Probability Density Function Distribution Research Articles

Dynamics and probability density function of a stochastic COVID-19 epidemic model with nonlinear incidence

In this paper, a stochastic SEIQ model with nonlinear incidence rate is proposed. The existence and uniqueness of global positive solution of the stochastic model are proved. Then, by constructing some Lyapunov functions, we derive a sufficient condition for the ergodic stationary distribution when [Formula: see text] is greater than one. By solving a four-dimensional Fokker–Planck equation, we get the exact expression of log-normal probability density function of stationary distribution for the stochastic model. Sufficient condition for the extinction of the exposed and infected population is also provided. Finally, numerical simulations are presented to verify the above theoretical results.

Reliability Analysis for RV Reducer by Combining PCE and Saddlepoint Approximation Considering Multi-Failure Modes

Abstract RV (Rotate Vector) reducer is an essential mechanical transmission device extensively used in industrial machinery, robotics, aerospace and other fields. The dynamic transmission characteristics and strength of the cycloidal pin gear, turning arm bearing of RV reducer significantly affect the motion accuracy and reliability of the whole equipment. Uncertainties from manufacturing and assembly error, working loads add complexity to these effects. Developing effective methods for uncertainty propagation and reliability analysis for the RV reducer is crucial. In this work, the mail failure modes of RV reducer are studied, and an effective reliability analysis method for RV reducer considering the correlation between multi-failure modes by combining polynomial chaos expansions (PCE) and saddlepoint approximation method (SPA) is proposed. This paper develops an uncertainty propagation strategy for RV reducer based on dynamic simulation and PCE method with high accuracy. On this basis, a surrogated cumulant generating function (CGF) and SPA are combined to analyze the stochastic characteristic for the failure behavior. Based on the probability density function (PDF) and cumulative distribution function (CDF) calculated by SPA, copula function is employed to quantify the correlations between the multi-failure modes. Then, the system reliability with multi-failure modes is estimated by SPA and optimal copula function. The proposed method provides an effective reliability assessment technology with high-accuracy for complex system under unknown physical model and distribution characteristics. The validity of the proposed approach is illustrated RV-320E reducer reliability estimation, offering a basis to improve the performance of complex dynamic system. .

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

MDE and LLM Synergy for Network Experimentation: Case Analysis of Wireless System Performance in Beaulieu-Xie Fading and κ-µ Co-Channel Interference Environment with Diversity Combining.

Channel modeling is a first step towards the successful projecting of any wireless communication system. Hence, in this paper, we analyze the performance at the output of a multi-branch selection combining (SC) diversity receiver in a wireless environment that has been distracted by fading and co-channel interference (CCI), whereby the fading is modelled by newer Beaulieu-Xie (BX) distribution, and the CCI is modelled by the κ-µ distribution. The BX distribution provides the ability to include in consideration any number of line-of-sight (LOS) useful signal components and non-LOS (NLOS) useful signal components. This distribution contains characteristics of some other fading models thanks to its flexible fading parameters, which also applies to the κ-µ distribution. We derived here the expressions for the probability density function (PDF) and cumulative distribution function (CDF) for the output signal-to-co-channel interference ratio (SIR). After that, other performances are obtained, namely: outage probability (Pout), channel capacity (CC), moment-generating function (MGF), average bit error probability (ABEP), level crossing rate (LCR), and average fade duration (AFD). Numerical results are presented in several graphs versus the SIR for different values of fading and CCI parameters, as well as the number of input branches in the SC receiver. Then, the impact of parameters on all performance is checked. From our numerical results, it is possible to directly obtain the performance for all derived and displayed quantities for cases of previously known distributions of fading and CCI by inserting the appropriate parameter values. In the second part of the paper, a workflow for automated network experimentation relying on the synergy of Large Language Models (LLMs) and model-driven engineering (MDE) is presented, while the previously derived expressions are used for evaluation. Due to the aforementioned, the biggest value of the obtained results is the applicability to the cases of a large number of other distributions for fading and CCI by replacing the corresponding parameters in the formulas for the respective performances.

The [formula omitted]-[formula omitted] composite distribution with pointing errors: Theory and applications to RIS

The α-F composite fading distribution with pointing errors is investigated in this paper. New expressions for the probability density function and cumulative distribution function of the envelope/instantaneous signal-to-noise ratio (SNR), higher-order moments, and moment generating function of the instantaneous SNR are derived. Based on the aforementioned statistics, expressions for the outage probability, symbol error probability, and ergodic channel capacity are obtained. An asymptotic analysis is also provided. Furthermore, an application of the α-F model with pointing errors in a wireless emerging system, namely reconfigurable intelligent surfaces (RIS), is shown. Several curves, corroborated by Monte–Carlo simulations, are presented for different values that characterize the channel and pointing error parameters.

Dimension-Reduction Spectral Representation of Soil Spatial Variability and Its Application in the Efficient Reliability Analysis of Seismic Response in Tunnels

Reliability analysis of tunnels considering soil spatial variability was traditionally carried out using Monte Carlo simulations, which are computationally expensive. This study proposes a dimension-reduction spectral representation method (SRM) for simulating parameter stochastic fields to capture uncertainties in soil properties, which can be coupled with the probability density evolution method (PDEM). Additionally, the PDEM is employed to conduct seismic reliability assessments of tunnels in a more efficient manner. By integrating a non-intrusive dynamic random finite element method (FEM), this study explores the horizontal drift angle and vertical relative settlement of tunnel dynamic response under different coefficient of variations (COVs) and horizontal autocorrelation lengths of elastic modulus (E). Results show the changes in COVs have more pronounced effects on the mean and standard deviation of horizontal drift angle and vertical relative settlement of tunnel than alterations in horizontal autocorrelation lengths. A limit state pertaining to the horizontal drift angle and vertical relative settlement is established through the use of a probability density function (PDF) and cumulative distribution function (CDF). The results suggest that the combination of soil spatial variability and PDEM can serve as an effective approach for practical tunnel design.

Association of uninsured status and rurality with risk of financial toxicity after pediatric trauma

BackgroundPediatric traumatic injury is associated with long-term morbidity as well as substantial economic burden. Prior work has labeled the catastrophic out-of-pocket medical expenses borne by patients as financial toxicity. We hypothesized uninsured rural patients to be vulnerable to exorbitant costs and thus at greatest risk of financial toxicity. MethodsPediatric patients (<18 years) experiencing traumatic injury were identified in the 2016–2019 National Inpatient Sample. Patients were considered to be at risk of financial toxicity if their hospitalization cost exceeded 40% of post-subsistence income. Individual family income was computed using a gamma distribution probability density function with parameters derived from publicly available US Census Bureau data, in accordance with prior work. A multivariable logistic regression was developed to assess factors associated with risk of financial toxicity. ResultsOf an estimated 225,265 children identified for study, 34,395 (15.3%) were Rural. Rural patients were more likely to experience risk of financial toxicity (29.1 vs 22.2%, P < .001) compared to Urban patients. After adjustment, rurality (reference: urban status; adjusted odds ratio 1.45, 95% confidence interval 1.36–1.55) and uninsured status (reference: private; adjusted odds ratio 1.85, 95% confidence interval 1.67–2.05) remained linked to increased odds of risk of financial toxicity. Specifically among those with private insurance, Rural patients experienced markedly higher predicted risk of financial toxicity, relative to Urban. ConclusionOur findings suggest a complex interplay between rural status and insurance type in the prediction of risk of financial toxicity after pediatric trauma. To target policy interventions, future studies should characterize the patients and communities at greatest risk of financial devastation among rural pediatric trauma patients.

Estimation of Stress - Strength Reliability for Parallel Redundant System Via Burr of type X Distribution

Estimation for the reliability of a parallel redundant system with independent stress and strength Burr distribution (type ) probability density functions is considered. Estimation of the reliability parameters is conducted according to the non-Bayesian estimation methods, namely the maximum likelihood and shrinkage methods. The Bayesian estimation is also considered using the Jeffery and Gamma priors with squared error, quadratic and weighted loss functions. Finally, the reliability estimate is calculated and the best method for estimation for each case is given using the mean squared error criteria.

The Tail Characteristics of Several Asymmetric Distributions and Their Applications in the Field of Financial Data Modelling and Machine Learning

Asymmetric distributions play a pivotal role in various fields, including finance, machine learning, and artificial intelligence. In finance, asymmetric distributions, characterized by negative skewness, peakedness, heavy tails, and asymmetric fluctuations, provide a more accurate representation of financial data. These distributions are particularly useful in capturing the complex behavior of assets and risk management. In the field of machine learning, data disturbance, noise, outliers and other disturbances will have a negative impact on the performance and reliability of the model, asymmetric distributions offer a valuable tool for describing the tail behavior of noise and interference. This is crucial in designing more robust machine learning models that can handle outliers and noise effectively. Additionally, when dealing with unbalanced data classification, asymmetric distributions can be leveraged by adjusting the decision threshold of classifiers or employing specialized loss functions. In this paper, the asymptotic tail ratio behavior of probability density function(pdf) and cumulative distribution function (cdf) of three asymmetric distributions (asymmetric Laplace, generalized Logistic and asymmetric normal distribution) and Student-t distribution were considered respectively under some regular conditions. The detailed characteristics of these asymmetric tails will have a profound impact on the fields of financial data analysis, artificial intelligence, and unbalanced classification.

Transform coefficient distribution modeling based frame-level adaptive rate control for VVC

Rate control is a key issue in the research of video coding optimization. In this work, we propose a statistical modeling based frame-level distortion estimation model and a distortion dependency based rate control optimization algorithm for Versatile Video Coding (VVC). VVC has incorporated into more advanced coding tools, resulting in the distribution of transform coefficient more sharper. In response to this phenomenon, the TCD of VVC is modeled by the probability density function (PDF) of Cauchy distribution and generalized Gaussian distribution (GGD) individually. Then, a sliding window-based frame-level distortion model is proposed, which is used for derivation of inter-frame distortion dependency factor. According to the derived distortion dependency factor, a frame-level rate control optimization algorithm is presented to update the coding parameters in practical coding process. Experiments have shown that the proposed method could effectively improve rate–distortion performance, achieving an average rate distortion performance improvement of 0.72% in sequences blow 4K resolution, and 1.47% in 4K sequences in low delay P frame (LDP) configuration.

Performance analysis of 5G and beyond mixed THz/FSO relaying communication systems

This paper explores the potential of relay-assisted transmission to mitigate fading in free-space optical (FSO) systems. Our investigation focuses on assessing the performance of a dual-hop relay system for Terahertz/FSO (THz/FSO) communication. We develop an aggregated channel model incorporating various factors, including pointing errors, channel fading, and deterministic path loss. Specifically, the THz link encounters α−μ fading with pointing errors, while the FSO link experiences Gamma–Gamma fading and pointing errors. We utilize amplify-and-forward relaying and derive mathematical expressions for the probability density function and cumulative distribution function of the end-to-end signal-to-noise ratio, considering the combined effects of channel fading and pointing errors. Employing the derived statistical expressions, we evaluate crucial performance metrics for the considered relaying schemes, including the outage probability and the average bit error rate. To validate our analytical findings, we conducted Monte-Carlo simulations. The results demonstrate a strong correlation between the performance of the system and the particular pointing errors and fading parameters linked to the THz/FSO connections.

Analysis of boundary layer characteristics in supergravitational turbulent thermal convection

We investigate the boundary layer characteristics within annular centrifugal Rayleigh–Bénard convection (ACRBC) considering a Rayleigh number Ra∈[108,1011], a Prandtl number Pr = 10.7, and an inverse Rossby number Ro−1=16. Our study is based on the temperature and velocity data obtained from direct numerical simulations. Different from the flow over a flat plate, the ACRBC system bifurcates into three regions: the plume-impacting regions, plume-ejecting regions, and plume-sweeping regions, and all three regions are moving with the zonal flow. Our focus is primarily on the temperature dynamics within the plume-sweeping region, where the wind of large-scale circulation shears the boundary. We determine the transient thermal boundary layer thickness over time using the slope method, relying on the temperature curve's orientation relative to the wall. Notably, the probability density function distribution of the thermal boundary layer thickness is reminiscent of traditional RBC systems, albeit with a more extended exponential tail. Employing a dynamic frame based on time resampling, we discern that the temperature boundary layer traits align with the Prandtl–Blasius boundary layer theory. In conclusion, we show that the exponential decay index for the thermal boundary layer thickness harmonizes with the system's heat transfer scaling law. It is found that the ratio between the inner and outer boundary layer thickness remains stable, providing theoretical guidance for the design and control of the internal flow field of high-speed rotating machinery.

Time development of clear-water scour around a pile foundation: Phenomenological theory of turbulence-based approach

Existing prediction formulas for clear-water scour development are typically empirical fittings of lab-scale results. However, it is unreasonable to evaluate the in-situ clear-water scour process around a pile based on small-scale flume tests due to inherent scale effect. This study proposes a time-dependent model of clear-water scour development around a pile foundation under steady currents. A scaling expression of shear stress acting on sediment particles at the front of a circular pile is established based on the phenomenological theory of turbulence. By applying the sediment transport model of flat-bed to local scour around a circular pile, a physics-based ordinary differential equation for predicting the scour depth development is derived. The analytical solution of scour depth development is generally more consistent with the experimental data compared with previous models. The probability density function distribution of the proposed model's error mainly concentrates within the range of ±10%, which is significantly superior to previous models. The proposed model integrates all pertinent parameters that govern the scour process using fundamental principles, rendering it free from scale issues and applicable to prototype conditions. The present model is applied to evaluating clear-water scour development around typical prototype piles with diameters ranging from 2.0 m to 10.0 m. The predicted variations of equilibrium scour time with pile diameter, flow velocity and sediment particle size aligns closely with previous experimental observations.

Reliability risk modelling of asphalt pavement structure performance under the impact of freeze-thaw cycles

This paper delivers an in-depth risk analysis of asphalt pavement structural strength in the cold Qinghai-Tibet Plateau region. It encompasses a wide range of risk factors, including environmental conditions, traffic dynamics, pavement structures and materials, and various human-related factors. These risk factors are quantified using probability distributions, with emphasis on the changes in their mean and variance to simulate the effects of risk. A novel risk metric, termed “CVall”, is introduced to encapsulate the cumulative risk associated with each random variable. The paper describes the risk in the load and resistance equations, which govern the asphalt pavement strength, using the probability density function distribution. This approach takes into account the variation coefficient of each parameter. The study highlights that the risk related to the pavement structure number following freeze-thaw cycles significantly influences the reliability of pavement structural strength. These insights are particularly crucial for highway design, construction, and maintenance in cold regions, where the durability and longevity of pavement are paramount.

A P–S–N curve fitting method based on mixed Weibull distribution and expectation-maximization algorithm

In practical engineering, there are many factors affecting the fatigue life of actual components, and a single Weibull distribution is insufficient to accurately describe the impact of various factors on fatigue life. In order to solve the above problems, 316L stainless steel is taken as the experimental object to study the effects of phase difference and stress levels on fatigue life based on the mixed Weibull distribution model. Firstly, the mixed Weibull distribution model is converted into the mixed extreme value distribution model, and used Euler's constant to calculate relevant parameters of extreme value distribution and Expectation-Maximization (EM) algorithm to determine the probability density function of the mixed Weibull distribution. Secondly, the probability density function is integrated to obtain the distribution function and the fatigue life under different failure probabilities is calculated. Finally, the influence of non-proportional additional reinforcement and stress amplitude on fatigue life is studied by taking them as hidden variables of mixed Weibull distribution, which is used to obtain P-S-N curves for various failure probabilities. Through the proposed method, the influence of different factors on fatigue life can be considered from the perspective of statistics, and the accuracy of fatigue life prediction can be promoted.

Underwater image enhancement using multi-task fusion.

Underwater images are often scattered due to suspended particles in the water, resulting in light scattering and blocking and reduced visibility and contrast. Color shifts and distortions are also caused by the absorption of different wavelengths of light in the water. This series of problems will make the underwater image quality greatly impaired, resulting in some advanced visual work can not be carried out underwater. In order to solve these problems, this paper proposes an underwater image enhancement method based on multi-task fusion, called MTF. Specifically, we first use linear constraints on the input image to achieve color correction based on the gray world assumption. The corrected image is then used to achieve visibility enhancement using an improved type-II fuzzy set-based algorithm, while the image is contrast enhanced using standard normal distribution probability density function and softplus function. However, in order to obtain more qualitative results, we propose multi-task fusion, in which we solve for similarity, then we obtain fusion weights that guarantee the best features of the image as much as possible from the obtained similarity, and finally we fuse the image with the weights to obtain the output image, and we find that multi-task fusion has excellent image enhancement and restoration capabilities, and also produces visually pleasing results. Extensive qualitative and quantitative evaluations show that MTF method achieves optimal results compared to ten state-of-the-art underwater enhancement algorithms on 2 datasets. Moreover, the method can achieve better results in application tests such as target detection and edge detection.

A Comparison of Probability Density Functions Fitted by Moments and Maximum Likelihood Estimation Methods Used for Diameter Distribution Estimation

Modeling diameter distribution is a crucial aspect of forest management, requiring the selection of an appropriate probability density function or cumulative distribution function along with a fitting method. This study compared the suitability of eight probability density functions—A Charlier, beta, generalized beta, gamma, Gumbel, Johnson’s SB, and Weibull (two- and three-parameter)—fitted using both derivative methods (Moments) fitted in SAS/STATTM and optimization methods (MLE) fitted with the ‘optim’ function in R for diameter distribution estimation in forest stands. The A Charlier and Gumbel functions were used for the first time in this type of comparison. The data were derived from 167 permanent sample plots in an Atlantic forest (Quercus robur) and 59 temporary sample plots in tropical forests (Tectona grandis). Fit quality was assessed using various indices, including Kolmogorov–Smirnov, Cramér–von Mises, mean absolute error, bias, and mean squared error. The results indicated that Johnson’s SB function was more suitable for describing the diameter distribution of the stands. Johnson’s SB, three-parameter Weibull, and generalized beta consistently performed well across different fitting methods, while the fits produced by gamma, Gumbel, and two-parameter Weibull were of poor quality.

A New Sparse Bayesian Learning-Based Direction of Arrival Estimation Method with Array Position Errors

In practical applications, the hydrophone array has element position errors, which seriously degrade the performance of the direction of arrival estimation. We propose a direction of arrival (DOA) estimation method based on sparse Bayesian learning using existing array position errors to solve this problem. The array position error and angle grid error parameters are introduced, and the prior distribution of these two errors is determined. The joint probability density distribution function is established by means of a sparse Bayesian learning model. At the same time, the unknown parameters are optimized and iterated using the expectation maximum algorithm and the corresponding parameters are solved to obtain the spatial spectrum. The results of the simulation and the lake experiments show that the proposed method effectively overcomes the problem of array element position errors and has strong robustness. It shows a good performance in terms of its estimation accuracy, meaning that the resolution ability can be greatly improved in the case of a low signal-to-noise ratio or small number of snapshots.

A flexible extension of asymmetric power-t distribution

In this article, a new generalized modified slash-power-t (GMSLPT) distribution, as an extension of the power t (PT) distribution, is constructed by using independent PT and one parameter gamma random variables. The resulting distribution is an asymmetric model whose kurtosis is greater than other slash distributions or power distributions to fit skewed and heavy-tailed data. The probability density function and identifiability of GMSLPT distribution are obtained. The hazard rate function, main properties, moments, skewness, and kurtosis coefficients are studied in detail. The parameters in the model are estimated by the maximum likelihood method. A simulation study is given to illustrate the good behavior of MLEs. The advantages of the GMSLPT distribution are confirmed by two actual data examples to model asymmetric data with heavy tail and excess kurtosis.

Performance of STAR-RIS-aided cooperative NOMA networks under Nakagami-[formula omitted] fading

In this work, we investigate the performance of the cooperative non-orthogonal multiple access (CNOMA) downlink wireless communication system assisted by the newly emerged technology of simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) over Nakagami-m fading channels. Specifically, outage probability (OP), spectral efficiency (SE), and energy efficiency (EE) are used as the performance metrics. The near user’s mathematically intractable probability density and cumulative distribution functions were approximated through the Gamma moment-matching technique. This was followed by the derivation of the users’ closed-form OP and ergodic rates expressions, where the latter was used to determine the SE and EE of the system. Further, extensive Monte-Carlo simulations confirmed the correctness of the obtained analytical findings. In addition, to inspect the usefulness of CNOMA in the proposed communication system, the comparison with its NOMA counterpart was incorporated into the numerical results. Finally, it was found that the cooperative link can further enhance the SE and EE of the STAR-RIS-based NOMA network.