating the parametric pain score at rest and on movement. Cumulative probability value was utilized to rank the procedures under examination. The inconsistency would also be tested by node-splitting models. Twelve articles containing 661 patients were included. Intrathecal analgesia plus intravenous analgesia played the most effective role in pain controlling at post-operative 4-8 h (both at rest and on movement, P = 0.49 and P = 0.62, respectively) and at post-operative 24 h (both at rest and on movement, P = 0.46 and P = 0.29, respectively). Node-splitting models test revealed that no significant inconsistency existed in this research. Intrathecal analgesia plus intravenous analgesia revealed the most effective clinical pain-control value for open liver surgery. More importantly, we believed that creating a better comprehensive and systematic combined pain-control procedure should be considered as the developing direction in this field.

Techno-economic analysis for CO2 reforming of a medium-grade landfill gas in a membrane reactor for H2 production

In this paper, we report techno-economic analysis for CO2 reforming of a medium-grade landfill gas in a membrane reactor (MR) for a H2 production capacity of 7 m3 h−1 in Korea. Parametric studies for the effect of key operating conditions like a H2 permeance, a H2O sweep gas flow rate, and temperature on the performance in a conventional packed-bed reactor (PBR) and a MR were conducted using Aspen HYSYS®, a commercial process simulator. Based on process simulation studies, economic analysis was carried out to find a unit H2 production cost for both a PBR and a MR. Respective unit H2 production costs of 9.72 and 6.46 $ kgH2−1 were obtained for a PBR and a MR showing about 34% reduction in the MR. Sensitivity analysis was employed to identify key economic factors to determine a unit H2 production cost with labor the most influential factor for both reactors. Probability analysis (PA) was performed with influential factors based on a Monte-Carlo simulation method as uncertainty analysis and a cumulative probability (CP) curve was created for a PBR and a MR under various discount rates from 2 to 10% and key factor ranges from ±10 to ±40%. PA using stochastic approach provided a wide range of a unit H2 production cost coupled with its probability and a critical CP value at which the effect of key factor range on a unit H2 production cost was reversed.

The best surgical strategy for anal fistula based on a network meta-analysis.

ObjectiveTo determine a superior surgical treatment for anal fistula through a network meta-analysis and to provide the best direction for development in this field.MethodsWe conducted a systematic literature search of the PubMed, Embase and Cochrane Library databases and extracted data from randomized controlled trials, which compared healing time, incontinence and recurrence associated with surgical strategies for anal fistula. A network meta-analysis was conducted using ADDIS software by evaluating the 3 parameters. Cumulative probability values were utilized to rank the strategies under examination. Inconsistencies were also tested using node-splitting models.ResultsTwenty articles with 1663 patients were included. Fistulotomy plus marsupialisation had the shortest healing time (P = 0.69). Seton placement was the best procedure to avoid postoperative incontinence (P = 0.66). Fistulectomy exhibited the lowest recurrence rate (Probability P = 0.40). In general, fistulotomy plus marsupialisation and surgical ligation plus biomaterial plugging revealed superior clinical efficacy. Node-splitting model testing revealed that no significant inconsistency existed in this research.ConclusionsFistulotomy plus marsupialisation exhibited preliminary superior surgical utility for anal fistula. Additionally, combination of surgical treatment with biomaterials may provide better clinical efficacy. These techniques may warrant consideration for future development in this field.

The best strategy for HCC patients at each BCLC stage: a network meta-analysis of observational studies.

Background and AimsCurrently, the Barcelona Clinic Liver Cancer staging system remains huge controversies in the management of hepatocellular carcinoma. To determine the best therapeutic strategy for patients at each stage, we conducted a network meta-analysis and aimed to provide a new treatment concept.Materials and MethodsPubMed, Embase and Cochrane Library database were searched for observational studies up to August 31, 2016. We extracted data on overall survival rate from studies that compared various strategies for use with patients at different stages. Network meta-analysis was conducted by evaluating the different overall survival rate of each stage. Cumulative probability value was utilized to rank the strategies under examination. A node-splitting model was employed to assess consistency and inconsistency.ResultsA total of 198 observational studies were included in the network meta-analysis with a focus on Stages 0-D. By comparing the overall survival rate of each stage, the results revealed that liver transplantation and liver transplantation plus transcatheter arterial chemoembolization were the best options for patients with Stages 0 and A. The applications of surgical resection plus transcatheter arterial chemoembolization and surgical resection plus sorafenib were the best strategies for Stages B and C. For Stage D, whole net connection could not be established, but intra-arterial infusion chemotherapy and liver transplantation could be potential primary options.ConclusionsThe existing therapeutic flowchart needs to be updated. Potential best strategies relating to all stages were identified and should be used as references for clinical treatments.

Climate change impacts on agriculture and irrigation in the Lower Mekong Basin

According to hydrological simulations by the Mekong River Commission, average annual flow of the Mekong will not change significantly despite climate change. However, they projected increased variability in wet and dry season flows, which will tend to increase the flood and drought risks to crops. To learn the implications of climate change for rice farming in the Lower Mekong Basin (LMB), a lower part of the Basin from China-Lao PDR border to the South China Sea, climate and hydrological figures related to rice production were compared in between the baseline in 1985–2000 and the climate change scenario in 2010–2050. Special attention was given to their 10 and 90 % exceedance values, which are rough equivalence of 10 and 90 % cumulative probabilities, to see changes in the frequency and extent of extreme weather events. Major findings of this study include the followings: (1) evapo-transpirations will increase in both average and 90 % cumulative probability values, raising irrigation demand. (2) Deviation of the annual rainfall will become larger, causing water shortage in reservoirs more frequently in the future. (3) The transplanting date of rain-fed rice will be delayed more likely due to insufficient precipitation in the early wet season, which may result in decreasing rice production. (4) Longer dry spells will be observed during the wet season, raising the drought risk to rain-fed rice. (5) These changes will be generally observed across the LMB, while the extent of the changes varies among regions.

Impact of prosthesis-patient mismatch on early and late mortality after aortic valve replacement

BackgroundThe influence of prosthesis-patient mismatch (PPM) on survival after aortic valve replacement (AVR) remains controversial. In this study, we sought to determine the effect of PPM on early (≤30 days) and late mortality (>30 days) after AVR or AVR combined with coronary artery bypass grafting (AVR with CABG).MethodsBetween January 1998 and March 2012, 2976 patients underwent AVR (n= 1718) or AVR with CABG (n=1258) at a single institution. PPM was defined as an indexed effective orifice area (EOAI) ≤0.85 cm2/m2 and patients were divided into two groups based on the existence of PPM. Cumulative probability values of survival were estimated with Kaplan-Meier method and compared between groups using Breslow test. Univariate and multivariate independent predictors of early mortality were identified using logistic regression. Cox proportional-hazard regression analysis was used to determine univariate and multivariate independent predictors of late mortality.ResultsEarly mortality was 6.7% in the PPM group vs 4.7% in the group with no PPM (p=0.013). Late mortality for the PPM group at 1, 5 and 10 years was 4%, 16% and 43%, respectively. Late mortality for the group with no PPM at 1, 5 and 10 years was 4%, 15% and 33% respectively. Independent predictors of early mortality included age, severely impaired left ventricular (LV) function, endocarditis, renal dysfunction, chronic obstructive pulmonary disease (COPD) and cardiopulmonary bypass (CPB) time. Multivariate independent predictors of late mortality included age, severely impaired LV function, diabetes, peripheral vascular disease (PVD), renal dysfunction, history of a cerebrovascular accident (CVA), CPB time and a history of previous cardiac surgery. PPM was not an independent predictor of early or late mortality.ConclusionPPM is not an independent predictor of both early and late mortality after AVR or AVR combined with CABG.

Time Domain Detection of Shocks and Impacts in Whole-body Vibration

A method for detecting shocks and impacts in whole-body vibration time histories has been developed that is suitable for implementation as a computer algorithm. The procedure consists of comparing the magnitudes of a higher-order mean value and the impulsiveness calculated for successive time segments of the acceleration-time history. The indicators were the ratio of the 12th-order root mean value to the root mean square RMT/RMS, and the impulsiveness corresponding to a cumulative probability value of 0.97, I(0.97) (i.e., the magnitude of the positive and negative excursions exceeded 3% of the time divided by 2RMS). Both indicators have a value of 2.16 for random vibration with a Gaussian amplitude distribution, and deviate from this value when the motion possesses other characteristics. For seat motion in the Z-direction analyzed using frequency weighting W(b), and time segments of ~20 s, shocks and impacts could be identified when RMT/RMS ≥ 2.5, and I(0.97) ≤ 2.6. A subjective visual classification of 160 exposures to vibration recorded in a range of military vehicles operating under different conditions was performed by a jury of two observers. The subjective classification agreed with computer identification of shocks and impacts in 94% of the cases.

Evaluating failure time probabilities for a Markovian wear process

We present simplified analytical results for the numerical evaluation of failure time probabilities for a single-unit system whose cumulative wear over time depends on its external environment. The failure time distribution is derived as a one-dimensional Laplace–Stieltjes transform with respect to the temporal variable using a direct solution approach and by inverting an existing two-dimensional result with respect to the spatial failure threshold variable. Two numerical examples demonstrate that accurate cumulative probability values can be obtained in a straightforward manner using standard computing environments. Scope and purpose Reliability models that incorporate the effect of a stochastic and dynamic environment on a unit's lifetime have attracted a moderate amount of attention in the past decade. However, evaluating failure time probabilities using such models is nontrivial in all but a few cases. Kharoufeh [1] provided a closed-form lifetime distribution for a continuous Markovian wear process as a two-dimensional Laplace transform. The main purpose of this paper is to reduce the lifetime distribution to a one-dimensional Laplace transform in order to facilitate simpler numerical implementation.

Integrating Large-Scale Soft Data by Simulated Annealing and Probability Constraints

Interpretation of geophysical data or other indirect measurements provides large-scale soft secondary data for modeling hard primary data variables. Calibration allows such soft data to be expressed as prior probability distributions of nonlinear block averages of the primary variable; poorer quality soft data leads to prior distributions with large variance, better quality soft data leads to prior distributions with low variance. Another important feature of most soft data is that the quality is spatially variable; soft data may be very good in some areas while poorer in other areas. The main aim of this paper is to propose a new method of integrating such soft data, which is large-scale and has locally variable precision. The technique of simulated annealing is used to construct stochastic realizations that reflect the uncertainty in the soft data. This is done by constraining the cumulative probability values of the block average values to follow a specified distribution. These probability values are determined by the local soft prior distribution and a nonlinear average of the small-scale simulated values within the block, which are all known. For each realization to accurately capture the information contained in the soft data distributions, we show that the probability values should be uniformly distributed between 0 and 1. An objective function is then proposed for a simulated annealing based approach to enforce this uniform probability constraint. The theoretical justification of this approach is discussed, implementation details are considered, and an example is presented.

An algorithm to generate discrete probability distributions: Binomial, hypergeometric, negative binomial, inverse hypergeometric, and Poisson

A recursion procedure for generating point probability values, cumulative probability values, and interval probability values of discrete distributions is described. Algorithms and associated FORTRAN functions for five representative discrete probability distributions are presented : binomial, hypergeometric, negative binomial, inverse hypergeometric, and Poisson. The joint use of recursion and a small arbitrary initial value ensures computational efficiency.