Best-fit Distribution Research Articles

Modeling of COVID-19 Cases in Pakistan Using Lifetime Probability Distributions.

The Coronavirus Disease (COVID-19) is a respiratory disease that caused a large number of deaths all over the world since its outbreak. The World Health Organization (WHO) has declared the outbreak a global pandemic. The understanding of the random process related to the behavior infection of COVID-19 is an important health and economic problem. In the proposed study, we analyze the frequency of daily confirmed cases of COVID-19 using different two-parameter lifetime probability distributions. We consider the data from the period of March 11, 2020, to July 25, 2020, of Pakistan. We consider nine lifetime probability distributions for the analysis purpose and the selection of best fit was carried out using log-likelihood, AIC, BIC, RMSE, and R2 goodness-of-fit measures. Results indicate that Weibull distribution provides generally the best-fit probability distribution.

Distribution identification and information loss in a measurement uncertainty network

Measurement uncertainty is an increasingly important consideration in many applications demanding extreme performance levels. In the era of the internet of things and 5G connectivity we can learn more about device performance by utilising the increasing amount of data produced. These data require appropriate information infrastructure to facilitate continuous updating of device performance knowledge. This paper presents the results of a study which NPL undertook with a leading test and measurement device manufacturer to examine how measurement uncertainty propagates through the data traceability chain from national standards to end devices. A hierarchy of siloed calculations and heuristics did not enable a satisfactory metadata exchange within the dataflow to ensure an internally consistent calculation of measurement uncertainty. We therefore propose a novel measurement uncertainty network which contains a set of internally consistent measurement models, traceable to national standards and connected through common quantities. The network facilitates sharing and programmatic processing of measurement data with due regard to timeliness, privacy preservation and adherence to FAIR principles in measurement data exchange. An illustrative example of this network is presented with techniques to determine the best-fitting standard probability distribution for a given dataset and the resulting change in information content.

Frequency analysis of annual maximum rainfall series of fifteen meteorological observatories of Sindh, Pakistan

The study is an application of L-moments based regional frequency analysis using annual maximum rainfall series of fifteen sites of Sindh, Pakistan. Initial screening reveals that the observed data series at each site has no serial correlation and is randomly and identically distributed. The discordancy measure (Di) show that none of the site in a group of fifteen sites is discordant. The regional heterogeneity measure (H) shows that the region of fifteen sites is homogeneous. L-moment ratio diagram and |ZDIST| statistic are in favor of generalized logistic distribution (GLO) as best-fitted regional distribution. Parameters of GLO distribution and regional as well as at-site quantiles for various return periods have been estimated. Results show that the estimated quantiles of each site are greater than the average values of observed data series at corresponding sites. Random forest regression has been used for the estimation of quantiles at ungauged sites.

Shear Strength Evaluation of Silt-Clay Soil Under Uni-Axial Compression

Effect of different moisture content and applied pressure to soil shear strength parameters are evaluated. Silt-Clay soil from Ngemplak, Kalikotes, Klaten Regency becomes the subject of the experiment. The research was conducted using a simulation in the laboratory to determine the relationship between water content and soil pressure. The expected values are the pressure that arises and the shear strength of the soil when using four water constructions of 20%, 25%, 30%, and 35%. For each variation of moisture content, three different pressure in the form of uni-axial compression that considered based on the different energy given by equipment used to do compaction will affect the soil density. The applied pressure used is 1.5 kN, 2.5 kN, and 3.5 kN. The result showed that moisture content having a great impact on soil shear strength parameter. The cohesion of soil decreases due to an increase in water content. The friction angle works in linear conditions with moisture content but decreases at the value of 35% water content. The best-fitted distribution for the relationship between soil shear strength and moisture content is polynomial order two. Follow the equation for 1.5 kN applied pressure is y = -0.0036x 2 + 0.2236x - 2.4898, for 2.5 kN applied pressure the equation is y = -0.0025x 2 + 0.1545x-1.3383, and for 3.k kN applied pressure the equation is y = -0.0022x 2 + 0.1357x - 1.0344.

Methodology for Selection and Analysis of Representative Test Roads Required for Vehicle Durability Evaluation

Measurement of customer usage loads is one of the essential and critical activity for evaluation of vehicle durability. The customer usage loads are measured on representative public roads of finite lengths, typically for about 500 km to 1000 km consisting of a mix of different road types. It is always a big challenge for the test engineer to make sure that these selected road patches are good representatives of the diverse road conditions of the target market. In this paper, a methodology is presented for the selection of these test roads, with the use of objective road roughness values (in terms of International Roughness Index –IRI). Detail study was carried out to analyse the best-fit probability distribution model for road roughness values, and the lognormal (three-parameter) distribution model is observed to be the best suitable model. It is shown that this model provides a better objective definition and classification of customer usage of the target market. The proposed methodology is generic, vehicle independent, and objectively helps to select the best representative test roads with 95% confidence. Thereby also helps in optimising the cost and time of the service load measurement campaign.

THE BEST FIT PROBABILITY DISTRIBUTION MODEL FOR THE ESTIMATION OF EXTREME RAINFALL IN LIMBANG, SARAWAK

In Malaysia, the increment of annual rainfall patterns is causing frequent floods, mainly in Sabah and Sarawak.Limbang river basin was selected as a case study due to it was facing of high-risk flooding problem mainly during the transition of climate. This study was aimed to estimate the frequency of rainfall under various return periods and to identify the best fit model probability distribution of annual maximum rainfall based on twenty-four hours sample in Limbang. The three statistical models were used, which are Gumbel, Log-Pearson type III, and Log-Normal. Based on the goodness of fit tests, Chi-Square, Kolmogorov Smirnov test, and the Log-Normal was found to be the best fit model for the station of Panduran. The Log-Pearson type III was found to be the best-fit distribution model for the rest of the stations, which occupies almost more than 90%. The maximum values of expected rainfall were calculated using the best fit probability distributions and could be used by a design engineer in the future.Keywords: flood, return period, Gumbel distribution

Service time variability at manual operated tollbooths under mixed traffic environment: Towards level-of-service thresholds

Abstract Comprehending the variation in service time is essential for evaluating the capacity and level of service of the toll-plaza and developing policies for effective management of tollbooth operations. The present study analyzes the variation in service time using statistical distribution at manually operated toll plazas in India. For this purpose, traffic video data were collected for five toll-plazas in India. The vehicles approaching the toll plaza are divided broadly into seven different categories. The service time of different vehicle classes was extracted manually from the recorded video. The variation in service time for a total of 13 leader-follower pairs (small car as leader and follower) were modeled using statistical distributions. Based on the Chi-squared, Anderson Darling (AD), and Kolmogorov-Smirnoff (KS) test statistics, log-normal distribution was found as the best-fitted distribution among other potential statistical distributions. Investigations revealed that traffic composition, vehicular characteristics, variation in toll rates, drivers' and tollbooth operators’ behavior significantly influence the variability in service time. The important outcome of this study is the development of service time based level of service (LOS) criteria, which were developed using k-mean clustering technique. The developed LOS thresholds can be very useful to field engineers and practitioners for evaluating the existing performance of tollbooth and accordingly facilitating the development of appropriate policies for effective management of toll plaza operations.

A probabilistic epidemiological model

We construct a model for the progress of the 2020 coronavirus epidemic in the United States of America, using probabilistic methods rather than the traditional compartmental model. We employ the generalized beta family of distributions, including those supported on bounded intervals and those supported on semi-infinite intervals. We compare the best-fit distributions for daily new cases and daily new deaths in America to the corresponding distributions for United Kingdom, Spain, and Italy. We explore how such a model might be justified theoretically in comparison to the apparently more natural compartmental model. We compare forecasts based on these models to observations, and find the forecasts useful in predicting total pandemic deaths.

Regional Frequency Analysis of Maximum Monthly Rainfall in Haryana State of India Using L-Moments

The paper aims to select the appropriate regional frequency distribution for the maximum monthly rainfall and estimation of quantiles using L-moments for the 27 rain gauge stations in Haryana. These 27 rain gauge stations were grouped into three homogeneous regions (Region-1, Region-2, and Region-3) using Ward’s method of cluster analysis. To confirm the homogeneity of each region, L-moments based measure of heterogeneity was used. For each homogeneous region, a regional distribution was selected with the help of the L-moments ratio diagram and goodness-of-fit test. Results of the goodness-of-fit test and L-moments ratio diagram indicated that Generalized Logistic and Generalized Extreme Value distributions were best- fitted regional frequency distributions for the Region-1 and Region-2 respectively while for Region-3, Pearson Type-3) was best-fitted distribution. The quantiles for each region were calculated and the regional growth curves were developed. The accuracy measurements were determined using Monte Carlo simulations for the regional quantiles. Results of simulations showed that uncertainty in regional quantiles measured by Root Mean Square Error value and 90 percent error limits were small when the return period was low but uncertainty in quantiles increases as the return period increases.

Spatiotemporal variation characteristics of extreme precipitation in the upper reaches of the Hongshui River Basin during 1959–2016

AbstractUnderstanding changes in the intensity and frequency of extreme precipitation is vital for flood control, disaster mitigation, and water resource management. In this study, 12 extreme precipitation indices and the best-fitting extreme value distribution were used to analyze the spatiotemporal characteristics of extreme precipitation in the upper reaches of the Hongshui River Basin (UHRB). The possible links between extreme precipitation and large-scale circulation were also investigated. Most extreme precipitation indices increased from west to east in the UHRB, indicating that the eastern region is a humid area with abundant precipitation. The indices for consecutive wet days (CWD) and precipitation events (R0.1) decreased significantly, indicating that the UHRB tends to be dry, with few precipitation events. The probability distribution functions of most extreme precipitation indices, especially that of R0.1, shifted significantly to the left in 1988–2016 compared with 1959–1987, further indicating that the UHRB has experienced a significant drying trend in recent decades. The East Asian summer monsoon and the El Niño–Southern Oscillation/Pacific Decadal Oscillation were confirmed to influence extreme precipitation in the UHRB. These findings are helpful for understanding extreme precipitation variation trends in the UHRB and provide references for further research.

Bicycle Speed Modelling Considering Cyclist Characteristics, Vehicle Type and Track Attributes

Cycling is an increasingly popular mode of transport as part of the response to air pollution, urban congestion, and public health issues. The emergence of bike sharing programs and electric bicycles have also brought about notable changes in cycling characteristics, especially cycling speed. In order to provide a better basis for bicycle-related traffic simulations and theoretical derivations, the study aimed to seek the best distribution for bicycle riding speed considering cyclist characteristics, vehicle type, and track attributes. K-means clustering was performed on speed subcategories while selecting the optimal number of clustering using L method. Then, 15 common models were fitted to the grouped speed data and Kolmogorov–Smirnov test, Akaike information criterion, and Bayesian information criterion were applied to determine the best-fit distribution. The following results were acquired: (1) bicycle speed sub-clusters generated by the combinations of bicycle type, bicycle lateral position, gender, age, and lane width were grouped into three clusters; (2) Among the common distribution, generalized extreme value, gamma and lognormal were the top three models to fit the three clusters of speed dataset; and (3) integrating stability and overall performance, the generalized extreme value was the best-fit distribution of bicycle speed.

A Probabilistic Method for Estimating the Influence of Corrosion on the CuAlNi Shape Memory Alloy in Different Marine Environments

This paper gives an approach to the probabilistic percent corrosion depth estimation model for the CuAlNi Shape Memory Alloy (SMA) in different marine environments. Real testing was performed for validation of the theoretical model, where CuAlNi SMAs were exposed to 6 and 12 months in different seawater environments. Focus Ion Beam (FIB) analysis was used to measure the real corrosion depth on the surfaces of tested samples. A statistical approach to the investigation of the corrosion rate of CuAlNi SMA is given, where the corrosion rate is observed as a continuous random variable described by a linear corrosion model, with the assumption that corrosion starts immediately upon alloy surfaces being exposed to the influences of the marine environment. The three best-fitted two-parameter distributions for estimating the cumulative density function and the probability density function of the random variable were obtained by applying adequate statistical tests. Furthermore, using EDX analyses, we identified the chemical composition of the corroded materials, and with the help of Principal Component Analyses, we determined which corrosion environment had the most dominant influence on the corrosion process. The research results indicated that the changeable environment in the tides had a more heterogenic chemical content, which accelerated the corrosion rate.

High gene flow through pollen partially compensates spatial limited gene flow by seeds for a Neotropical tree in forest conservation and restoration areas

Gene flow may occur both through pollen movement and seed dispersal, although their relative contribution to overall species gene flow is not understood for most tropical trees, which compromises management recommendations. We investigated the implications of seed dispersal limitation, pollen dispersal capacity, and mating system to the spatial genetic structure of populations of the Neotropical legume tree, Centrolobium tomentosum, in Brazil’s Atlantic Forest. We estimated seed dispersal distribution by counting individuals around adult trees; pollen dispersal distribution and outcrossing rates from adult and offspring genotypes, using seven microsatellite loci. Spatial genetic structure was inferred through the correlation among kinship coefficients and geographical distances between pairs of individuals, using nuclear and chloroplast microsatellite markers. We observed restricted seed dispersal, with most seeds (78%) falling up to 10 m from the adult tree trunk. The best-fitted pollen dispersal distribution was the exponential power distribution, with a heavy tail and average pollen dispersal distance of 3191 m. The mating system was preferably allogamous, with an average of eight pollen donors. There was significant spatial genetic structure in all populations, with stronger structure obtained from chloroplast DNA, which suggests that the restricted gene flow by seed dispersal may be compensated by high outcrossing rates and long-distance pollen flow promoted by the large bees that pollinate the species. Our results emphasize the importance of pollination services in fragmented tropical landscapes, where most tree species are pollinated by animals and a large number of species experience seed dispersal limitation.

Cost-effectiveness of ribociclib plus endocrine therapy versus placebo plus endocrine therapy in HR-positive, HER2-negative breast cancer.

BACKGROUND: The 2015 American Society of Clinical Oncology guidelines recommend first-line treatment of hormone receptor (HR)-positive breast cancer with endocrine therapy plus or minus palbociclib, a selective cyclin-dependent kinase (CDK)4/6 inhibitor. In 2018, the U.S. Food and Drug Administration approved ribociclib, a new orally available selective CDK4/6 inhibitor. While gains in progression-free survival (PFS) and overall survival (OS) from ribociclib are important for clinical and treatment outcomes, trade-offs in adverse events (AEs) and additional costs necessitate cost-effectiveness analysis (CEA) to assist consideration by third-party payer systems, physicians, and patients. OBJECTIVES: To (a) develop a Markov model and (b) determine the cost-effectiveness of ribociclib plus endocrine therapy versus endocrine therapy alone as treatment for premenopausal and perimenopausal patients with HR-positive, human epidermal growth factor receptor 2 (HER2)-negative breast cancer. METHODS: A lifetime 3-state Markov model ("stable," "progressed," and "dead" health states) was developed using a U.S. payer perspective. Transition probabilities were calculated based on OS and PFS outcomes from the randomized controlled phase 3 trial MONALEESA-7. These Kaplan-Meier curves were extended to lifetime by estimating best-fit distributions using loglogistic distribution for ribociclib curves and Weibull distribution for placebo curves. Costs were obtained from national data sources using 2019 U.S. dollars (USD) and discounted by 3%. Utilities were obtained via published breast cancer literature and were included for each health state and for time spent with each AE. Results were expressed as an incremental cost-effectiveness ratio (ICER) expressed as USD per quality-adjusted life-year (QALY) saved. Treatments were assumed to be cost-effective based on a willingness-to-pay (WTP) threshold of $150,000 per QALY gained. Base-case, 1-way sensitivity tornado diagrams and probabilistic sensitivity analyses demonstrated changes in the ICER and were driven by the cost of ribociclib and the utility of remaining in the stable health state. RESULTS: Ribociclib plus endocrine therapy was cost-effective at an ICER of $124,513 per QALY when compared with endocrine therapy alone at a WTP threshold of $150,000. The ribociclib plus endocrine therapy arm had an effectiveness of 5.28 QALYs and a total cost of $385,112, while placebo plus endocrine therapy provided only 2.46 QALYs at a lower total cost of $67.246. The model was sensitive to the cost of ribociclib and the utility of time spent in the stable health state. Probabilistic sensitivity analysis demonstrated that endocrine therapy alone was cost-effective until a WTP of $125,000 and was cost-effective 72% of the time at the WTP threshold. CONCLUSIONS: Ribociclib plus endocrine therapy is more cost-effective than endocrine therapy alone. Professionals in managed care settings should consider the pharmacoeconomic benefits of ribociclib for the treatment of HR-positive, HER2-negative breast cancer as they make value-based formulary decisions. Further CEAs should be considered as direct treatment comparison trials between CDK4/6 inhibitors are completed in the future. DISCLOSURES: No outside funding supported this study. The authors have nothing to disclose.

Determination of the Feature Resolution of Processed Image Data via Statistical Analysis.

A method is presented to determine the feature resolution of physically relevant metrics of data obtained from segmented image sets. The presented method determines the best-fit distribution curve of a dataset by analyzing a truncated portion of the data. An effective resolvable size for the metric of interest is established when including parts of the truncated dataset results in exceeding a specified error tolerance. As such, this method allows for the determination of the feature resolution regardless of the processing parameters or imaging instrumentation. Additionally, the number of missing objects that exist below the resolution of the instrumentation may be estimated. The application of the developed method was demonstrated on data obtained via 2D scanning electron microscopy of a pressed explosive material and from 3D micro X-ray computed tomography of a polymer-bonded explosive material. It was shown that the minimum number of pixels/voxels required for the accurate determination of a physically relevant metric is dependent on the metric of interest. This proposed method, utilizing the prior knowledge of the distribution of metrics of interest, was found to be well suited to determine the feature resolution in applications where large datasets can be achieved.

Analysis of Magnitude and Frequency of Floods in the Damanganga Basin: Western India

Flood Frequency Analysis (FFA) method was introduced by Fuller in 1914 to understand the magnitude and frequency of floods. The present study is carried out using the two most widely accepted probability distributions for FFA in the world namely, Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). The Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) methods were used to select the most suitable probability distribution at sites in the Damanganga Basin. Moreover, discharges were estimated for various return periods using GEVI and LP-III. The recurrence interval of the largest peak flood on record (Qmax) is 107 years (at Nanipalsan) and 146 years (at Ozarkhed) as per LP-III. Flood Frequency Curves (FFC) specifies that LP-III is the best-fitted probability distribution for FFA of the Damanganga Basin. Therefore, estimated discharges and return periods by LP-III probability distribution are more reliable and can be used for designing hydraulic structures.

Energetic Electron Distribution of the Coronal Acceleration Region: First Results from Joint Microwave and Hard X-Ray Imaging Spectroscopy

Abstract Nonthermal sources located above bright flare arcades, referred to as the “above-the-loop-top” sources, have been often suggested as the primary electron acceleration site in major solar flares. The X8.2 limb flare on 2017 September 10 features such an above-the-loop-top source, which was observed in both microwaves and hard X-rays (HXRs) by the Expanded Owens Valley Solar Array and the Reuven Ramaty High Energy Solar Spectroscopic Imager, respectively. By combining the microwave and HXR imaging spectroscopy observations with multifilter extreme ultraviolet and soft X-ray imaging data, we derive the coronal magnetic field and energetic electron distribution of the source over a broad energy range from <10 keV up to ∼MeV during the early impulsive phase of the flare. The source has a strong magnetic field of over 800 G. The best-fit electron distribution consists of a thermal “core” from ∼25 MK plasma. A nonthermal power-law “tail” joins the thermal core at ∼16 keV with a spectral index of ∼3.6, which breaks down at above ∼160 keV to >6.0. Temporally resolved analysis suggests that the electron distribution above the break energy rapidly hardens with the spectral index decreasing from >20 to ∼6.0 within 20 s, or less than ∼10 Alfvén crossing times in the source. These results provide strong support for the above-the-loop-top source as the primary site where an ongoing bulk acceleration of energetic electrons is taking place very early in the flare energy release.

Prediction of flood frequency under a changing climate, the case of Hare watershed, Rift Valley Basin of Ethiopia

Climate change is causing unpredictable fluctuation in the rainfall patterns and, frequent heavy rainfall that led to catastrophic flooding and a significant risk on Hare watershed biodiversity in the Rift Valley of Ethiopia. Prediction of flood frequency under changing climate in the Hare watershed has not been well-studied in spite of the risk it poses to the human environment. Thus, this study aimed to predict flood frequency under changing climate in the Hare watershed relevant for effective flood management and early warning systems. The Soil Water Assessment Tool (SWAT) was used to simulate monthly stream flow. The model was calibrated and validated for the period of 1994 to 1998 and 1999 to 2001, respectively. The stationarity of annual peak flow was analyzed using Pettitt’s test. Flood Frequency Distribution (FFD) software package was deployed to determine the flood magnitude and frequency curve for the baseline period (1980–2009) and a predicted period (2021–2050). The result of the SWAT model performance evaluation statistics showed a high potential in the prediction of future streamflow. In addition, the goodness-of-fit test result showed that the Gumbel and Generalized Extreme Value (GEV) were the best-fit probability distribution for baseline and future flood events, respectively. The predicted annual peak flow results show an increasing trend by 60 and 106% under RCP 4.5 and RCP 8.5 emission scenarios, respectively. The future design flood may increase between 6.5 and 119.0% when compared to the baseline period. The study provides valuable information for policy and decision makers during the implementation of different flood events adaptation and mitigation measures for the Hare watershed.

Future Changes in Wave Conditions at the German Baltic Sea Coast Based on a Hybrid Approach Using an Ensemble of Regional Climate Change Projections

In this study, the projected future long-term changes of the local wave conditions at the German Baltic Sea coast over the course of the 21st century are analyzed and assessed with special focus on model agreement, statistical significance and ranges/spread of the results. An ensemble of new regional climate model (RCM) simulations with the RCM REMO for three RCP forcing scenarios was used as input data. The outstanding feature of the simulations is that the data are available with a high horizontal resolution and at hourly timesteps which is a high temporal resolution and beneficial for the wind–wave modelling. A new data interface between RCM output data and wind–wave modelling has been developed. Suitable spatial aggregation methods of the RCM wind data have been tested and used to generate input for the calculation of waves at quasi deep-water conditions and at a mean water level with a hybrid approach that enables the fast compilation of future long-term time series of significant wave height, mean wave period and direction for an ensemble of RCM data. Changes of the average wind and wave conditions have been found, with a majority of the changes occurring for the RCP8.5 forcing scenario and at the end of the 21st century. At westerly wind-exposed locations mainly increasing values of the wind speed, significant wave height and mean wave period have been noted. In contrast, at easterly wind-exposed locations, decreasing values are predominant. Regarding the changes of the mean wind and wave directions, westerly directions becoming more frequent. Additional research is needed regarding the long-term changes of extreme wave events, e.g., the choice of a best-fit extreme value distribution function and the spatial aggregation method of the wind data.

Impact Assessment in the Process of Propagating Climate Change Uncertainties into Building Energy Use

Buildings are subject to significant stresses due to climate change and design strategies for climate resilient buildings are rife with uncertainties which could make interpreting energy use distributions difficult and questionable. This study intends to enhance a robust and credible estimate of the uncertainties and interpretations of building energy performance under climate change. A four-step climate uncertainty propagation approach which propagates downscaled future weather file uncertainties into building energy use is examined. The four-step approach integrates dynamic building simulation, fitting a distribution to average annual weather variables, regression model (between average annual weather variables and energy use) and random sampling. The impact of fitting different distributions to the weather variable (such as Normal, Beta, Weibull, etc.) and regression models (Multiple Linear and Principal Component Regression) of the uncertainty propagation method on cooling and heating energy use distribution for a sample reference office building is evaluated. Results show selecting a full principal component regression model following a best-fit distribution for each principal component of the weather variables can reduce the variation of the output energy distribution compared to simulated data. The results offer a way of understanding compound building energy use distributions and parsing the uncertain nature of climate projections.