Probability Density Function Distribution Research Articles

Biophysical model for DNA mutations induced by retroviral genome insertion based on the probability density function of mutation distribution

Research into the biophysical properties of deoxyribonucleic acid (DNA) and the mechanisms underlying genetic mutations has undergone marked advancements. The intriguing nature of mutations resulting from retroviral DNA insertion has garnered considerable attention. Whether these mutations are random or region-specific, the distribution patterns of mutation sites have been the focus of numerous research endeavours. This mutation mechanism originates from interactions between host DNA and the pre-integration complex (PIC), comprising retroviral DNA and an integrase enzyme that facilitates its incorporation into the host DNA. Our study focused on the Zfp521 gene locus, recognised for its pronounced susceptibility to insertional mutations, particularly around unique palindromic sequences. We employed two biophysical models to predict mutation distribution within a range of 50 base pairs centred on these sequences. The first is a probabilistic collision model emphasising PIC and target DNA interactions. The second model is a DNA diffraction lattice, where the PIC behaves according to probability density. Although both models adeptly illuminated the probability distributions of target sites, the second model was more successful in predicting the PIC integration sites based on DNA biophysical properties. This highlights the pivotal role of intricate interactions between the PIC and target DNA, suggesting that mutations can be predicted in a stochastic manner.

UAV-assisted FSO communication system with amplify-and-forward protocol under AOA fluctuations: A performance analysis

Free space optical (FSO) communication has recently aroused great interest in academia due to its unique features, such as large transmission band, high data rates, and strong anti-electromagnetic interference. With the aim of evaluating the performance of an FSO communication system and extending the line-of-sight transmission distance, we propose an unmanned aerial vehicle (UAV)-assisted dual-hop FSO communication system equipped with amplify-and-forward protocol at the relay node. Specifically, we consider impairments of atmospheric absorption, pointing errors, atmospheric turbulence, and link interruptions due to angle-of-arrival fluctuations in the relay system. The Gamma-Gamma and Malaga distributions are used to model the influence of atmospheric turbulence on the source-to-UAV and UAV-to-destination links, respectively. We derive closed-form expressions of the probability density function (PDF) and cumulative distribution function (CDF) for the proposed communication system, in terms of the Meijer-G function. Based on the precise PDF and CDF, analytical expressions for the outage probability, average bit error rate, and ergodic capacity are proposed with the aid of the extended generalized bivariate Fox's H function. Finally, we show that there is a match between the analytical results and numerical results, and we analyze the influence of the system and channel parameters on the performance.

Statistic investigation on chloride ions distribution based on numerical reconstruction of in situ meso-structure of concrete

To study the non-uniform corrosion of steel rebar induced by chloride ions invasion under marine environment, the three-dimensional characteristic distribution of aggregates and pores in concrete was numerically extracted and reconstructed through X-ray CT technique. Based on the 3D in-situ meso-structure model of concrete, the random characteristics of chloride ions transport in concrete was investigated by numerical simulation. Through a fitting and hypothesis test on the concentration distribution histogram of chloride ions, a reliable probability density distribution function of chloride ions concentration was proposed. And the influence of ITZ and aggregate shape on the random diffusion of chloride ions was studied. The research indicates that that the spatial distribution of coarse aggregates and pores is the main reason leading to the non-uniform distribution of chloride ions. The chloride ions concentration under a certain time follows the Lognormal distribution. The discreteness of chloride ions distribution in concrete decreases when the interfacial transition zone is not considered in the model. And an increase of the irregularity of aggregate shape will cause an increase in the tortuosity of chloride ions transport path, and the discreteness of chloride ions distribution will enhance accordingly.

An adaptive algorithm for voice quality based on big data voiceprint identification

Abstract This paper improves the speech amplitude in Bayesian speech enhancement estimation by introducing a super-Gaussian cardinality distribution probability density function in the filter's construction. The derivation is combined with the perceptual error function, the new probability density function and the perceptual error cost function to better exploit and utilize the prior statistical information of the speech. The results show that the proposed method can improve the signal-to-noise ratio up to 0.7 dB under different noises and different signal-to-noise ratios, and the processed speech has better feasibility, which provides good speech enhancement for the processing of noisy speech quality in vocal identification practice without significantly increasing the computational complexity and can be better adapted to the application.

Brash ice macroporosity and piece size distribution in ship channels

Merchant vessels' performance on brash ice plays an important role in navigation in fast ice conditions in Northern Baltic ports. Among many parameters, the piece size distribution and macroporosity of the brash ice influence the accuracy of the model simulations of ship performance in brash ice. These properties also govern the brash ice accumulation and consolidation in ship channels. The current work presents analyses of macroporosity and piece size distribution from three full-scale brash ice channels investigated during winters 2020–21 and 2021–22. The results provide insights into brash ice macroporosity and piece size distribution. Smaller brash ice pieces exhibited higher porosity. On each measured cross-section, the average macroporosity ranged from 1.4% to 23%, with standard deviations of 3.8% and 16%, respectively. Porosity variations were observed in relation to equivalent brash ice thickness, the number of ship passages, and cumulative freezing air temperatures. Total porosity and the channel's brash ice porosity initially increased with breaking events and then stabilized at approximately 23% and 30%, respectively, after 9 passages. In contrast, side ridge porosity increased initially (up to 23%) and subsequently decreased. The initial total, brash ice and side ridge maximal porosities after the breaking event were estimated equal to 25%, 35% and 30%, respectively. The first two channels, which were navigated a total of 9 and 10 times, had an average degree of brash ice consolidation equal to 0.84 and 0.76, and an average degree of side ridge consolidation equal to 1.1 and 1.0, respectively. The third channel, characterized by frequent navigation, exhibited a consolidation degree of 0.82 for brash ice and 1.35 in the side ridges. The average vertical piece size across all cross-sections ranged from 0.28 m to 0.52 m with standard deviations of 0.16 m and 0.25 m. The average horizontal piece size ranged from 0.33 m to 0.4 m with standard deviations between 0.2 m and 0.34 m. The horizontal piece size distribution of brash ice was best described by the probability density function of a three-parameter lognormal distribution.

Digital Cartographic Generalization – Study of Its Thresholds and Stages in Example of Cartographic Line

Digital generalization of spatial data has been the goal of the research in many research centers around the world. This article presents the evolution of cartographic generalization, drawing the reader’s attention to the change of its nature from analog to digital. Despite the passage of time and developing technologies, scientists have unfortunately yet to develop a uniform automatic generalization algorithm. One of the factors that hinder this process is the high complexity and complication of the whole process. The article is an attempt to answer this problem and addresses the issue of digital cartographic generalization by creating a proposal of thresholds and stages of cartographic generalization depending on the ratios of the numbers of points of generalized objects. The publication attempts to examine the possibility of applying an objective criterion of drawing recognition by examining digital generalization algorithms and setting its thresholds. The practical aim of the publication is to present generalization thresholds on the example of Chrobak’s algorithm. The proposal to make the selection of generalization thresholds dependent on the percentage share of points is a solution that is as simple to use as it is to implement. The method of defining intervals based on the three-sigma rule is a solution that guarantees that the obtained results will be characteristic of the probability density function of the normal distribution, which will define individual intervals most objectively.

Inverse Lindley distribution: different methods for estimating their PDF and CDF

The probability density and cumulative distribution functions are essential statistical forms in modelling data and characterizing their respective distributions. This study addresses the estimation problem of these basic functions for the inverse Lindley distribution. The maximum likelihood, uniformly minimum variance unbiased and Bayes estimators are considered here. The exact confidence intervals for the probability density and cumulative distribution functions of the inverse Lindley distribution are also derived. A real data application and simulation studies are performed for illustrating and comparing among the so developed methods.

Intelligent Connectivity Through RIS-Assisted Wireless Communication: Exact Performance Analysis With Phase Errors and Mobility

The current research offers only approximations for evaluating the performance of wireless systems that use reconfigurable intelligent surfaces (RIS) over generalized fading channels with phase error caused by imperfect phase compensation at the RIS. This paper presents an exact analysis of RIS-assisted vehicular communication considering uniformly distributed phase error and generalized fading channels with a coherent combining of received signals reflected by RIS elements and direct transmissions from the source terminal. We use a generalized- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> shadowed distribution for the direct link and asymmetrical channels for the RIS-assisted transmission with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> distribution for the first link and double generalized Gamma (dGG) distribution for the second link, combined with a statistical random waypoint (RWP) model for the moving vehicle. We employ a novel approach to represent the probability density function (PDF) and cumulative distribution function (CDF) of the resultant channel in terms of a single univariate Fox-H function and use the multivariate Fox-H approach to develop an exact statistical analysis of the end-to-end signal-to-noise ratio (SNR) for the RIS-assisted system. We also use the inequality between the arithmetic and geometric means to simplify the statistical results of the considered system in terms of the univariate Fox-H function. Our analysis also provides exact, upper bound, and asymptotic expressions of the outage probability and average bit-error-rate (BER) performance using the derived density and distribution functions. We conduct computer simulations in various practically relevant scenarios to assert that mitigating phase errors is achievable by augmenting the number of elements in the RIS module and employing a higher quantization level.

Multifractal analysis on CT soil images: Fluctuation analysis versus mass distribution

The combined action of physical, chemical and biological processes at different scales creates a highly complex soil architecture. At the same time, this soil pores' complexity is crucial in maintaining soil biogeochemical and biophysical processes. The development of digital image processing and a multiscaling analysis allow a better study to quantify pore complexity and evaluate pore spatial variability. This study took saline soils from coastal reclamation areas as an example and aimed to compare the multifractality of porosity series using different methods on sample cubes of 512 pixels in length extracted at different soil depths. Two measures were selected to represent the porosity series: the average grey values (AVG) of each slice and the CT-porosity (CTP) of binarized slices. The mass distribution (MD), detrended fluctuation analysis (DFA), and the moments function (K) were the methods applied in the multiscaling study. Shuffled and surrogated series were used to analyze the two possible multifractality sources, the probability distribution density function (PDF) and long-range correlations, respectively.The results showed that MD gave the minimum multifractal spectrum, which appeared as a point in AGV and a narrow concave parabola in CTP. On the other hand, both AGV and CTP showed a higher complexity, a clear and significant multifractal behaviour when DFA and K were used. The shuffled and surrogated series pointed out that the long-range correlations were the main factor of the multifractal sources of the porosity series. Both long-range correlations and PDF influenced more heavily on the multifractality of porosity in topsoil (0– 20 cm) than in the deeper soil (20– 60 cm), implying that the porosity series in topsoil had stronger multifractality. In addition, the DFA and K, combined with shuffled and surrogated series analysis, can distinguish between different factors in the multiscaling behaviour of different soil textures and time reclamation.

Comparison between least squares and percentile methods in estimating Rayleigh Kumaraswamy distribution, a simulation study

In this research, a new generalization of the Rayleigh distribution called the Rayleigh-Kumaraswamy distribution was introduced. The extended formulas for the probability density function (PDF) and cumulative distribution function (CDF) were derived. Furthermore, some uses of distribution properties such as moments and moments generating function were also derived. The PDF property of the distribution was preserved. Additionally, A simulation study was conducted using different sample sizes and various assume .Two different methods for estimating the parameters of the new distribution are presented: the least squares method, and the method based on percentiles. Simulation studies are conducted to compare the performance of these estimation methods using different sample sizes and assumed parameter values. The comparison is based on statistical criteria such as mean square error and bias. The results indicate that the least squares method performs the best

Impact of AWiFS derived land use/land cover over the intensely urbanised domain of National Capital Region (NCR) - Delhi in simulating monsoon weather

Land-Use/Land-Cover (LULC) plays a crucial role in meteorological models because they determine the crustal properties that interfere with the exchange of energy, momentum, and moisture between the land surface and the atmosphere. The current study integrates a legitimate ground-truth LULC based on the Advanced Wide Field Sensor (AWiFS) in the Weather Research and Forecasting (WRF) model framework for simulating short-term monsoon weather over the National Capital Region (NCR Delhi), the biggest urban settlement in the Monsoon Zone. AWiFS provides LULC data at 56 m spatial resolution. The newly implemented AWiFS LULC precisely distinguishes the WRF model default Moderate Resolution Imaging Spectroradiometer (MODIS) classification and urban representation. Both simulations most well capture the urban meteorological influence over the urban core. However, the AWiFS more accurately depicts NCR urban Land Use (LU), highlighted in the spatial and Probability Density Function (PDF) distributions of various meteorological variables, and captures numerous small-scale suburban settlements outside the central core zone. The impact of the omission of the Noida suburban in MODIS LU is also notable in the planetary boundary layer (PBL). Convective parameters and precipitation correlate strongly, and the AWiFS simulation considerably enhanced Convective Available Potential Energy (CAPE), Convective Inhibition (CIN) and other associated variables. Further, it indicates that a higher magnitude (>200 J kg−1 in difference) of CAPE is simulated over Faridabad, likely an urban-induced downwind effect due to the accurate representation of the Noida suburban in AWiFS. The study highlights the importance of updated LULC in enhancing model realisation, and AWiFS-based simulation showed improved performance.

ED based spectrum sensing over IRS-assisted Rayleigh-FTR fading channels

A recent study has revealed that incorporating intelligent reflecting surfaces (IRS) into wireless systems improves their performance within various signal propagation conditions. This research paper focuses on evaluating the spectrum-sensing abilities of cognitive radio in wireless environments enhanced by IRS technology. To achieve this, the paper develops a statistical model to describe the connections between the primary user (PU) and IRS, as well as between IRS and the secondary user (SU). This model calculates a precise approximation of the probability density function (PDF) of the end-to-end instantaneous signal-to-noise ratio (SNR). The SNR considers both the PU-to-IRS link, which follows a Rayleigh fading distribution, and the IRS-to-SU link, which follows an FTR fading distribution. By utilizing this PDF distribution, the paper derives analytical expressions for the average probability of detection (APD) for single and cooperative secondary users. These APD expressions are then employed to establish the exact closed-form expression for the average area under the receiver operating characteristics (AUC), system throughput, and transmission probability of the SU. To validate these theoretical findings, the paper conducts Monte Carlo simulations. The results from these simulations indicate an improved detection probability when operating in an IRS-enhanced wireless propagation environment. Consequently, the study suggests that incorporating IRS technology can significantly enhance the reliability of communication systems based on cognitive radio principles.

Performance analysis of mixed IRS-aided RF-FSO system with pointing errors and link blockage

This research investigates the performance of the mixed intelligent reflecting surface (IRS) aided radio frequency-free space optical (RF-FSO) communication network system. IRS-aided RF link experiences Nakagami-m distribution, while FSO link undergoes F distribution turbulence with pointing errors and link blockage. Based on amplify-and-forward (AF) relay scheme, the end-to-end signal-to-noise ratio (SNR), the probability density function (PDF) and cumulative distribution function (CDF) are obtained. Novel expressions about the performance metrics including outage probability, average bit error rate (BER) and ergodic capacity are deduced and asymptotic expression for outage probability is also given at high SNR regime. By using these expressions, the system performance influenced by the number of IRS elements, pointing errors, blocking probability, atmospheric turbulence, detection techniques are further studied. The results demonstrate that IRS can effectively improve the mixed network performance. Eventually, using Monte Carlo simulations verify the results well.

DETERMINING THE PROBABILITIES OF THE OUTCOMES OF LOTTO GAME USING HYPERGEOMETRIC DISTRIBUTION

The probability density function (PDF) of the hypergeometric is used to model the probability of outcomes of lotto game given some selected predetermined scenarios (K) from (n = 5) samples at the instances of six sample scenarios x = 0, 1, 2, 3, 4, 5. This is exactly mimicking the Nigerian Premier Lotto game where interested players are expected to choose five random numbers from 1 to 90. That ‘A’ win implies that at least three of the randomly chosen 5 numbers are drawn from the national lotto draw often televised to the players. In this paper, different predetermined scenarios are defined and the probability is computed using the probability density function of the hypergeometric distribution. The data are results from 31625 games played on premier lotto in a span of 3 years. The data are for morning, afternoon, night, in Enugu center, regional and national premier lotto results during the period. The chi-square test of goodness of fit shows that the premier lotto is random, fair, and validates the results of the adoption of the PDF of hypergeometric distribution. Players of lotto games are advised to be aware of the slim chances of winning and play reasonably and sensibly.

Study of the Free Randomly Moving Electron Transport Peculiarities in Metals

In this study, we review some aspects of the application of free randomly moving (RM) electron density and its probability density function distribution to the main free electron transport characteristics of elemental metals. It is shown that metal atom thermal vibrations not only produce free RM electrons, but also produce the same number of electronic defects (weakly shielded ions). The general expressions for the drift mobility, diffusion coefficient, and mean free path of randomly moving electrons are presented. It is shown that the scattering of free RM electrons is mainly due to electronic defects, which cause the distortion of the periodic potential (or the charge density) distribution in the periodic lattice. The resistivity of the elemental metal is caused by electronic defect scattering, taking into account the exchange in the thermal energies between phonons and free RM electrons. Special attention is paid to the analysis of the Hall effect measurement data: the Hall coefficient is presented for two types of RM electrons and holes, taking into account electron-like and hole-like densities of states. The paramagnetism and diamagnetism of the free RM electrons are simply explained using the definition of free RM electron density.

Design of Orthogonal Pulse Waveforms With Tunable Frequency and Bandwidth for Carrier-Free THz Communications

Carrier-free pulse-based waveforms are desired in terahertz (THz) communications since pulse-based systems have simpler transceiver architectures than carrier-based systems. For such a pulse-based THz communication system, there still lacks pulse waveforms that can support high-order modulation and flexible multiple access. In this paper, a pulse-based waveform with continuously tunable center frequencies and bandwidths is designed for carrier-free THz communications. More specifically, a Gaussian pulse is utilized as the basic pulse, and then the weighted sum of its high-order derivatives is used to generate waveforms with tunable frequencies and bandwidths according to the probability density function of Rice distribution. Such a pulse-based waveform is called frequency and bandwidth continuously tunable (FBCT) pulse. By making the derivative orders of all weighted terms odd or even, a pair of orthogonal FBCT pulses can be generated. Based on the pair of orthogonal FBCT pulses, a basic pulse-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary quadrature amplitude modulation (P <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> QAM) scheme can be readily achieved. Moreover, with frequency and bandwidth tunability, FBCT pulse can support pulse division multiple access (PDMA) with tunable bandwidth, through which frequencies with high molecular absorption loss can be avoided. Numerical results demonstrate that FBCT pulse is significantly effective and flexible in supporting carrier-free THz communications.

Nonlinear optimal perturbation of turbulent channel flow as a precursor of extreme events

This work aims at studying the mechanisms behind the occurrence of extreme dissipation events in a channel flow, identifying nonlinear optimal perturbations as potential precursors of these events. Nonlinear optimal perturbations with respect to a generic turbulent instantaneous snapshot are computed for the first time using a direct-adjoint algorithm in the channel flow at $Re_{\tau }\approx 180$ . The resulting initial perturbation displays the upstream tilting characteristic of Orr's mechanism and is positioned along the interfaces between two opposite-sign velocity streaks of the pre-existing turbulent field. Such a perturbation induces a sudden breakdown of the pre-existing structures and a heavier tail in the dissipation probability density function distribution. Different mechanisms are at play during this process: the high shear present at the interface between coherent low- and high-momentum regions is exploited to break down the larger structures and drive energy to small scales. This energy cascade is fed by an enhanced lift-up effect that produces intense streaks near the wall. It is found that the optimal perturbation grows exponentially during the first phase of its evolution reflecting the existence of a secondary modal instability of the streaks. To corroborate the results, the conditional spatiotemporal proper orthogonal decomposition (POD) analysis of Hack &amp; Schimdt (J. Fluid Mech., vol. 907, 2021, A9) is performed both in the perturbed and in the unperturbed flow, showing a clear agreement between the two cases and with the reference study. Thus, the optimal perturbation at initial time can be considered as a precursor of extreme events.

What Sets the Star Formation Rate of Molecular Clouds? The Density Distribution as a Fingerprint of Compression and Expansion Rates

We use a suite of 3D simulations of star-forming molecular clouds, with and without stellar feedback, magnetic fields, and driven turbulence, to study the compression and expansion rates of the gas as functions of density. We show that, around the mean density, supersonic turbulence promotes rough equilibrium between the amounts of compressing and expanding gas, consistent with continuous gas cycling between high- and low-density states. We find that the inclusion of protostellar jets produces rapidly expanding and compressing low-density gas. We find that the gas mass flux peaks at the transition between the lognormal and power-law forms of the density probability distribution function (PDF). This is consistent with the transition density tracking the post-shock density, which promotes an enhancement of mass at this density (i.e., shock compression and filament formation). At high densities, the gas dynamics are dominated by self-gravity: the compression rate in all of our runs matches the rate of the run with only gravity, suggesting that processes other than self-gravity have little effect at these densities. The net gas mass flux becomes constant at a density below the sink formation threshold, where it equals the star formation rate. The density at which the net gas mass flux equals the star formation rate is one order of magnitude lower than our sink threshold density, corresponds to the formation of the second power-law tail in the density PDF, and sets the overall star formation rates of these simulations.

Techno-economic assessment of wind power generation feasibility in Sabang

Utilization of renewable energy in Aceh is still limited mainly to small-scale electricity through micro-hydro and solar power plants, accounting for less than 1% of the energy composition. Sabang stands out as a region with significant wind energy potential, boasting a speed of 8 m/s and an average power density of 537 W/m2 for the windiest 10% of the region. Therefore, to explore the viability of harnessing wind energy, a pre-feasibility study is needed. This study aimed to assess the techno-economic feasibility of constructing a wind power plant for electricity generation in Sabang by evaluating the region's wind energy. The statistical method of the Weibull Distribution probability density function was employed to evaluate Wind Power Density (WPD), Wind Turbine Capacity Factor, and Energy Output. Additionally, economic feasibility analysis involved calculating Net Present Value (NPV), Benefit Cost Ratio (BCR), Internal Rate of Return (IRR), Discounted Payback Period (DPP), and Levelized Cost of Energy (LCOE). The results showed that Sabang exhibited favorable[UMN1] wind characteristics with a shape parameter (k) of 1.6, average wind speed (Vm) of 7.9 m/s, and scale parameter (c) of 9 m/s. These features classified Sabang as wind power class 6 with a WPD of 735 watts/m2 at a height of 50 m, and the results were categorized as excellent. The study concluded that constructing a wind power plant in Sabang using the Enercon E-70 turbine at a hub height of 100m was technically feasible. The shape parameter (k) was 1.6, the average wind speed (Vm) was 9.3 m/s, scale parameter (c) was 11 m, and the WPD reached 1213 W/m2, leading to a turbine capacity factor of 0.53 and an annual energy production (AEP) of 64,876,560 kW. The economic analysis yielded promising results for wind power projects. The DPP value was estimated at 5.6 years, the BCR at 1.96, the NPV amounted to USD 14,434,994, the IRR reached 17.9%, and the LCOE was assessed at USD 32.50/MWh. Considering all these economic indicators, it was evident that constructing a wind power plant in Sabang was highly feasible and financially viable

Time-varying up-crossing theory-based non-stationary extreme estimation of gust-loading on rectangular cylinder due to thunderstorm-like wind

An active wind tunnel test was conducted to experimentally investigate the nonstationary time-varying extreme characteristics of the aerodynamic force on a 5:1 rectangular cylinder under a thunderstorm-like gust. Previous studies have primarily estimated the time-varying extremes of nonstationary surface wind pressure under the assumption of a nonstationary, uniformly modulated stochastic process. This study employed the time-varying upcrossing theory to precisely calculate the time-varying extreme values and peak factors of transient loads on a 5:1 rectangular cylinder subjected to a thunderstorm-like wind. The findings revealed that the wind pressures and aerodynamic lifts of a rectangular cylinder subjected to thunderstorm-like gusts present distinct time-varying and non-stationary features The extreme value distribution (probability density function and cumulative distribution function) estimated by applying the time-varying upcrossing theory also demonstrates significant temporal evolution. Accordingly, utilizing conventional stationary stochastic process estimation methods may generate considerable disparities. A comparison of the findings derived from the theory proposed in this work with those under the uniform modulation assumption suggests that the latter leads to an underestimation of the extreme values of the actual wind load.