Monte Carlo Simulation Experiments Research Articles

Inference for Compound Exponential XLindley Model with Applications to Lifetime Data

The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions.

Simulation Method for the Impact of Atmospheric Wind Speed on Optical Signals in Satellite–Ground Laser Communication Links

To analyze the intensity of atmospheric turbulence in a satellite–ground laser communication link, it is important to consider the effect of increased atmospheric turbulence caused by wind speed. Atmospheric turbulence causes a change in the refractive index, which negatively impacts the quality and focusing ability of the laser beam by altering its phase front. To simulate the changes in amplitude and phase characteristics of laser beam propagation in atmospheric turbulence caused by wind speed, a transverse translation phase screen is used. To better understand and address the influence of atmospheric wind speed on the phase of optical signals in satellite–ground laser communication links, this paper proposes a Monte Carlo simulation method. This method utilizes the spatial and temporal variations in the refractive index in the atmosphere and integrates the principles of optical signal propagation in the atmosphere to simulate changes in the phase of optical signals under different wind speed conditions. By analyzing the variations in the received optical signal’s power, the Monte Carlo method is employed to simulate phase screens and logarithmic amplitude screens. Additionally, it models the probability density of the statistical behavior of received optical signal’s fluctuations, as well as the time autocorrelation coefficient of optical signals. This paper, under the coupling condition in satellite–ground laser communication links, conducted a Monte Carlo simulation experiment to analyze the characteristics of the optical signal’s fluctuations in the link and discovered that atmospheric wind speed affects the shape of the power spectral density model of the received optical signal. Increasing wind speed leads to a decrease in the time autocorrelation coefficient of the received optical signal and affects the coupling efficiency. The paper then used a cubic spline interpolation fitting method to verify the models of the power spectral density and the autocorrelation time coefficient of the optical signal. This provides a theoretical foundation and practical guidance for the optimization of satellite–ground laser communication systems.

Testing distribution for multiplicative distortion measurement errors

. In this article, we study a goodness of fit test for a multiplicative distortion model under a uniformly distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. The proposed k-th power test statistic is based on logarithmic transformed observations and a correlation coefficient-based estimator without distortion measurement errors. The proper choice of k is discussed through the empirical coverage probabilities. The asymptotic null distribution of the test statistics are obtained with known asymptotic variances. Next, we proposed the conditional mean calibrated test statistic when a variable is distorted in a multiplicative fashion. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics.

Bayesian and empirical-Bayesian evaluations of the Topp–Leone lifetime model using lower record statistics

Record statistics are generally used to measure a process’ stochastic behavior at previously unheard-of values, either upper or lower. It can be obtained or calculated using order statistics from a sample whose size is dictated by the values and order of occurrence of observations. Due to its finite support and bathtub-shaped hazard function, the Topp–Leone (TL) distribution is appealing for reliability investigations. In today’s practical applications, estimating unknown parameters and predicting upcoming records is an essential issue. Thus, in this work, the TL distribution’s lower record values are taken into account. Against the symmetric squared-error loss, both Bayes and empirical-Bayes approaches are used to estimate the TL’s parameter and calculate prediction limits for upcoming lower record values. A Monte Carlo simulation experiment is performed to assess the accuracy of the estimation methodologies provided. To demonstrate the operability and usefulness of the various approaches, two useful applications are studied. The numerical evaluations show that the suggested approaches perform effectively and that the provided estimations are adequate in practice.

Testing conditional quantile independence with functional covariate.

We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer-von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the "curse of dimensionality" under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

A new unit distribution: properties, estimation, and regression analysis

This research commences a unit statistical model named power new power function distribution, exhibiting a thorough analysis of its complementary properties. We investigate the advantages of the new model, and some fundamental distributional properties are derived. The study aims to improve insight and application by presenting quantitative and qualitative perceptions. To estimate the three unknown parameters of the model, we carefully examine various methods: the maximum likelihood, least squares, weighted least squares, Anderson–Darling, and Cramér-von Mises. Through a Monte Carlo simulation experiment, we quantitatively evaluate the effectiveness of these estimation methods, extending a robust evaluation framework. A unique part of this research lies in developing a novel regressive analysis based on the proposed distribution. The application of this analysis reveals new viewpoints and improves the benefit of the model in practical situations. As the emphasis of the study is primarily on practical applications, the viability of the proposed model is assessed through the analysis of real datasets sourced from diverse fields.

A novel distributed bearing‐only target tracking algorithm for underwater sensor networks with resource constraints

AbstractUnderwater sensor networks hold immense potential for advancing the field of underwater target tracking, yet they encounter significant resource constraints stemming from energy storage and communication methods. In order to balance tracking accuracy and energy consumption, the authors present a distributed bearing‐only target tracking algorithm that can be used in underwater sensor networks with resource constraints. Anchored in the diffusion cubature information filter framework, this algorithm achieves fusion for non‐linear bearing measurements and state estimation. During the incremental update stage, individual nodes leverage the Posterior Cramer‐Rao Lower Bound as a metric for tracking performance. Subsequently, a strategy for selecting neighbouring nodes is introduced, ensuring tracking accuracy while efficiently kerbing energy consumption. In the diffusion update stage, a multi‐threshold event triggering mechanism is employed to partially diffuse the intermediate estimation. Additionally, an adaptive convex combination weight is proposed for cases involving partial diffusion. Through theoretical analysis, the asymptotic unbiasedness and convergence of the algorithm have been proven. Through Monte Carlo simulation experiments, the authors verify that the algorithm is superior to existing algorithms. Furthermore, the algorithm significantly reduces energy consumption in information interaction, minimising tracking accuracy loss.

Modified score functions for von Mises regressions

We derive and evaluate a novel estimation approach for the von Mises regression model based on a modified score function whose solution ensures an estimator with a smaller asymptotic bias than the original maximum likelihood estimator. We consider Monte Carlo simulation experiments to show that the new estimation approach yields nearly unbiased estimates. An application to real data is also considered for illustrative purposes.

Autonomous navigation method of satellite constellation based on adaptive forgetting factors

To address the problem that model uncertainty and unknown time-varying system noise hinder the filtering accuracy of the autonomous navigation system of satellite constellation, an autonomous navigation method of satellite constellation based on the Unscented Kalman Filter with Adaptive Forgetting Factors (UKF-AFF) is proposed. The process noise covariance matrix is estimated online with the strategy that combines covariance matching and adaptive adjustment of forgetting factors. The adaptive adjustment coefficient based on squared Mahalanobis distance of state residual is employed to achieve online regulation of forgetting factors, equipping this method with more adaptability. The intersatellite direction vector obtained from photographic observations is introduced to determine the constellation satellite orbit together with the distance measurement to avoid rank deficiency issues. Considering that the number of available measurements varies online with intersatellite visibility in practical applications such as time-varying constellation configurations, the smooth covariance matrix of state correction determined by innovation and gain is adopted and constructed recursively. Stability analysis of the proposed method is also conducted. The effectiveness of the proposed method is verified by the Monte Carlo simulation and comparison experiments. The estimation accuracy of constellation position and velocity of UKF-AFF is improved by 30% and 44% respectively compared to those of the extended Kalman filter, and the method proposed is also better than other several adaptive filtering methods in the presence of significant model uncertainty.

Sub‐Model Aggregation for Scalable Eigenvector Spatial Filtering: Application to Spatially Varying Coefficient Modeling

This study proposes a method for aggregating/synthesizing global and local sub‐models for fast and flexible spatial regression modeling. Eigenvector spatial filtering (ESF) was used to model spatially varying coefficients and spatial dependence in the residuals by sub‐model, while the generalized product‐of‐experts method was used to aggregate these sub‐models. The major advantages of the proposed method are as follows: (i) it is highly scalable for large samples in terms of accuracy and computational efficiency; (ii) it is easily implemented by estimating sub‐models independently first and aggregating/averaging them thereafter; and (iii) likelihood‐based inference is available because the marginal likelihood is available in closed‐form. The accuracy and computational efficiency of the proposed method are confirmed using Monte Carlo simulation experiments. This method was then applied to residential land price analysis in Japan. The results demonstrate the usefulness of this method for improving the interpretability of spatially varying coefficients. The proposed method is implemented in an R package spmoran.

Statistical inference for a novel distribution using ranked set sampling with applications

Working on symmetrical or asymmetrical data is complicated since each requires a different probability density function. Many statistical distributions can be used for these data types, where choosing one should be satisfied with the correct data type. So, we apply the ranked set sampling technique, which is essential in gaining data when dealing with units in a population is expensive. However, their classification is simple according to the variable of interest. The Unit Generalized Rayleigh distribution has recently played a crucial role in analyzing symmetrical or asymmetrical complex data sets specifically in modeling claim and risk data used in actuarial and financial studies, and its density can take different symmetric and asymmetric possible shapes. It is proposed in various areas, such as reliability, survival, economics, actuarial science, and insurance. We applied the ranked set sampling design in this article for gaining the model parameter estimations of the unit generalized Rayleigh model. Different estimation procedures and risk measures are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Under different proposed estimators, we conduct the validation of the suggested ranked set sampling design via numerous Monte Carlo simulation experiments by computing average bias and mean squared errors. At the end, we illustrated two real applications of the financial area for demonstrating the potential and the supremacy of the proposed ranked set sampling estimators.

A nonparametric test for homogeneity of variances

. A nonparametric test is proposed for the two-sample variance equality problem based on the fact that the covariance of U = X + Y and W = X − Y is zero when X and Y have equal variances. It is shown that the test statistic has an asymptotic standard normal distribution, which is useful for obtaining critical values for moderate sample sizes. The results of a Monte Carlo simulation experiment conducted in order to study the power properties of the test are presented.

Linear mixed models and latent growth curve models for group comparison studies contaminated by outliers.

The linear mixed model (LMM) and latent growth model (LGM) are frequently applied to within-subject two-group comparison studies to investigate group differences in the time effect, supposedly due to differential group treatments. Yet, research about LMM and LGM in the presence of outliers (defined as observations with a very low probability of occurrence if assumed from a given distribution) is scarce. Moreover, when such research exists, it focuses on estimation properties (bias and efficiency), neglecting inferential characteristics (e.g., power and type-I error). We study power and type-I error rates of Wald-type and bootstrap confidence intervals (CIs), as well as coverage and length of CIs and mean absolute error (MAE) of estimates, associated with classical and robust estimations of LMM and LGM, applied to a within-subject two-group comparison design. We conduct a Monte Carlo simulation experiment to compare CIs and MAEs under different conditions: data (a) without contamination, (b) contaminated by within-subject outliers, (c) contaminated by between-subject outliers, and (d) both contaminated by within- and between-subject outliers. Results show that without contamination, methods perform similarly, except CIs based on S, a robust LMM estimator, which are slightly less close to nominal values in their coverage. However, in the presence of both within- and between-subject outliers, CIs based on robust estimators, especially S, performed better than those of classical methods. In particular, the percentile CI with the wild bootstrap applied to the robust LMM estimators outperformed all other methods, especially with between-subject outliers, when we found the classical Wald-type CI based on the t statistic with Satterthwaite approximation for LMM to be highly misleading. We provide R code to compute all methods presented here. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

MTTEGDM: A Moving Target Evolutionary Game Defense Model Based on Three-Way Decisions

Aiming at the fact that the moving target defense game model fails to accurately portray attack and defense gains, resulting in bias in attack and defense games and the inability to select effective defense strategies, we construct the moving target three-way evolutionary game defense model (MTTEGDM). Firstly, the model is defined and analyzed theoretically under the premise of uncertainty and irrationality. Then, combined with the three-way decisions, the attack intention is introduced into the target network loss calculation, and a dynamic weight adjustment algorithm based on the three-way decisions is proposed to accurately characterize the attack and defense gains from a multi-attribute perspective. Finally, the evolutionary game model is used to analyze the evolution trend of the multi-stage defense strategy, so as to carry out feasible and effective defense behavior. The simulation results show that the model can accurately predict the optimal defense strategy of moving targets in different stages. Through a Monte Carlo simulation experiment, the proposed algorithm is compared with the traditional evolutionary game model, and the effectiveness and security of the proposed algorithm are verified.

Self-starting monitoring of the progressive type II censoring data based on goodness-of-fit test

ABSTRACT Censoring is a common occurrence in life testing and reliability analysis, primarily due to constraints such as time and cost. In this paper, we construct control charts using goodness-of-fit test statistics to monitor novel and effective progressive Type II censoring data. In practice, scenarios where the number of samples in Phase I is insufficient often arise, prompting the proposal of self-starting exponentially weighted moving average (EWMA) control charts based on goodness-of-fit test statistics to monitor such processes. Numerous Monte Carlo simulation experiments demonstrate the excellent performance of the control charts proposed in this paper under different settings. A breakdown time of an insulating fluid example is utilized to illustrate the proposed EWMA and self-starting EWMA control charts.

A new fractional integration approach based on neural network nonlinearity with an application to testing unemployment hysteresis

This paper proposes a nonlinear fractional unit root approach which is known as the autoregressive neural network–fractional integration (ARNN–FI) test. This new fractional integration test is based on a new multilayer perceptron of a neural network process, proposed in Yaya et al. (Oxf Bull Econ Stat 83(4):960–981, 2021). The asymptotic theory and the properties of the proposed test are given. By setting up a Monte Carlo simulation experiment, the simulation results reveal that as the number of observations increases, size and power distortions would disappear in the test. The empirical application based on this new test reveals that the unemployment rates of three European countries are neither stationary nor mean-reverting in line with the hysteresis hypothesis.

Analyzing the effect of shot noise in indirect Time-of-Flight cameras

Continuous wave indirect Time-of-Flight cameras obtain depth images by emitting a modulated continuous light wave and measuring the delay of the received signal. In this paper we generalize the estimation of the effect of the shot noise when obtaining the phase delay with an arbitrary number of points in the Discrete Fourier Transform, extending and generalizing the analysis done in previous works for the case of four points. For that particular case, we compare our analysis with the state of art. Moreover, we extend the error model using a second order approximation in the error propagation analysis, which provides more accurate estimations according to the Montecarlo simulation experiments. The analysis, based on both analytical and numerical methods, shows that the phase error is, in general, related to the exposure time and weakly to the number of points in the Discrete Fourier Transform. It also depends on the background illumination level, on the amplitude of the received signal, and, when using a three point DFT, on the distance to the objects.

EFAW: a new mining attack model combining FAW attacks with the Eclipse attack

Aim The Proof-of-Work consensus mechanism is the core mechanism of the blockchain, but the existing Fork After Withholding (FAW) attack can earn more rewards by launching attacks on the mining pools under the Proof-of-Work consensus mechanism. This paper proposes a new attack model based on the FAW attack, which further increases the attacker’s reward to explore the impact of the attack method on the blockchain network and the losses caused by the attack, which is helpful for maintaining the blockchain. Methods This paper proposes a new mining attack model called the "Eclipse Fork After Withholding (EFAW) attack" by combining FAW attacks with the eclipse attack. In the EFAW attack, the attacker infiltrates the victim pool by dispatching infiltrator miners. At the same time, they isolate a portion of miners in the victim pool through eclipse attacks, intercepting the valid information transmitted by these isolated miners. The attacker selectively discards or strategically releases the information to gain extra rewards. Results In this paper, we launch an EFAW attack against a single mining pool and two mining pools, respectively, and evaluate the relative extra rewards of the attacker with theoretical analysis and Monte Carlo simulation experiments. Our experimental data indicate that this attack can earn more rewards than FAW attacks. Conclusion The experimental results demonstrate that the lower bound of earnings in the EFAW attack is higher than in FAW attacks, and it is directly proportional to the number of miners isolated by the attacker’s eclipse attack in the victim pool. This indicates that the EFAW attack poses a greater threat compared to FAW attacks, representing one of the major conclusions drawn from the study.

Unbiased Proxy Calibration

AbstractThe linear calibration model is a powerful statistical tool that can be utilized to predict an unknown response variable, Y, through observations of a proxy or predictor variable, X. Since calibration involves estimation of regression model parameters on the basis of a limited amount of noisy data, an unbiased calibration slope estimation is of utmost importance. This can be achieved by means of state-of-the-art, data-driven statistical techniques. The present paper shows that weighted least-squares for both variables estimation (WLSXY) is able to deliver unbiased slope estimations under heteroscedasticity. In the case of homoscedasticity, besides WLSXY, ordinary least-squares (OLS) estimation with bias correction (OLSBC) also performs well. For achieving unbiasedness, it is further necessary to take the correct regression direction (i.e., of Y on X) into account. The present paper introduces a pairwise moving block bootstrap resampling approach for obtaining accurate estimation confidence intervals (CIs) under real-world climate conditions (i.e., non-Gaussian distributional shapes and autocorrelations in the noise components). A Monte Carlo simulation experiment confirms the feasibility and validity of this approach. The parameter estimates and bootstrap replications serve to predict the response with CIs. The methodological approach to unbiased calibration is illustrated for a paired time series dataset of sea-surface temperature and coral oxygen isotopic composition. Fortran software with implementation of OLSBC and WLSXY accompanies this paper.

Covariance ratio under multiplicative distortion measurement errors

We propose a covariance ratio measure for symmetry or asymmetry of a probability density function. This measure is constructed by the ratio of the covariance connected with the density function and the distribution function. We first propose a non parametric moment-based estimator of the covariance ratio measure and study its asymptotic results. Next, we consider statistical inference of the covariance ratio measure by using the empirical likelihood method. The empirical likelihood statistic is shown to be asymptotically a standard chi-squared distribution. Last, we study the covariance ratio measure when the random variable is unobserved under the multiplicative distortion measurement errors setting. The density function and the distribution function of the unobserved variable are estimated by using four calibrated variables. Appealing to these estimators, the calibrated covariance ratio measures are proposed and further shown to be asymptotically efficient as if there are no multiplicative distortion effects. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test procedures. These methods are applied to analyze two real datasets for illustration.