Lognormal Probability Distribution Research Articles

Anisotropic Heating and Cooling within Interplanetary Coronal Mass Ejection Sheath Plasma

This study presents the first comprehensive investigation of the relationship between heating and cooling, temperature anisotropy, turbulence level, and collisional age within interplanetary coronal mass ejection (ICME) sheaths, which are highly compressed, heated, and turbulent. Using Wind spacecraft data, we analyze 333 ICME sheaths observed at 1 au from 1995 to 2015. The proton temperature within the ICME sheaths has a log-normal probability distribution. Irrespective of instability growth rates, plasma unstable to proton-cyclotron (PC) and firehose instabilities appear to be statistically hotter, at least by a factor of 5 to 10, compared to stable plasma. We also observe relatively enhanced magnetic fluctuations and low collisional age, especially in regimes unstable to PC and firehose instabilities at low proton betas β p ≤ 2. In the case of high beta β p ≥ 2, we observe high magnetic fluctuations close to the instabilities and less collisional age to the plasma unstable to firehose instability rather than near the mirror mode and PC threshold. Our findings suggest that heating processes dominate over cooling processes in producing proton temperature anisotropy in the ICME sheath region. Moreover, collisional age and magnetic fluctuations are critical in maintaining anisotropic and isotropic conditions.

Enhancing Drought Risk Assessment in the Punjab, Pakistan: A Copula-Based Modeling Approach for Future Projections

Abstract Drought is one of the most complicated and challenging natural hazards, which occurs nearly in every part of the world and poses recurring challenges to agriculture, food security, livestock, human health, and water management. Pakistan has a long history of drought; however, this study focuses on drought analysis and projection in the province of Punjab, Pakistan, as it provides around 60% of the country’s food product, significantly contributing to the national food supply and economy. This study utilized the previous 56 years (1962–2017) of climate data to calculate the reconnaissance drought index (RDI) and then extracted the drought variables of durations and severity for each meteorological station. The best-fit marginal probability distribution and copula models were chosen for the stations based on numerical as well as graphical evaluation. Lognormal and exponential probability distributions, as well as Gumbel, are selected as the best-fit probability distributions for both drought characteristics and bivariate copula model, respectively, for projections. From the projections, we can infer that the smaller return periods indicate high vulnerability while longer return periods with low vulnerability. The results suggest that Faisalabad, Bahawalpur, Bahawalnagar, and Multan stations have the lowest return periods, indicating high vulnerability, and may experience drought more frequently in the future. Mianwali, Khanpur, Lahore, and Sialkot stations may have an intermediate vulnerability to drought events. The stations of Jhelum, Murree, and Sargodha have larger return periods, implying lower susceptibility to drought events in the future. The projected results provide insights for policymakers and stakeholders to optimize the risk of droughts on agriculture production, livestock, water management, human health, and food security in Punjab, Pakistan.

Time Is Ripe for Targeting Per- and Polyfluoroalkyl Substances-Induced Hormesis: Global Aquatic Hotspots and Implications for Ecological Risk Assessment.

Globally implemented ecological risk assessment (ERA) guidelines marginalize hormesis, a biphasic dose-response relationship characterized by low-dose stimulation and high-dose inhibition. The present study illuminated the promise of hormesis as a scientific dose-response model for ERA of per- and polyfluoroalkyl substances (PFAS) represented by perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic acid (PFOS). A total of 266 hormetic dose-response relationships were recompiled from 1237 observations, covering 30 species from nine representative taxonomic groups. The standardized hormetic amplitudes followed the log-normal probability distribution, being subject to the limits of biological plasticity but independent of stress inducers. The SHapley Additive exPlanations algorithm revealed that the target endpoint was the most important variable explaining the hormetic amplitudes. Subsequently, quantitative frameworks were established to incorporate hormesis into the predicted no-effect concentration levels, with a lower induction dose and a zero-equivalent point but a broader hormetic zone for PFOS. Realistically, 10,117 observed concentrations of PFOA and PFOS were gathered worldwide, 4% of which fell within hormetic zones, highlighting the environmental relevance of hormesis. Additionally, the hormesis induction potential was identified in other legacy and emerging PFAS as well as their alternatives and mixtures. Collectively, it is time to incorporate the hormesis concept into PFAS studies to facilitate more realistic risk characterizations.

Modelling diameter at breast height distribution of jack pine and black spruce natural stands in eastern Canada

Individual tree diameter at breast height (DBH) distribution is an important information for forest management planning. Forest managers obtain the DBH data either by field measurements or estimations using predictive models. However, probability distribution models are still lacking or need improvement. Therefore, we aimed to construct and fit diameter distribution models that reflect forest structure and composition change. We evaluated gamma, log-normal, and Weibull probability distribution functions (PDFs) for two commercially important tree species, black spruce ( Picea mariana (Mill) B.S.P.) and jack pine ( Pinus banksiana Lamb), grown in natural stands across Ontario, Canada. We modelled the parameters of the distributions as a function of stand-level variables for these species. We used DBH data from 735 permanent sample plots. Our results showed that all three evaluated PDFs reflected observed DBH distribution. We demonstrated that the moment-based recovered parameters could represent the maximum likelihood-estimated parameters precisely, and parameters of the PDFs can be modelled as a function of stand-level dynamic covariates. The models unbiasedly predicted the PDF parameters DBH means and DBH classes. The R2 of the model fit ranged between 0.35 and 0.98 for the predicted parameters and 0.90 and 0.97 for the predicted DBH.

Variability in jacking resistance of adjacent steel pipe piles under controlled pile installation

The pile bearing capacity varies even within the same site. This study aims to gain a better understanding of the effect of pile penetration techniques on the variability of bearing capacity. The study uses data from 83 jack-in test piles to explore the variations in penetration resistance at the pile head, base, and shaft. The semivariance increases with an increase of the horizontal distance, so we focus on the semivariance between 5 m range, whose error was defined as the error due to piling workmanship. The analysis shows that the errors follow a lognormal probability distribution, and the coefficient of variation (COV) in penetration resistance at the heads and bases is about 10%, while the COV in extracted resistance varies widely, with a range of 5–25%. Little difference in the variations due to piling workmanship was observed among different penetration motions, speeds, and soil types.

Integrating renewable energy and V2G uncertainty into optimal power flow: A gradient bald eagle search optimization algorithm with local escaping operator

AbstractHere, a new approach is proposed for solving the optimal power flow (OPF) problem in transmission networks using a Gradient Bald Eagle Search Algorithm (GBES) with a Local Escaping Operator (LEO). The method takes into account uncertainty of the renewable energy sources (wind energy and photovoltaic systems) and Vehicle‐to‐Grid (V2G) in the stochastic OPF problem. To improve the efficiency of the proposed technique and enhance its local exploitation capability, the LEO method's selection features are utilized. Monte Carlo methods are employed to estimate the generation costs of the renewable sources and PEVs and study their feasibility. The uncertainty of the renewable sources and PEVs is represented by Weibull, lognormal, and normal probability distribution functions (PDFs). The GBES approach is experimentally compared with well‐known meta‐heuristics using twenty‐three different test functions, and the results indicate its superiority over BES and other recently developed algorithms. Furthermore, the proposed method's effectiveness is evaluated using IEEE 30‐bus test system under various scenarios, and the simulation results demonstrate that it can effectively address OPF issues considering renewable energy sources and V2G, providing superior optimal solutions compared to other algorithms.

Multi-objective optimal power flow of thermal-wind-solar power system using an adaptive geometry estimation based multi-objective differential evolution

Sustainable energy is a key component of sustainable development. The current grid can be supplied by fossil fuel generators and renewable energy sources (RESs)-based generators, such as solar photovoltaic (PV) and wind power generators. In an electrical network, power generation from several sources must be optimally coordinated to ensure efficient and economical operation. However, the intermittent and uncertain nature of RESs complicate the operation of power systems. In this study, an adaptive geometry estimation-based multi-objective differential evolution (AGE-MODE) method is proposed for multi-objective optimal power flow in a hybrid power system of thermal, wind, and solar energy sources (MOOPF-TWS). In the proposed approach, wind and solar PV power outputs are predicted based on Weibull and lognormal probability distribution functions, respectively. Therefore, the generation costs for solar and wind power can be divided into direct costs, penalty costs for underestimation, and reserve costs for overestimation. Furthermore, the emissions, voltage deviation, and real power loss are considered in particular cases. AGE-MODE is applied to modified IEEE 30-bus and 57-bus systems, where different case studies are simulated with combinations of two-, three-, and four-objective optimizations in MOOPF-TWS problems. Comparisons between AGE-MODE and other recently developed multi-objective methods demonstrate its effectiveness in resolving MOOPF-TWS problems, particularly for cases with more than two objectives.

Comparison of Monte Carlo Schemes in the Modeling of Extreme Flood in Tropical Rain Forest Basins

Insufficient length of streamflow record poses challenges in capturing extreme events, frequencies, and sequences crucial for effective water resources systems design. Consequently, simulation and application of statistically similar streamflow values becomes imperative. In this study, two Markov-based models, namely the Thomas-Fiering (T-F) model and the Autoregressive (AR) model, were developed based on a log-normal probability distribution to synthesize monthly and annual flows using a decade of historical data (1980–1989) collected from the Umulokpa gauging station in the Adada River catchment of Enugu State, Nigeria. Except for the month of December (p = 0.03), no significant difference (p > 0.05) was observed between the monthly and annual model-predicted streamflows. However, both models demonstrated limitations in fully capturing the characteristics of the observed flows, particularly regarding Kurtosis. Further accuracy assessment from computed correlation coefficients (0.018 for T-F and 0.122 for AR), along with root mean square error (RMSE) values (12.84 for T-F and 11.95 for AR), indicate that while both models deviated from the observed flows, the AR model demonstrated superior performance compared to the T-F model. However, to apply these models reliably, for future flow prediction in the Adada catchment, streamflow data from rivers with comparable catchment characteristics is essential.

Analysis of Annual Rainfall Distribution and Planned Rain Intensity at 11 (Eleven) Rain Post Stations in Serang District

This research aimed to find the best rainfall probability model and planned rain intensity using the Mononobe formula for 11 rain stations in Serang Regency. Annual rainfall data is processed and evaluated as secondary data using the rain data consistency test method, the Gumbel probability distribution, the Normal probability distribution, the Log Normal probability distribution, and the Pearson Type III Log probability distribution. The consistency test results reveal that the rainfall data is consistent. The Gumbel probability distribution is used to examine the design rain intensity based on the analysis. This study is intended to guide estimating the design rainfall intensity to develop the design flood discharge and run-off calculations. Suggestions for future research include improving the accuracy of rain data processing and making longer-term data available to provide a more accurate frequency analysis

Seismic fragility analysis of coupled building‐slope systems

AbstractBuildings located on hill slopes are subjected to additional effects under seismic action compared with those on flat ground. This article presents Incremental Dynamic Analyses of coupled building‐slope systems incorporating topographic amplification, nonlinear slope movement and irregular structural configuration of hill‐side buildings. Two different stable slopes, supporting single and multiple adjacent ductile moment resisting reinforced concrete frame buildings with step‐back configuration, prevalent in Indian and Chinese hilly regions, are modelled and analyzed using the finite element software ABAQUS. A suite of 21 ground motions is incrementally scaled and used to compute the seismic response of the coupled system. Fragility curves for different damage states, derived as lognormal probability distributions in terms of three different Intensity Measures (IMs) and damage probabilities of the considered buildings, are derived and compared. The spectrum‐based IMs (e.g., spectral acceleration at fundamental period, and average of the spectral acceleration over a period range) result in lower record‐to‐record variability, compared with the peak ground acceleration as the IM. The results reveal that ignoring the effect of slope significantly underestimates the fragility for all the damage states.

On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading

This paper proposes an optimal trading algorithm based on a novel application of conventional control engineering (CE). We consider a fundamental CE concept, namely, the feedback control, and apply it to algorithmic trading (AT). The concrete feedback control strategy is designed in a form of the celebrated proportional–integral–derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realization of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above enables the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in financial engineering, namely, the “stock market energy” concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python-based prototype software. We finally apply the corresponding prototype software to a data set from the Binance BTC/USDT (Bitcoin/Tether) stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT.

A novel approach to the investigation and quantification of the stop/start process for pedestrian traffic using motion capture devices

Characterising the stop/start walking process of individuals in a crowded and congested space is an important consideration in modelling pedestrian movement. However, the reaction of pedestrians to speed changes, especially to the person in front, has not been fully characterised nor quantified for full adoption in computer models. This study, therefore, explored the different phases of the stop/start process through a series of novel experiments conducted at University College Dublin (UCD) in which individual movements were captured precisely using motion capture equipment. The overall aim of the study was to develop a novel methodology (inspired from vehicle traffic flow) to break down and quantify the components of the stop/start walking process, i.e., the perception-reaction time, slow-down time, and start-up time of individuals walking in a single-file. These times, together with the total stopping distance and inter-person distances of each follower to their leader at the beginning and the end of each phase were quantified successfully and their inter-relationships were explored. The results showed the mean perception-reaction time, slow-down time, and start-up time delay were 0.48, 0.58, and 0.39 s, respectively. Where applicable, normal, lognormal, Weibull, gamma, and log-logistic probability distributions were fitted to the data to determine the best fit. The novel methodology developed in this study can be used in the future to investigate pedestrians’ behaviour in response to any changes in leaders’ speed, i.e. quantify the reaction of individuals in different phases. The results of this study can inform the representation of the stop/start process in microscopic pedestrian models.

A Quasi-periodic Oscillation of ∼4.6 yr in the Radio Light Curves of Blazar PKS 0607-157

We present periodicity search analyses on long-term radio light curves at 4.8, 8, and 14.5 GHz of blazar PKS 0607–157 observed by the University of Michigan Radio Astronomical Observatory telescope. The highly variable radio emissions are approximately distributed as a log-normal probability distribution function. The Power Spectral Density for the radio light curves can be well characterized by a power-law model. Using the Weighted Wavelet Z-transform and Lomb-Scargle periodogram methods, significant Quasi-periodic Oscillation (QPO) of ∼4.6 yr in the radio light curve has been observed above the 3σ confidence level, which presents an interesting case among blazar QPO phenomena. We explore three plausible physical models to explain the observed QPOs: a supermassive binary black hole system, Lense-Thirring precession of the disk, and helical motion of plasma blobs within the jet.

Bayesian multilevel hidden Markov models identify stable state dynamics in longitudinal recordings from macaque primary motor cortex.

Neural populations, rather than single neurons, may be the fundamental unit of cortical computation. Analysing chronically recorded neural population activity is challenging not only because of the high dimensionality of activity but also because of changes in the signal that may or may not be due to neural plasticity. Hidden Markov models (HMMs) are a promising technique for analysing such data in terms of discrete latent states, but previous approaches have not considered the statistical properties of neural spiking data, have not been adaptable to longitudinal data, or have not modelled condition-specific differences. We present a multilevel Bayesian HMM addresses these shortcomings by incorporating multivariate Poisson log-normal emission probability distributions, multilevel parameter estimation and trial-specific condition covariates. We applied this framework to multi-unit neural spiking data recorded using chronically implanted multi-electrode arrays from macaque primary motor cortex during a cued reaching, grasping and placing task. We show that, in line with previous work, the model identifies latent neural population states which are tightly linked to behavioural events, despite the model being trained without any information about event timing. The association between these states and corresponding behaviour is consistent across multiple days of recording. Notably, this consistency is not observed in the case of a single-level HMM, which fails to generalise across distinct recording sessions. The utility and stability of this approach is demonstrated using a previously learned task, but this multilevel Bayesian HMM framework would be especially suited for future studies of long-term plasticity in neural populations.

Stochastic Multi-Objective Optimal Reactive Power Dispatch with the Integration of Wind and Solar Generation

The exponential growth of unpredictable renewable power production sources in the power grid results in difficult-to-regulate reactive power. The ultimate goal of optimal reactive power dispatch (ORPD) is to find the optimal voltage level of all the generators, the transformer tap ratio, and the MVAR injection of shunt VAR compensators (SVC). More realistically, the ORPD problem is a nonlinear multi-objective optimization problem. Therefore, in this paper, the multi-objective ORPD problem is formulated and solved considering the simultaneous minimization of the active power loss, voltage deviation, emission, and the operating cost of renewable and thermal generators. Usually, renewable power generators such as wind and solar are uncertain; therefore, Weibull and lognormal probability distribution functions are considered to model wind and solar power, respectively. Due to the unavailability and uncertainty of wind and solar power, appropriate PDFs have been used to generate 1000 scenarios with the help of Monte Carlo simulation techniques. Practically, it is not possible to solve the problem considering all the scenarios. Therefore, the scenario reduction technique based on the distance metric is applied to select the 24 representative scenarios to reduce the size of the problem. Moreover, the efficient non-dominated sorting genetic algorithm II-based bidirectional co-evolutionary algorithm (BiCo), along with the constraint domination principle, is adopted to solve the multi-objective ORPD problem. Furthermore, a modified IEEE standard 30-bus system is employed to show the performance and superiority of the proposed algorithm. Simulation results indicate that the proposed algorithm finds uniformly distributed and near-global final non-dominated solutions compared to the recently available state-of-the-art multi-objective algorithms in the literature.

Modeling the area of co-seismic landslides via data-driven models: The Kaikōura example

The last three decades have witnessed substantial developments in data-driven models for landslide prediction. However, this improvement has been mostly devoted to models that estimate locations where landslides may occur, i.e., landslide susceptibility. Although susceptibility is crucial when assessing landslide hazard, another equally important piece of information is the potential landslide area once landslides initiate on a given slope.This manuscript addresses this gap in the literature by using a Generalized Additive Model whose target variable is the topographically-corrected landslide areal extent at the slope unit level. In our case, the underlying assumption is that the variability of landslide areas across the geographic space follows a Log-Normal probability distribution. We test this framework on co-seismic landslides triggered by the Kaikōura earthquake (7.8 Mw on November 13th 2016). The model performance was evaluated using random and spatial cross-validation. Additionally, we simulated the expected landslide area over slopes in the entire study area, including those that did not experience slope failures in the past.The performance scores revealed a moderate to strong correlation between the observed and predicted landslide areas. Moreover, the simulations show coherent patterns, suggesting that it is worth extending the landslide area prediction further. We share data and codes in a GitHub repository https://github.com/mmorenoz/GAM_LandslideSize to promote the repeatability and reproducibility of this research.

Towards seismic performance quantification of viscous damped steel structure: Site-specific hazard analysis and response prediction

With an emphasis on predictable performance, the paramount importance of performance-based earthquake engineering (PBEE) in quantifying earthquake risks and facilitating the better-informed design of the built environment to achieve earthquake resilience has been widely acknowledged. And the uses of damping systems, i.e., structures incorporated with supplemental damping devices, have been recognized as an effective structural development to increase the resilience of structures to earthquakes. This paper presents a uniform hazard spectrum (UHS) based site-specific ground motion selection procedure, to implement the PBEE framework to relate earthquake hazard to structural performance for structures with variable dynamic properties. This ground motion selection procedure accounts for the effect of variable structural dynamic properties on hazard characterization for structures with damping systems. A paradigm building site, on which the site-specific hazard from the probabilistic seismic hazard analysis (PSHA) is consistent with the risk-targeted hazard from the design maps of ASCE/SEI 7-10, is selected for the implementation of the procedure. Three suites of 40 ground motions representing various hazard intensities at the building site are selected for time history dynamic analysis of a prototype structure with nonlinear viscous damping system. Evaluated is the probability distribution of major engineering demand parameters (EDPs) including story drift, residual story drift, floor velocity, and floor acceleration. The results demonstrated that the major EDPs of a building structure with supplemental nonlinear viscous dampers at a paradigm site can be estimated using the lognormal probability distribution, and the proposed UHS-based site-specific ground motion selection procedure is critical to the performance assessment of structures with variable dynamic properties in the PBEE framework.

Computation of Reinsurance Premiums by Incorporating a Composite Lognormal Model in a Risk-Adjusted Premium Principle

In this paper, a formula for calculating a premium for reinsurance is presented. This formula was determined by incorporating a lognormal-burr probability distribution model into the PH-transform principle which is one of the risk-adjusted premium calculating principles. The lognormal-burr probability distribution model was selected, modelled, classified and validated as the best fitting model to 2016 GAM’s automobile insurance claims data among the eight candidates of composite lognormal probability distribution models. Then, the formula was applied in calculating reinsurance premiums for an automobile insurance branch under an excess of loss non-proportional reinsurance treaty.

Deriving rainfall intensity–duration–frequency (IDF) curves and testing the best distribution using EasyFit software 5.5 for Kut city, Iraq

Abstract The intensity of rainfall can be considered as an essential factor in designing and operating hydraulic structures. The intensity–duration–frequency (IDF) curve is used for designing hydraulic projects such as drainage networks, road culverts, bridges, and many other hydraulic structures. In the field of water resources engineering, IDF curve is dependent widely on the plan, designing, and operating the project. Additionally, it can be used for different flood engineering structures. The purpose of this research is to get the frequency of the intensity of rain duration for Al KUTcity, Iraq, and find curves. Three essential techniques of frequency analysis (Gumbel distribution, lognormal, and log Pearson Type III) were depended to formulate this relationship based on data of rainfall intensity during the period between 1992 and 2019. Distribution methods involving lognormal, Gumbel, and log Pearson Type III were applied by Indian Meteorological Department (IMD) for short periods of 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 12, and 24 h with 2, 5, 10, 25, 50, and 100 years return periods. The results showed that rainfall intensity reduced as the duration of the storm increased, and if the return period of the rainfall was large, rainfall of any specific duration showed a higher intensity. Using EasyFit 5.5 software, for all durations, the lognormal probability distribution showed the best fit for the data group and estimated intensities of precipitation for return periods of 2, 5, 10, 25, 50, and 100 years. According to the obtained results, one can notice that the intensity of rainfall increased with the increment in return periods, but decreased with the increment in duration. The resulting IDF models could be used to improve accuracy and results.

Amplification Efficiency and Template Accessibility as Distinct Causes of Rain in Digital PCR: Monte Carlo Modeling and Experimental Validation.

Partitions in digital PCR (dPCR) assays do not reach the detection threshold at the same time. This heterogeneity in amplification results in intermediate endpoint fluorescence values (i.e., rain) and misclassification of partitions, which has a major impact on the accuracy of nucleic acid quantification. Rain most often results from a reduced amplification efficiency or template inaccessibility; however, exactly how these contribute to rain has not been described. We developed and experimentally validated an analytical model that mechanistically explains the relationship between amplification efficiency, template accessibility, and rain. Using Monte Carlo simulations, we show that a reduced amplification efficiency leads to broader threshold cycle (Ct) distributions that can be fitted using a log-normal probability distribution. From the fit parameters, the amplification efficiency can be calculated. Template inaccessibility, on the other hand, leads to a different rain pattern, in which a distinct exponential tail in the Ct distribution can be observed. Using our model, it is possible to determine if the amplification efficiency, template accessibility, or another source is the main contributor of rain in dPCR assays. We envision that this model will facilitate and speed up dPCR assay optimization and provide an indication for the accuracy of the assay.