Probability Distribution Function Research Articles

Beyond radial profiles: using log-normal distributions to model the multiphase circumgalactic medium

ABSTRACT Recent observations and simulations reveal that the circumgalactic medium (CGM) surrounding galaxies is multiphase, with the gas temperatures spanning a wide range at most radii, ∼104 K to the virial temperature (∼106 K for Milky Way). Traditional CGM models using simple density profiles are inadequate at reproducing observations that indicate a broad temperature range. Alternatively, a model based on probability distribution functions (PDFs) with parameters motivated by simulations can better match multiwavelength observations. In this work, we use log-normal distributions, commonly seen in the simulations of the multiphase interstellar and circumgalactic media, to model the multiphase CGM. We generalize the isothermal background model by Faerman et al. to include more general CGM profiles. We extend the existing probabilistic models from 1D-PDFs in temperature to 2D-PDFs in density–temperature phase space and constrain its parameters using a Milky Way-like Illustris TNG50-1 halo. We generate various synthetic observables such as column densities of different ions, UV/X-ray spectra, and dispersion and emission measures. X-ray and radio (Fast Radio Burst) observations mainly constrain the hot gas properties. However, interpreting cold/warm phase diagnostics is not straightforward since these phases are patchy, with inherent variability in intercepting these clouds along arbitrary lines of sight. We provide a tabulated comparison of model predictions with observations and plan to expand this into a comprehensive compilation of models and data. Our modelling provides a simple analytical framework that is useful for describing important aspects of the multiphase CGM.

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Improving and extending non-Poissonian distributions for satellite galaxies sampling in HOD: applications to eBOSS ELGs

ABSTRACT Halo occupation distribution (HOD) models help us to connect observations and theory, by assigning galaxies to dark matter haloes. In this work, we study one of the components of HOD models: the probability distribution function (PDF), which is used to assign a discrete number of galaxies to a halo, given a mean number of galaxies. For satellite galaxies, the most commonly used PDF is a Poisson Distribution. PDFs with super-Poisson variances have also been studied, allowing for continuous values of variances. This has not been the case for sub-Poisson variances, for which only the nearest integer distribution, with a single variance, has been used in the past. In this work, we propose a distribution based on the binomial one, which provides continuous sub-Poisson variances. We have generated mock galaxy catalogues from two dark-matter only simulations, unit and outerrim, with HOD models assuming different PDFs. We show that the variance of the PDF for satellite galaxies affects the one-halo term of the projected correlation function, and the count-in-cells (CIC) one point statistics. We fit the clustering of eBOSS emission line galaxies, finding results consistent with the literature, when we only vary the parameter controlling the PDF variance and the fraction of satellites. Using a mock catalogue as a reference, we have also included both the clustering and CIC to constrain the parameters of the HOD model. CIC can provide strong constraints to the PDF variance of satellite galaxies.

Structural properties of different sphere packings with arbitrary porosities for planetary-science applications

Granular solids in planetary science are found in the regolith that covers planetary surfaces as well as in the bulk of rubble-pile asteroids, comets and planetesimals. To help understand the physics of these planetary bodies, we aim at deriving the structural properties of granular packings over a large range of porosities. Relevant to fluid flow and gas diffusion are the void spaces inside the granular packings so that we analyze the mean free path of point-like particles, their diffusion constant and their total traveled path lengths. For mechanical and heat-transport properties, the coordination number and the absolute chain length of the inter-connected particles are important. Generally, we also derive the homogeneity and isotropy of the granular solids. We compare granular packings generated by four algorithms for porosities in the range between 85 and 42%, which are the upper and lower limits for natural packings of equal-sized spheres. All produced sphere packings arrive at very similar quantities for the mean free path, the free path probability distribution function, the diffusion constant and the total traveled path length for the entire range of porosities. Hence, transport processes governed by the void-space properties are independent of the specific generation algorithm for the granular packing. In contrast, heat conduction or mechanical stresses almost exclusively depend on the existence and properties of particle contacts and particle chains in the network of spheres. In this case, the four algorithms deliver very different results.Graphic abstract

Connecting flow duration curve and precipitation duration curve based on the relationship deduced from machine learning in the watersheds of northern China

Obtaining reliable hydrological data for ungauged watersheds has always been a significant challenge in the water resources management. The flow duration curve (FDC) and precipitation duration curve (PDC) are classical methods to address this challenge. However, traditional FDC and PDC methods mostly rely on pre-assumed probability distribution function form, which may result in sub-optimal model parameters and consequently sub-optimal simulation results of hydrological data, and the common function forms are not applicable to deal with the data including zero-values, which often occurs in the discharge data of arid region and daily rainfall data. To address the issues in FDC and PDC , this study firstly determines the most suitable function form to describe FDC and PDC from various distribution functions, i.e., Log Normal, Generalized Pareto Distribution and H2018 function, from 1960 to 2010 in 7 watersheds in the north of China. The multiple methods including Random Forest, polynomial, Multilayer Perceptron and K-Nearest Neighbor are employed to simulate the parameters of the functions, aiming to deduce the optimal parameters of FDC functions. The results show that, H2018 function form has the best performance in simulating the PDC and FDC and in general, parameter a and b of H2018 function indicate an opposite trend, and parameter k declines in mostly condition at the annual scale from 1960 to 2010. The results of different methods indicate that the Random Forest method is the most efficient and accurate approach to deduce FDC parameters from measured precipitation and climate factors, compared with polynomial, Multilayer Perceptron and K-Nearest Neighbor. Based on the relationship between PDC parameters and FDC parameters, the FDC of ungauged basins can be deduced from the observed precipitation data. The research findings provide a new method to estimate FDC for the water resources management in the ungauged basins.

Hydrological drought assessment using the standardized groundwater index and the standardized precipitation index in the Berg River Catchment, South Africa

Study regionBerg River Catchment (BRC), South Africa (SA). Study focusHydrological droughts threaten water security and climate Change and groundwater abstractions may exacerbate their impact. Thus, early detection and prediction of droughts is essential. The integration of the Standardised Groundwater Index (SGI) with the Standardised Precipitation Index (SPI), has been applied worldwide, it but not explored in South Africa (SA). The aim of this study was to evaluate the integration of the SGI and SPI for hydrological drought assessment within the BRC, SA. New hydrological insights for the regionThe sensitivity of the SGI to selected Probability Distribution Functions (PDFs) was examined, resulting in the Gamma and Log-Normal PDFs being preferred in the BRC. SGI-Gamma and SPI-Gamma comparisons validated the SGI method and shed light on the key factors influencing groundwater-related droughts in the BRC. The following was revealed: Hydrological droughts in the BRC are influenced by climate factors, surface and groundwater interactions, and groundwater abstractions. When conducting hydrological drought assessments using the SGI and the SPI, the initial focus should be on catchment-scale assessments before expanding to national-scale evaluations. Groundwater in the BRC exhibit significant resilience to droughts induced by climate factors, and thus useful to mitigate the risk of future droughts. Finally, The SGI performed satisfactorily in the BRC with limited groundwater level data.

Probability-Distribution-Configurable True Random Number Generators Based on Spin-Orbit Torque Magnetic Tunnel Junctions.

The incorporation of randomness into stochastic computing can provide ample opportunities for applications such as simulated annealing, non-polynomial hard problem solving, and Bayesian neuron networks. In these cases, a considerable number of random numbers with an accurate and configurable probability distribution function (PDF) are indispensable. Preferably, these random numbers are provided at the hardware level to improve speed, efficiency, and parallelism. In this paper, how spin-orbit torque magnetic tunnel junctions (SOT-MTJs) with high barriers are suitable candidates for the desired true random number generators is demonstrated. Not only do these SOT-MTJs perform excellently in speed and endurance, but their randomness can also be conveniently and precisely controlled by a writing voltage, which makes them a well-performed Bernoulli bit. By utilizing these SOT-MTJ-based Bernoulli bits, any PDF, including Gaussian, uniform, exponential, Chi-square, and even arbitrarily defined distributions can be realized. These PDF-configurable true random number generators can then promise to advance the development of stochastic computing and broaden the applications of the SOT-MTJs.

Effects of H2 enrichment on combustion characteristics in inverse swirl diffusion flames of H2-doped jet fuel using OH, CH2O, fuel and temperature imaging

Hydrogen (H2) and jet fuel co-firing is regarded as a promising transition strategy of decarbonization in aviation industry. Considering the simplicity and safety during highly hydrogen enrichment conditions, the inverse swirl diffusion (ISD) combustion holds research value. Given the current lack of understanding for the flame properties of H2-enriched pre-evaporative jet fuel ISD co-combustion, in this work, the simultaneous planar laser-induced fluorescence (PLIF) of hydroxyl (OH), formaldehyde (CH2O), and fuel, as well as the non-linear excitation regime two-line atomic fluorescence (NTLAF) thermography imaging, are used to study the effects of hydrogen enrichment on ISD flame intricate structure and temperature field. The results show the positive effects of H2 enrichment. The ISD flames display a blue hue and the increase in doping hydrogen helps the flames stabilize under global-lean conditions with almost no CO emission and low CO2 emission at the chamber exit. And the H2 enrichment contributes to inhibiting the CH2O formation upstream, reducing the generation of isolated reaction islands and promoting the strength of the flame wings, favoring the suppression of flame instability. In contrast, when at low H2 enrichment rate, the shift of the heat release zone and high-temperature zone, and the enlargement of the cold zone, are found in flame upstream. The analysis of the probability distribution functions (PDF) of temperatures confirms the effective effects of hydrogen on inhibiting the local flame fluctuations. Although the increase in the overall temperature level due to the hydrogen addition would lead to a promotion in NOx generation, the discussion on the structural analysis and flame propagation stability of ISD flames demonstrates the significance of H2 enrichment for the achievement of leaner low-NOx combustion of ultra-H2-enriched jet fuel in the future.

Characterization of the future northeast monsoon rainfall based on the clustered climate zone under CMIP6 in Peninsular Malaysia

The Northeast monsoon (NEM) exerts a significant influence on the climate system of Peninsular Malaysia (PM) and has profound implications for water resource management, flood control, and disaster preparedness in the region. This study employed CHIRPS rainfall data from 1981 to 2022 at a spatial resolution of 0.25° to generate climate zones. The performance of global climate models (GCMs) in replicating monthly rainfall was evaluated using multiple statistical metrics, with the top-ranked ones being used for the generation of future projection downscaled ensemble models. The NEM months (November, December, January, February, and March) were used as input parameters to form clustered homogeneous groups using the Ward hierarchical method. The optimal number of climate zones was determined using the elbow method, silhouette width values, and spatial evaluation. Ultimately, a 7-cluster solution was chosen due to its consistency and meaningful cluster formation. The zones were categorized into two regions: the West Coast and the East Coast, based on their geographical location and distinctive monthly NEM rainfall patterns. The analysis of the probability distribution function (PDF) showed that rainfall in the West Coast region had a more spread-out pattern with varying amounts, while rainfall in the East Coast region was more concentrated and consistent. The Northeast climate zone received the highest rainfall, attributed to its proximity to the South China Sea, mountainous areas, and the NEM convergence zone. In contrast, the Northwest and Lower Central-West climate zones received the lowest rainfall due to the rain shadow effect, limited moisture availability, and distance from major moisture sources. The CMCC-ESM2, CMCC-CM2-SR5, EC-Earth3, and CanESM5 consistently ranked among the highest performing models. After linear scaling bias correction, validated GCMs showed significant improvements, with improvements in MAE, NRMSE, PBIAS, RSR, NSE, MD, CP, R2, and KGE by 11–45%, 15–47%, 96–100%, 15–47%, 10–79%, 5–37%, 68–113%, 11–73%, and 9–51%, respectively. Analysis of NEM season rainfall patterns across climate zones indicated consistent mid-future increases for the Northwest and Lower Central-West zones (12.4–19.8%) and the Upper Central-West and Southwest zones (0.2–5.4%) across all scenarios. In the far-future, the Southeast zone saw an overall increase in rainfall (4.9–11.4%), while the Central-West zone exhibited mixed results (−4.0 to 5.6%). The results also highlighted spatial variability and the need to consider specific climate zones when assessing the impacts of climate change on the NEM, emphasizing the importance of incorporating these projections into long-term planning and decision-making processes.

An Extension of the Fréchet Distribution and Applications

This paper presents the Slash-Exponential-Fréchet distribution, which is an expanded version of the Fréchet distribution. Through its stochastic representation, probability distribution function, moments and other relevant features are obtained. Evidence supports that the updated model displays a lighter right tail than the Fréchet model and is more flexible as for skewness and kurtosis. Results on maximum likelihood estimators are given. Our proposition’s applicability is demonstrated through a simulation study and the evaluation of two real-world datasets.

Assessing future changes in flood frequencies under CMIP6 climate projections using SWAT modeling: a case study of Bitlis Creek, Turkey

ABSTRACT Climate change is altering flood risk globally, with local variations prompting the necessity for regional assessments to guide the planning and management of water-related infrastructures. This study details an integrated framework for assessing future changes in flood frequencies, using the case of Bitlis Creek (Turkey). The precipitation and temperature simulations of 21 global circulation models (GCMs) from the coupled model intercomparison project phase 6 (CMIP6) are used to drive the developed soil and water assessment tool (SWAT) model in generating daily streamflow projections under the CMIP6 historical experiment and the shared socio-economic pathway (SSP) scenarios of SSP245 and SSP585. Five probability distribution functions are considered to calculate the 5-, 10-, 25-, 50-, 100-, and 500-year flood discharges for the historical period 1955–2010 and the future periods 2025–2074 and 2025–2099. The quantification of climate change impacts on the design discharges is based on the medians of the flood discharges obtained for the climate data of each GCM, using the best-fitted distribution functions. The findings illustrate significant increases in discharge rates, ranging from 21.1 to 31.7% for the 2025–2099 period under the SSP585 scenario, highlighting the necessity of considering changing climate conditions in designing water-related infrastructures.

A hydro-climatic approach for extreme flood estimation in mountainous catchments

Prediction of rainfall-runoff process, peak discharges, and finally flood hydrograph is essential for flood risk management and river engineering projects. In most previous studies in this field, the precipitation rates have been entered into the models without considering seasonal and monthly distribution. In this study, the daily precipitation data of 144 climatology stations in Iran were used to evaluate the seasonal and monthly pattern of flood-causing precipitation. Then, by determining the rainy seasons and seasonal fit of precipitation with a probabilistic model and using regional precipitation, a semi-distributed conceptual model of rainfall-runoff (MORDOR-SD) was trained and validated using the observed discharge data. Flood prediction was performed using climatic data, modeling of hydrological conditions, and extreme flow data with high performance. According to the results, the Nash–Sutcliffe and Kling–Gupta coefficients were 0.69 and 0.82 for the mean daily streamflow, 0.98 and 0.98 for the seasonal streamflow, 0.98 and 0.94 for the maximum discharges, and 0.57 and 0.78 for low flows, respectively. Moreover, the maximum daily discharges in different return periods were estimated using the results of the MORDOR-SD model, considering the probability distribution function of the probabilistic model of central precipitation (MEWP), the probabilistic model of adjacent precipitation, and probability distribution function of the previous precipitation. Finally, the extreme flows were predicted and compared using different methods including the SCHADEX, regional flood analysis, GRADEX, and AGREGEE. The results showed that the methods GRADEX, AGREGEE, and SCHADEX have the highest performance in predicting extreme floods, respectively.

Cosmic string influence on a 2D hydrogen atom and its relationship with the Rytova–Keldysh logarithmic approximation in semiconductors

A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a cosmic string. Reducing the hydrogen atom to two dimensions enhances its suited to capture the cylindrical/conical symmetry associated with the cosmic string, providing a more appropriate description of the physical system. After solving Schrd̈inger’s equation, we calculate the eigenenergies, probability distribution function, and expected values for the hydrogen atom with logarithmic potential under the influence of the topological defect. The calculations for the 2D hydrogen atom are performed for the first time using the Finite Difference Method. The results are presented through graphics, tables, and diagrams to elucidate the system’s physical properties. We have verified that our calculations agree with a linear variational method result. Our model leads to an interesting analogy with excitons in a two-dimensional monolayer semiconductor located within a specific semiconductor region. To elucidate this analogy, we present and discuss some interaction potentials and their exciton eigenstates by comparing them with the results from the literature.

An Active Distribution Grid Exceedance Testing and Risk-Planning Simulation Based on Carbon Capture and Multisource Data from the Power Internet of Things

In order to achieve peak carbon and carbon neutrality targets, a high number of distributed power sources have been connected to distribution networks. How to realize the planning of a distribution network containing integrated energy under the condition of carbon capture and complete the exceedance test of the distribution network under the condition of accessing a large number of distributed generators has become an urgent problem. To solve the above problem while promoting sustainable development, this work proposes an active distribution network risk-planning model based on multisource data from carbon capture and the Power Internet of Things. The model calculates the semi-invariants of each order of the node state vectors and branch circuit current vectors and then utilizes Gram–Charlier-level expansion to obtain the exceeding probability density function and the probability distribution functions of the node voltages and line powers in the distribution network. Combined with multisource data, an active distribution network with an integrated energy system designed for carbon capture was modeled. According to the risk scenario of the distribution network, the nonconvex constraints in the model were simplified by second-order cone relaxation, and the optimal planning scheme of the distribution network was solved by combining the Gurobi solver with the risk index as the first-level objective and the economic benefit as the second-level objective. The simulation results of a coupled network consisting of a 39-node distribution network and an 11-node transportation network verified the effectiveness of the proposed model.

Towards a collective opinion generation approach with multiple objectives for evaluating rail transit station accessibility in urban areas

Urban rail transit can alleviate traffic congestion if sufficient ridership is achieved. The accessibility to rail transit stations largely determines public willingness to utilize urban rail transit. The current studies on the accessibility to rail transit stations tend to concentrate solely on individual rail transit lines or stations, neglecting the impact of the external macro-environment. Consequently, the outcomes of these measurements cannot accurately reflect the overall accessibility level of the region, nor do they furnish decision-makers with references for devising plans for rail transit development. This study introduces a novel approach for evaluating the accessibility to urban rail transit stations from a macro-level standpoint, utilizing expert knowledge. The present study conducts an analysis of the impact of political, economic, social, and technological factors on the accessibility to rail transit stations in urban areas. Subsequently, a comprehensive evaluation indicator system is developed based on the aforementioned analysis. Then, experts are summoned to provide their subjective evaluations for every indicator, which are depicted as probability distribution functions. The collective evaluation is derived through the aggregation of individual evaluations utilizing a bi-objective optimization approach that factors in both the collective fairness utility and the confidence level. Finally, the quantile average method is employed to consolidate the collective assessment outcomes of individual indicators, thereby deriving the level of accessibility to rail transit stations in urban areas. We design a small-scale application experiment and attempt to evaluate the accessibility to rail transit stations in Wuchang District, Wuhan with the proposed approach in order to demonstrate the feasibility of the approach.

On the integration of inspection data with seismic resilience assessment of corroded reinforced concrete structures

This research aims to improve the traditional statistical approach to evaluate the seismic resilience of concrete structures exposed to chloride attack. In the mentioned approach, the uncertain parameters are modeled using certain probability distribution functions (PDFs) selected from some standards such as fib. However, the mentioned PDFs should contain the actual conditions of the desired structure. This paper introduces a Bayesian framework for updating PDFs used in deterioration analysis, which is an important part of the life-cycle seismic resilience assessment process of corroded concrete structures. The proposed methodology was applied to a two-story reinforced concrete school in Iran that suffered from chloride corrosion for twenty years. The seismic resilience of the structure was investigated for a 50-year life cycle. The results showed that the updated model can significantly reduce the uncertainty of the influencing parameters in the seismic resilience evaluation process. Using the updated model resulted in a conservative seismic resilience index compared to the non-updated model. This research shows that the role of inspection data in periodically updating the seismic-resistance calculations of corroded concrete structures is not only necessary but also possible and beneficial.

Electrical power projects: the role of risk management and reliability

The management of power outages caused by severe weather disasters such as earthquakes, tornadoes, and weather disturbances is critical in power transmission and distribution systems. The transmission system is the key to any power system and can trigger severe or significant effects if it fails. Different causes of fires, extreme weather conditions, ageing components, poor maintenance and malfunctions, human error, mal-operative procedures, and high operating network variables may cause transmission components to fail. System reliability is the probability that, despite component failures, a system remains available or functional. Risk management of the failures describes it. There are several methods to predict the failure rate, including exponential and Bayesian distributions. In this study, Poisson distribution forecasted the outage patterns for transmission and distribution networks for one and five years. A probability distribution function generated this pattern. Moreover, previous data were obtained from the National Electric Power Regulatory Authority (NEPRA). On comparing the acquired results with previous outage data, it was reported that the average outages in the transmission system were 567. The average outages in the distribution system stood at 37 for five years with a 100% confidence level. However, the probability of getting 620 transmission outages and 50 distribution outages was the highest in the probability distribution function for five years. Poisson distribution proved to be a useful tool to assess the transmission and distribution system reliability by estimating the failure rate over the years. It would allow the risk professionals to schedule, reduce, and track the systems’ risks. It would also help to improve the system’s reliability.

Value of information from fatigue monitoring of the monopile foundation of an offshore wind turbine

Value of information (VoI) allows quantifying benefits of adopting structural health monitoring (SHM) even before implementation by altering the prior risk of structural failure using the probabilities of damage detection from SHM data. The VoI is the reduction in the expected failure cost when SHM data becomes available. In this study, an optimized time of SHM deployment for fatigue crack growth in an offshore wind turbine (OWT) monopile foundation is achieved by maximising VoI. The prior probabilities of failure are obtained from stochastic analysis of dynamic responses to random wind and waves characteristic of North Sea environment. Short-term stress time histories are statistically processed to determine the probability distribution functions of their extrema and ranges and statistical extrapolation techniques are then implemented to analyse the long-term probability distributions of axial stresses. The long-term stress ranges and numbers of cycles are determined by the rainflow count and used in fatigue reliability analysis. The probability of detecting a fatigue crack by SHM is modelled and used for calculating the OTW failure risk after repair is conducted based on SHM outcome. The optimal deployment time of the fatigue crack monitoring system for the analysed 5-MW OWT is determined as 21 years past erection.

Thermalization of long range Ising model in different dynamical regimes: A full counting statistics approach

We study the thermalization of the transverse field Ising chain with a power law decaying interaction \sim 1/r^{\alpha}∼1/rα following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths \alphaα, whereas thermalization occurs in the region with weak confinement.

Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application

In this study, the scale and shape parameters of the Weibull probability distribution function (W.pdf) used in determining the profitability of wind energy projects are estimated using optimization algorithms and the moment method. These parameters are then used to estimate the wind energy potential (WEP) in Foça region of İzmir in Turkey. The values of Weibull parameters obtained using Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), Social Group Optimization (SGO), and Bat Algorithm (BA) were compared with the estimation results of the Moment Method (MM) as reference. Root mean square error (RMSE) and chi-square (χ^2) tests were used to compare the parameter estimation methods. The wind speed measurement values of the observation station in Foça were used. As a result of Foça speed data analysis, the annual average wind speed was determined as 6.15 m/s, and the dominant wind direction was found as northeast. Wind speed frequency distributions were compared with the measurement results and calculated with the estimated parameters. When RMSE and χ^2 criteria are evaluated together; it can be concluded that each used method behaves similarly for the given parameter estimation problem, with minor variations. As a result, it has been found that the optimization parameters produce very good results in wind speed distribution and potential calculations.