Probability Distribution Function Research Articles

Enhanced Security Access Control Using Statistical-Based Legitimate or Counterfeit Identification System

With our increasing reliance on technology, there is a growing demand for efficient and seamless access control systems. Smartphone-centric biometric methods offer a diverse range of potential solutions capable of verifying users and providing an additional layer of security to prevent unauthorized access. To ensure the security and accuracy of smartphone-centric biometric identification, it is crucial that the phone reliably identifies its legitimate owner. Once the legitimate holder has been successfully determined, the phone can effortlessly provide real-time identity verification for various applications. To achieve this, we introduce a novel smartphone-integrated detection and control system called Identification: Legitimate or Counterfeit (ILC), which utilizes gait cycle analysis. The ILC system employs the smartphone’s accelerometer sensor, along with advanced statistical methods, to detect the user’s gait pattern, enabling real-time identification of the smartphone owner. This approach relies on statistical analysis of measurements obtained from the accelerometer sensor, specifically, peaks extracted from the X-axis data. Subsequently, the derived feature’s probability distribution function (PDF) is computed and compared to the known user’s PDF. The calculated probability verifies the similarity between the distributions, and a decision is made with 92.18% accuracy based on a predetermined verification threshold.

Three-parameters Gumbel Distribution: Formulation and Parameter Estimation

Modeling extreme value theories is really gaining interest in the world with scientist working to improve the flexibility of the distributions by adding parameter(s). Extreme value distributions are always described to include families of Gumbel, Weibull and Frechet distributions. Of the three distributions, Gumbel distribution is the most commonly used in the extreme value theory analysis. Existing literature has shown that the addition of parameter to a distribution makes it robust and/or more flexible hence the study intends to improve the existing two parameters Gumbel distribution using the Marshall and Olkin proposed method for introducing a new estimator/parameter to an existing distribution. The developed distribution will be important to the applications in some life time studies like high temperature, earthquakes, network designs, horse racing, queues in supermarket, insurance, winds, risk management, ozone concentration, flood, engineering and financial concepts. The parameters for the introduced distribution was estimated using Maximum Likelihood Estimation method. The introduced three parameters Gumbel distribution is a probability distribution function which can be used in modelling statistical data. The maximum likelihood estimates for the three parameters namely shape, location and dispersion are efficient, sufficient and consistent and this makes the function more flexible and better for application. The three parameters Gumbel distribution can be used in modeling and analysis of normal data, skewed data and extreme data since it will provide efficient, sufficient and consistent estimates.

On the stochastic significance of peaks in the least-squares wavelet spectrogram and an application in GNSS time series analysis

In this paper, the mathematical derivation of the underlying probability distribution function for the normalized least-squares wavelet spectrogram is presented. The impact of empirical and statistical weights on the estimation of the spectral peaks and their significance are demonstrated from the statistical point of view both theoretically and practically. The simulation results show an improvement of approximately 0.02mm (RMSE) for annual signal estimation when statistical weights are considered in the least-squares wavelet analysis (LSWA). The weighted LSWA estimates the signals more accurately than the ordinary LSWA for different percentage amount of missing data. As a real-world application, Global Navigation Satellite Systems (GNSS) time series for a station in Rome, Italy are analyzed. The analyses of the GNSS time series provided by different agencies for the same station reveal statistically significant annual peaks, more significant in 2010 but less significant between 2018 and 2020, while the higher frequency components show different spectral patterns over time. A declining trend of approximately −0.42 mm/year since 2004 is estimated for the GNSS height time series, likely due to gradual land subsidence. The results not only highlight the advantages of LSWA but can also help to better understand the uncertainties involved in signal estimation.

Optimal reconfiguration, renewable DGs, and energy storage units’ integration in distribution systems considering power generation uncertainty using hybrid GWO-SCA algorithms

ABSTRACT To optimize radial distribution systems, this study suggests the utilization of the Grey Wolf Optimizer (GWO), a hybrid metaheuristic optimization method, combined with the Sine Cosine method (SCA). The primary objective of this work is to enhance the distribution system by determining the most efficient network reconfiguration, sizing, and placement of various distributed energy sources in distribution system. The energy sources considered include capacitors, solar cells, wind turbines, biomass-based distributed generation units, and battery storage units. To achieve this goal, the proposed strategy incorporates the power loss sensitivity technique, which assists in identifying suitable candidate buses and accelerates the resolution process. Moreover, the model considers fluctuations in solar irradiance and wind speed using Weibull and Beta probability distribution functions, compensating for the intermittent nature of renewable energy sources and the variability in demand. To address power fluctuations, voltage surges, significant losses, and inadequate voltage stability challenges, battery energy storage, diesel generators, and dispatchable biomass DGs are employed to mitigate variability and enhance supply continuity. The proposed approach is evaluated and validated by comparing it to existing optimization strategies using IEEE 69-bus and 84-bus RDSs. The results demonstrate that the suggested technique achieves faster convergence to near-optimal solutions. The proposed methodology yields a significant reduction of up to 80% in power losses in the 69-bus system and a 35% reduction in the 84-bus system, signifying higher performance than existing methods.

Development of forecasting of monthly SAR time series in river systems: A multivariate data decomposition-based hybrid approach

The sodium adsorption ratio (SAR) is a critical variable in assessing the quality of water resources, and accurately forecasting its time series is operationally valuable. This study developed a hybrid approach using the multivariate variational mode decomposition (MVMD) model for signal analysis, Boruta model for feature selection, pure linear neural network (PLNN), support vector regression (SVR), Lasso regression, and Elman neural network (ENN) models to forecast monthly SAR time series for rivers. Data from two rivers were used to enhance result reliability, and the developed models were compared with corresponding basic models to evaluate their impact. Numerical and graphical criteria demonstrated the significant superiority of the developed models over the basic ones. Among the basic models, the ENN model exhibited the highest accuracy, while the MVMD-Boruta-ENN model surpasses all investigated models. This finding suggested that the ENN model's structure is more suitable for SAR time series forecasting than other basic models. Analyzing the models' residuals revealed lower mean, standard deviation, skewness, and error range in the developed models, indicating their robust behavior in forecasting the SAR time series. Notably, forecasting extreme SAR values holds greater importance than other values. Anderson-Darling and Kolmogorov-Smirnov tests identified the dominance of the generalized logistic and log-logistic (3-parameters) functions in SAR time series. Probability distribution functions were used to estimate extreme values, and the studied models exhibited more accurate estimations compared to the basic models, indicating their enhanced resilience. The consistent patterns observed in comparing developed and basic models for the entire series, as well as extreme values and residuals across the two investigated rivers, emphasized the reliability of the results.

Employing generative adversarial neural networks as surrogate model for reactive transport modeling in the hyporheic zone

This study explores the application of advanced deep learning techniques, specifically conditional deep convolutional generative adversarial networks (cDC-GANs), to model and predict the complex dynamics of the hyporheic zone (HZ) driven by river stage fluctuations. The HZ is a critical transitional mixing zone between surface water and groundwater, where significant biogeochemical reactions occur. Traditional process-based reactive transport modeling methods are computationally intensive and require fine-scale parameterization. To overcome these challenges, we employ the cDC-GAN as a deep-learning-based surrogate model to predict zones of enhanced biogeochemical activity (i.e., hotspots) and reaction product concentrations in the HZ under varying bimodal sedimentary heterogeneity scenarios. The cDC-GAN model can efficiently capture nonlinear relationships between input data and output parameters without extensive parameterization, making it computationally less demanding. The model’s generative capabilities allow for the creation of new data instances, enabling the exploration of diverse scenarios and interpolation between observed data points. The model uses maps of liquid saturation and solute concentrations at different time steps to generate corresponding maps of reaction rates and reaction product concentrations. Results demonstrate the model’s qualitative and quantitative ability to capture complex relationships without relying on rigid assumptions about linearity or specific probability distribution functions. Notably, even amid variations in aquifer heterogeneity, the model consistently exhibits robust performance, validating its ability to adapt to dynamic geological settings. Our use of a simplified reaction scheme serves as a proof of concept for the cDC-GAN model’s ability to simulate solute transport in the HZ, opening avenues for future applications including more complex reaction networks within HZ system such as nutrient cycling, organic matter degradation, redox reactions, and beyond.

Distributionally robust optimization configuration method for island microgrid considering extreme scenarios

The marine climate conditions are intricate and variable. In scenarios characterized by high proportions of wind and solar energy access, the uncertainty regarding the energy sources for island microgrid is significantly exacerbated, presenting challenges to both the economic viability and reliability of the capacity configuration for island microgrids. To address this issue, this paper proposes a distributionally robust optimization (DRO) method for island microgrids, considering extreme scenarios of wind and solar conditions. Firstly, to address the challenge of determining the probability distribution functions of wind and solar in complex island climates, a conditional generative adversarial network (CGAN) is employed to generate a scenario set for wind and solar conditions. Then, by combining k-means clustering with an extreme scenario selection method, typical scenarios and extreme scenarios are selected from the generated scenario set, forming the scenario set for the DRO model of island microgrids. On this basis, a DRO model based on multiple discrete scenarios is constructed with the objective of minimizing the sum of investment costs, operation and maintenance costs, fuel purchase costs, penalty costs of wind and solar curtailment, and penalty costs of load loss. The model is subjected to equipment operation and power balance constraints, and solved using the columns and constraints generation (CCG) algorithm. Finally, through typical examples, the effectiveness of this paper’s method in balancing the economic viability and robustness of the configuration scheme for the island microgrid, as well as reducing wind and solar curtailment and load loss, is verified.

Fidelity and entanglement of random bipartite pure states: insights and applications

We investigate the fidelity of Haar random bipartite pure states from a fixed reference quantum state and their bipartite entanglement. By plotting the fidelity and entanglement on perpendicular axes, we observe that the resulting plots exhibit non-uniform distributions. The distribution depends on the entanglement of the fixed reference quantum state used to quantify the fidelity of the random pure bipartite states. We find that the average fidelity of typical random pure bipartite qubits within a narrow entanglement range with respect to a randomly chosen fixed bipartite qubit is 14 . Extending our study to higher dimensional bipartite qudits, we find that the average fidelity of typical random pure bipartite qudits with respect to a randomly chosen fixed bipartite qudit remains constant within a narrow entanglement range. The values of these constants are 1d2 , with d being the dimension of the local Hilbert space of the bipartite qudit system, suggesting a consistent relationship between entanglement and fidelity across different dimensions. The probability distribution functions of fidelity with respect to a product state are analytically studied and used as a reference for the benchmarking of distributed quantum computing devices.

Multi-objective optimal power flow with wind–solar–tidal systems including UPFC using Adaptive Improved Flower Pollination Algorithm(AIFPA)

ABSTRACT Among the most significant non-linear challenges for power network design and smooth functioning of current modern updated power system networks is the optimum power flow (OPF) problem. Importance of the electrical system modeling has recently come to light due to the incremental use of energy from renewable sources in power systems networks. The goal is to use wind, solar and tidal sources to recreate the issue of OPF. In this work, Weibull, Lognormal, and also Gumbel probability distribution functions were applied to simulate the uncertainties of wind, photovoltaic, and tidal energy system. Additionally, by adding test scenarios of unpredictable wind, solar and tidal energy systems involving minimization of the cost function, loss of active power, voltage deviation, and increase stability of voltage. In accordance with the chosen thermal producing units, the solutions were evaluated using different locations using IEEE 30-bus systems of testing that incorporate renewable energy sources. The proposed power system planning problem was solved by multi-objective function where unified power flow controller are utilized as flexible AC transmission systems controllers via recently introduced optimization algorithms and the simulation outcomes of the aforementioned technique have been compared with Multi Objective Adaptive Guided Differential Evolution algorithms. The adaptive improved flower pollination algorithm (AIFPA) is a strong and reliable algorithm that is presented in this work. The AIFPA can efficiently deal with many kinds of high-complexity objective regions in multi-objective optimization situations. Utilizing an IEEE 30-bus test system, the suggested approaches’ performance was examined and evaluated for a range of objective functions. The simulation results obtained from the proposed algorithm were effective in finding the optimal solution compared to the results of the meta-heuristic algorithm and were reported in the literature.

The Information Length Concept Applied to Plasma Turbulence.

A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, which is studied in a novel manner using statistical methods. The simulation data exhibit transport processes with both medium and long correlation length along the radius. A typical example of a phenomenon with long correlation length is avalanches. In order to investigate the evolution of the turbulent state, two basic configurations are studied, one flux-driven and one gradient-driven with decaying turbulence. The information length concept in tandem with Boltzmann-Gibbs and Tsallis entropy is used in the investigation. It is found that the dynamical states in both flux-driven and gradient-driven cases are surprisingly similar, but the Tsallis entropy reveals differences between them. This indicates that the types of probability distribution function are nevertheless quite different since the higher moments are significantly different.

The miniJPAS survey: Evolution of luminosity and stellar mass functions of galaxies up to z~0.7

We aim to develop a robust methodology for constraining the luminosity and stellar mass functions (LMFs) of galaxies by solely using photometric measurements from multi-filter imaging surveys. We test the potential of these techniques for determining the evolution of these functions up to $z 0.7$ in the Javalambre Physics of the Accelerating Universe Astrophysical Survey (J-PAS), which will image thousands of square degrees in the northern hemisphere with an unprecedented photometric system that includes $54$ narrow band filters. As J-PAS is still an ongoing survey, we used the miniJPAS dataset (a stripe of $1$ deg$^2$ dictated according to the J-PAS strategy) for determining the LMFs of galaxies at $0.05 z 0.7$. Stellar mass and $B$-band luminosity for each of the miniJPAS galaxies are constrained using an updated version of our fitting code for spectral energy distribution, MUlti-Filter FITting (MUFFIT), whose values are based on non-parametric composite stellar population models and the probability distribution functions of the miniJPAS photometric redshifts. Galaxies are classified according to their star formation activity through the stellar mass versus rest-frame colour diagram corrected for extinction (MCDE) and we assign a probability to each source of being a quiescent or star-forming galaxy. Different stellar mass and luminosity completeness limits are set and parametrised as a function of redshift, for setting the limitations of our flux-limited sample ($r_ SDSS 22$) for the determination of the miniJPAS LMFs. The miniJPAS LMFs are parametrised according to Schechter-like functions via a novel maximum likelihood method accounting for uncertainties, degeneracies, probabilities, completeness, and priors. Overall, our results point to a smooth evolution with redshift ($0.05 z 0.7$) of the miniJPAS LMFs, which is in agreement with previous studies. The LMF evolution of star-forming galaxies mainly involve the bright and massive ends of these functions, whereas the LMFs of quiescent galaxies also exhibit a non-negligible evolution in their faint and less massive ends. The cosmic evolution of the global $B$-band luminosity density decreases by $ 0.1$ dex from $z=0.7$ to $0.05$; whereas for quiescent galaxies, this quantity roughly remains constant. In contrast, the stellar mass density increases by $ dex in the same redshift range, where the evolution is mainly driven by quiescent galaxies, owing to an overall increase in the number of this type of galaxy. In turn, this covers the majority and most massive galaxies, namely, $60$--$100$<!PCT!> of galaxies at $ (M_

Correlated non-Gaussian and Gaussian noises induced transition and mean first-passage time in a fractional-order bistable system

The transition and mean first-passage time(MFPT) in a fractional-order bistable system, excited by multiplicative non-Gaussian noise and additive Gaussian white noise, are investigated. Utilizing the fractional-order minimum mean square error criterion and the path integral approach, we derive approximate expressions for both the steady-state probability distribution function and the MFPT. The results show that the noise correlation strength, non-Gaussian parameter, Gaussian noise strength and fractional order can induce phase transitions. The MFPT exhibits a peak as a function of non-Gaussian noise intensity, demonstrating the noise-enhanced stability phenomenon, while the MFPT displays a consistent, monotonic relationship as a function of Gaussian white noise intensity. Numerical simulations are conducted to validate theoretical results, which show a reasonably high degree of consistency.

Modelling Diameter at Breast Height Distribution for Eight Commercial Species in Natural-Origin Mixed Forests of Ontario, Canada

Diameter at breast height (DBH) is a unique attribute used to characterize forest growth and development for forest management planning and to understand forest ecology. Forest managers require an array of DBHs of forest stands, which can be reconstructed using selected probability distribution functions (PDFs). However, there is a lack of practices that fit PDFs of sub-dominating species grown in natural mixed forests. This study aimed to fit PDFs and develop predictive models for PDF parameters, so that the predicted distribution would represent dynamic forest structures and compositions in mixed forest stands. We fitted three of the simplest forms of PDFs, log-normal, gamma, and Weibull, for the DBH of eight tree species, namely balsam fir (Abies balsamea [L.] Mill.), eastern white pine (Pinus strobus L.), paper birch (Betula papyrifera Marshall), red maple (Acer rubrum L.), red pine (Pinus resinosa Aiton), trembling aspen (Populus tremuloides Michx), and white spruce (Picea glauca [Moench] Voss), all grown in natural-origin mixed forests in Ontario province, Canada. We estimated the parameters of the PDFs as a function of DBH mean and standard deviation for these species. Our results showed that log-normal fit the best among the three PDFs. We demonstrated that the predictive model could estimate the recovered parameters unbiasedly for all species, which can be used to reconstruct the DBH distributions of these tree species. In addition to prediction, the cross-validated R2 for the DBH mean ranged between 0.76 for red maple and 0.92 for red pine. However, the R2 for the regression of the standard deviation ranged between 0.00 for red pine and 0.69 for sugar maple, although it produced unbiased predictions and a small mean absolute bias. As these mean and standard deviations are regressed with dynamic covariates (such as stem density and stand basal area), in addition to climate and static geographic variables, the predicted DBH distribution can reflect change over time in response to management or any type of disturbance in the regime of the given geography. The predictive model-based DBH distributions can be applied to the design of appropriate silviculture systems for forest management planning.

A Tempered Fractional Kinetic Transport Theory for Energetic Particle Interaction with Quasi-two-dimensional Turbulence in the Large-scale Solar Wind

Observational evidence is accumulating that turbulence in the solar wind is intermittent (non-Gaussian) because of the strong presence of a quasi-two-dimensional (quasi-2D), low-frequency turbulence component containing nonpropagating, closed, small-scale magnetic flux ropes with open meandering field lines in between. le Roux & Zank showed how one can derive fractional focused and Parker-type transport equations that model large-scale anomalous transport in the solar wind as the outcome of energetic particle interaction with quasi-2D turbulence. In this follow-up paper this theory is developed further to address certain limitations. (i) The second moment of the Lévy probability distribution function (PDF) specified in the theory for the particle step size is infinite, indicating unphysical transport. (ii) The expected transition of energetic particle transport from anomalous to normal diffusion beyond a certain critical transport distance was not included. (iii) The competition between anomalous diffusion and advection is not properly sustained at late times. Shortcomings (i) and (ii) are addressed by introducing an exponentially truncated Lévy PDF for the energetic particle step size in the theory, resulting in revised tempered fractional focused and Parker-type transport equations featuring tempered fractional derivatives that enable modeling of tempered Lévy flights. Furthermore, these equations are cast in a tempered fractional telegrapher form to investigate whether the fractional wave equation part of the equation can restore causality in unscattered particle transport during early times and in Lévy flights during intermediate times (Lévy walks). They are also transformed into a tempered fractional Fokker–Planck form to overcome limitation (iii).

Is GN-z11 powered by a super-Eddington massive black hole?

Context. Observations of z ∼ 6 quasars powered by supermassive black holes (SMBHs; MBH ∼ 108 − 10 M⊙) challenge our current understanding of early black hole (BH) formation and evolution. The advent of the James Webb Space Telescope (JWST) has enabled the study of massive BHs (MBHs; MBH ∼ 106 − 7 M⊙) up to z ∼ 11, thus bridging the properties of z ∼ 6 quasars to their ancestors. Aims. The JWST spectroscopic observations of GN-z11, a well-known z = 10.6 star-forming galaxy, have been interpreted with the presence of a super-Eddington (Eddington ratio ≡ λEdd ∼ 5.5) accreting MBH. To test this hypothesis, we used a zoom-in cosmological simulation of galaxy formation and BH co-evolution. Methods. We first tested the simulation results against the observed probability distribution function (PDF) of λEdd found in z ∼ 6 quasars. Then, in the simulation we selected the BHs that satisfy the following criteria: (a) 10 < z < 11, (b) MBH > 106 M⊙. Next, we applied the extreme value statistics to the PDF of λEdd resulting from the simulation. Results. We find that the probability of observing a z ∼ 10 − 11 MBH accreting with λEdd ∼ 5.5 in the volume surveyed by JWST is very low (< 0.2%). We compared our predictions with those in the literature, and discussed the main limitations of our work. Conclusions. Our simulation cannot explain the JWST observations of GN-z11. This might be due to: (i) poor resolution and statistics in simulations, (ii) simplistic sub-grid models (e.g. BH accretion and seeding), (iii) uncertainties in the data analysis and interpretation.

Control Charts for a Novel Exponent Power Rayleigh Distribution

Abstract: In this Paper, we presented the distribution as A Novel Exponent Power Rayleigh (NovEPRD) probability density function, Distribution, and Survival and Hazard functions introduced by Bharathi et al (2022) and A Novel Exponent Power Rayleigh (NovEPR) distribution Properties and its Applications studied by Bharathi et al (2022) and then here we derived the Weighted Variance (WV), Weighted Standard Deviation (WSD) and Correction Factor (CF) for existed A Novel Exponent Power Rayleigh (NovEPR) distribution , this paper obtains the parameters of the control lines X̅ and R drawn from the A Novel Exponent Power Rayleigh (NovEPR) distribution. These methods are compared with Newton Raphson’s simulations. For these control charts, Type I risk is compared with different groups of A Novel Exponent Power Rayleigh (NovEPR) distribution. Simulation results show that the Skewness Correction (SC) method of Type I carries less risk than other methods. When the distribution is approximately equal, the type I risk of the Shewhart, W V, WSD and SC X̅ plans is comparable, while the type I risk of the SC R plan is smaller

Incorporating flowpaths as an explicit measure of river-floodplain connectivity to improve estimates of floodplain sediment deposition

Variation in floodplain topography can lead to gradual flooding and increase river-floodplain connectivity. We show that incorporating flowpaths as an explicit measure of river-floodplain connectivity can improve estimates of floodplain sediment deposition. We focus on the floodplain of the South River, downstream of Waynesboro, Virginia, where measurements of mercury accumulation have been used to estimate decadal-scale sedimentation rates. We developed a two-dimensional Hydrologic Engineering Center's River Analysis System (2D HEC-RAS) hydrodynamic model and used simulated model results with sediment deposition data to create regression models describing sedimentation across the floodplain. All of our statistical models incorporated a flowpath length from the location on the floodplain downstream to the riverbank as an explicit measure of river-floodplain connectivity that improved our estimates of floodplain sediment deposition (r2 = 0.514). We applied our best regression model to our hydrodynamic model results to create a map of floodplain sedimentation rate and discuss differences of three separate sections of floodplain. We found that floodplains with variable topography had wider, bimodal probability distribution functions (PDFs) of sedimentation rate (aggregated spatially) than floodplains without this topographic relief (with narrower log-normal PDFs). Our work highlights how floodplain topography and river-floodplain connectivity affect sedimentation rates and can help inform the development of floodplain sediment budgets.

Estimate rainfall return period based on maximum pipe flow: A new framework to address mutual relationship

The unreasonable assumption that the rainfall return period is similar to the runoff return period may lead to unreasonable drainage system design. Hence, this study proposes a computational framework to calculate the rainfall return period according to the runoff return period. Based on the Akaike Information Criterion (AIC) and the optimal probability distribution functions, a novel approach was proposed to combine the rainfall and maximum pipe flow return periods. Copula functions were employed to construct a joint probability distribution for calculating the rainfall return period using the maximum pipe flow return period. Thus, this study reached the following results. (I) The Gamma, Logistic, and Weibull distributions provided better descriptions for the rainfall and maximum pipe flow probability distributions. The Gaussian, Gumbel, and Survival Clayton Copula functions were shown to be the optimal choices. (II) A calculation method for the rainfall return period was constructed based on the Satisfaction Percentage (SP). For instance, using a 2-year as the maximum pipe flow return period, the rainfall return period was determined to be 4.705 years (60 min of rainfall duration, Maluan community) with an SP value of 0.95. (III) The study area showed non-significant impacts (p < 0.05) in selecting the rainfall return periods. Therefore, simulations can be conducted in regions with missing pipe network data using similar underlying surface conditions from other study areas.

Exploring cumulative probability functions for streamflow drought magnitude: Global scale analysis and parametric vs. non-parametric comparisons

Streamflow droughts pose significant challenges to water resource management and environmental sustainability. The accurate characterization of streamflow drought magnitude is essential for effective mitigation, assessment and adaptation strategies. In this study, we explore the implications of choosing different cumulative probability distribution functions (cdfs) on the determination of streamflow drought magnitude, as assessed by the z-score values of the standardized streamflow index (SSI) and return periods. Our investigation encompasses a comprehensive global-scale analysis, with the aim of identifying the most suitable cdfs for characterizing streamflow droughts. To accomplish this objective, we incorporate global simulated streamflow values from the model WaterGAP 2.2d and observed streamflow values from 280 Global Runoff Data Centre (GRDC) stations for the period 1981 – 2010. We evaluate the performance of 118 parametric cdfs for each of the 12 calendar monthly streamflow values at each model grid cell and GRDC station to determine the best fitting parametric cdf. Moreover, we go beyond the conventional scope of such studies by further assessing the best-fitting cdfs alongside non-parametric cdfs such as the Empirical cumulative distribution function (ecdf) and the cumulative distribution function derived from the Kernel density estimation function (kcdf). Among our findings, we establish a subset of 23 parametric cdfs that exhibit the best fit for the global streamflow values concerning all 12 calendar monthly streamflow values at individual GRDC stations or grid cells within the specified period. Furthermore, we observe that the accuracy of streamflow simulation and the length of the reference period directly influence the selection of the most suitable parametric cdf. Our comparative analysis reaffirms the existing understanding that opting for the best-fitting parametric cdf, rather than a non-parametric alternative, mitigates the risk of overestimating drought magnitudes. However, we emphasize the crucial importance of considering the intended purpose, approach-specific sensitivities, and uncertainties when choosing the most suitable parametric cdf for any calendar monthly streamflow values.

Evidence of a Proximity Effect in a (AgI)x - C(1-x) Mixture Using a Simulation Model Based on Random Variable Theory.

Silver iodide is a prototype compound of superionic conductors that allows ions to flow through its structure. It exhibits a first-order phase transition at 420 K, characterized by an abrupt change in its ionic conductivity behavior, and above this temperature, its ionic conductivity increases by more than three orders of magnitude. Introducing small concentrations of carbon into the silver iodide structure produces a new material with a mixed conductivity (ionic and electronic) that increases with increasing temperature. In this work, we report the experimental results of the ionic conductivity as a function of the reciprocal temperature for the (AgI)x - C(1-x) mixture at low carbon concentrations (x = 0.99, 0.98, and 0.97). The ionic conductivity behavior as a function of reciprocal temperature was well fitted using a phenomenological model based on a random variable theory with a probability distribution function for the carriers. The experimental data show a proximity effect between the C and AgI phases. As a consequence of this proximity behavior, carbon concentration or temperature can control the conductivity of the (AgI)x - C(1-x) mixture.