Search Results (153)

This paper explores statistical techniques for estimating unknown lifetime parameters using data from a progressive first-failure censoring scheme. The failure times are modeled with a new Weibull–Pareto distribution. Maximum likelihood estimators are derived for the model parameters, as well as for the survival and hazard rate functions, although these estimators do not have explicit closed-form solutions. The Newton–Raphson algorithm is employed for the numerical computation of these estimates. Confidence intervals for the parameters are approximated based on the asymptotic normality of the maximum likelihood estimators. The Fisher information matrix is calculated using the missing information principle, and the delta technique is applied to approximate confidence intervals for the survival and hazard rate functions. Bayesian estimators are developed under squared error, linear exponential, and general entropy loss functions, assuming independent gamma priors. Markov chain Monte Carlo sampling is used to obtain Bayesian point estimates and the highest posterior density credible intervals for the parameters and reliability measures. Finally, the proposed methods are demonstrated through the analysis of a real dataset. Full article

A novel unified progressive hybrid censoring is introduced to combine both progressive and hybrid censoring plans to allow flexible test termination either after a prespecified number of failures or at a fixed time. This work develops both frequentist and Bayesian inferential procedures for estimating the parameters, reliability, and hazard rates of the inverted Nadarajah–Haghighi lifespan model when a sample is produced from such a censoring plan. Maximum likelihood estimators are obtained through the Newton–Raphson iterative technique. The delta method, based on the Fisher information matrix, is utilized to build the asymptotic confidence intervals for each unknown quantity. In the Bayesian methodology, Markov chain Monte Carlo techniques with independent gamma priors are implemented to generate posterior summaries and credible intervals, addressing computational intractability through the Metropolis—Hastings algorithm. Extensive Monte Carlo simulations compare the efficiency and utility of frequentist and Bayesian estimates across multiple censoring designs, highlighting the superiority of Bayesian inference using informative prior information. Two real-world applications utilizing rare minerals from gold and diamond durability studies are examined to demonstrate the adaptability of the proposed estimators to the analysis of rare events in precious materials science. By applying four different optimality criteria to multiple competing plans, an analysis of various progressive censoring strategies that yield the best performance is conducted. The proposed censoring framework is effectively applied to real-world datasets involving diamonds and gold, demonstrating its practical utility in modeling the reliability and failure behavior of rare and high-value minerals. Full article

Federated learning (FL) enables multiple participants to collaboratively train models while efficiently mitigating the issue of data silos. However, large-scale heterogeneous data distributions result in inconsistent client objectives and catastrophic forgetting, leading to model bias and slow convergence. To address the challenges under non-independent and identically distributed (non-IID) data, we propose DPAO-PFL, a Dynamic Parameter-Aware Optimization framework that leverages continual learning principles to improve Personalized Federated Learning under non-IID conditions. We decomposed the parameters into two components: local personalized parameters tailored to client characteristics, and global shared parameters that capture the accumulated marginal effects of parameter updates over historical rounds. Specifically, we leverage the Fisher information matrix to estimate parameter importance online, integrate the path sensitivity scores within a time-series sliding window to construct a dynamic regularization term, and adaptively adjust the constraint strength to mitigate the conflict overall tasks. We evaluate the effectiveness of DPAO-PFL through extensive experiments on several benchmarks under IID and non-IID data distributions. Comprehensive experimental results indicate that DPAO-PFL outperforms baselines with improvements from $5.41\%$ to $30.42\%$ in average classification accuracy. By decoupling model parameters and incorporating an adaptive regularization mechanism, DPAO-PFL effectively balances generalization and personalization. Furthermore, DPAO-PFL exhibits superior performance in convergence and collaborative optimization compared to state-of-the-art FL methods. Full article

This paper presents a visual active SLAM method considering measurement and state uncertainty for space exploration in urban search and rescue environments. An uncertainty evaluation method based on the Fisher Information Matrix (FIM) is studied from the perspective of evaluating the localization uncertainty of SLAM systems. With the aid of the Fisher Information Matrix, the Cramér–Rao Lower Bound (CRLB) of the pose uncertainty in the stereo visual SLAM system is derived to describe the boundary of the pose uncertainty. Optimality criteria are introduced to quantitatively evaluate the localization uncertainty. The odometry information selection method and the local bundle adjustment information selection method based on Fisher Information are proposed to find out the measurements with low uncertainty for localization and mapping in the search and rescue process. By adopting the method above, the computing efficiency of the system is improved while the localization accuracy is equivalent to the classical ORB-SLAM2. Moreover, by the quantified uncertainty of local poses and map points, the generalized unary node and generalized unary edge are defined to improve the computational efficiency in computing local state uncertainty. In addition, an active loop closing planner considering local state uncertainty is proposed to make use of uncertainty in assisting the space exploration and decision-making of MAV, which is beneficial to the improvement of MAV localization performance in search and rescue environments. Simulations and field tests in different challenging scenarios are conducted to verify the effectiveness of the proposed method. Full article

In this paper, we review Helmholtz–Boltzmann thermodynamics for mechanical systems depending on parameters, and we compute the Fisher information matrix for the associated probability density. The divergence of Fisher information has been used as a signal for the existence of phase transitions in finite systems even in the absence of a thermodynamic limit. We investigate through examples if qualitative changes in the dynamic of mechanical systems described by Helmholtz–Boltzmann thermodynamic formalism can be detected using Fisher information. Full article

The Gumbel Type-II distribution is a widely recognized and frequently utilized lifetime distribution, playing a crucial role in reliability engineering. This paper focuses on the statistical inference of the Gumbel Type-II distribution under a random censoring scheme. From a frequentist perspective, point estimates for the unknown parameters are derived using the maximum likelihood estimation method, and confidence intervals are constructed based on the Fisher information matrix. From a Bayesian perspective, Bayes estimates of the parameters are obtained using the Markov Chain Monte Carlo method, and the average lengths of credible intervals are calculated. The Bayesian inference is performed under both the squared error loss function and the general entropy loss function. Additionally, a numerical simulation is conducted to evaluate the performance of the proposed methods. To demonstrate their practical applicability, a real world example is provided, illustrating the application and development of these inference techniques. In conclusion, the Bayesian method appears to outperform other approaches, although each method offers unique advantages. Full article

The Gompertz distribution has long been a cornerstone for analyzing growth processes and mortality patterns across various scientific disciplines. However, as the intricacies of real-world phenomena evolve, there is a pressing need for more versatile probability distributions that can accurately capture a wide array of data characteristics. In response to this demand, we introduce the Marshall–Olkin Power Gompertz (MOPG) distribution, an innovative and powerful extension of the traditional Gompertz model. The MOPG distribution is crafted by enhancing the Power Gompertz cumulative distribution function through the Marshall–Olkin transformation. This distribution yields two pivotal contributions: a power parameter (c) that significantly increases the model’s adaptability to diverse data patterns and the Marshall–Olkin transformation, which modifies tail behavior to enhance predictive accuracy. Furthermore, we derived the distribution’s essential statistical properties and evaluate its performance through extensive Monte Carlo simulations, along with a maximum likelihood estimation of model parameters. Our empirical validation, utilizing three real-world data sets, compellingly demonstrated that the MOPG distribution not only surpasses several well-established lifetime distributions but is also superior in terms of flexibility and tail behavior characterization. The results highlight that the proposed MOPG stands out as a superior choice, delivering the most precise fit to the data when compared to various competing models, and its performance makes it a compelling option worth considering. Full article

In recent years, there has been an increasing interest in the application of progressive censoring as a means to reduce both cost and experiment duration. In the absence of explanatory variables, the present study employs a statistical inference approach for the inverse Weibull distribution, using a progressive type II censoring strategy with two independent samples. The article expounds on the maximum likelihood estimation method, utilizing the Fisher information matrix to derive approximate confidence intervals. Moreover, interval estimations are computed by the bootstrap method. We explore the application of Bayesian methods for estimating model parameters under both the squared error and LINEX loss functions. The Bayesian estimates and corresponding credible intervals are calculated via Markov chain Monte Carlo (MCMC). Finally, comprehensive simulation studies and real data analysis are carried out to validate the precision of the proposed estimation methods. Full article

In recent years, joint censoring schemes have gained significant attention in lifetime experiments and reliability analysis. A refined approach, known as the balanced joint progressive censoring scheme, has been introduced in statistical studies. This research focuses on statistical inference for two Lomax populations under this censoring framework. Maximum likelihood estimation is employed to derive parameter estimates, and asymptotic confidence intervals are constructed using the observed Fisher information matrix. From a Bayesian standpoint, posterior estimates of the unknown parameters are obtained under informative prior assumptions. To evaluate the effectiveness and precision of these estimators, a numerical study is conducted. Additionally, a real dataset is analyzed to demonstrate the practical application of these estimation methods. Full article

Middle-censoring is a general censoring mechanism. In middle-censoring, the exact lifetimes are observed only for a portion of the units and for others, we can only know the random interval within which the failure occurs. In this study, we focus on statistical inference for middle-censored data with competing risks. The latent failure times are assumed to be independent and follow Burr-XII distributions with distinct parameters. To begin with, we derive the maximum likelihood estimators for the unknown parameters, proving their existence and uniqueness. Additionally, asymptotic confidence intervals are constructed using the observed Fisher information matrix. Furthermore, Bayesian estimates under squared loss function and the corresponding highest posterior density intervals are obtained through the Gibbs sampling method. A simulation study is carried out to assess the performance of all proposed estimators. Lastly, an analysis for a practical dataset is provided to demonstrate the inferential processes developed. Full article

We present a Fisher information matrix study of the parameter estimation precision achievable by a class of future space-based, “mid-band”, gravitational wave interferometers observing monochromatic signals. The mid-band is the frequency region between that accessible by the Laser Interferometer Space Antenna (LISA) and ground-based interferometers. We analyze monochromatic signals observed by the TianQin mission, gLISA (a LISA-like interferometer in a geosynchronous orbit) and a descoped gLISA mission, gLISA_d, characterized by an acceleration noise level that is three orders of magnitude worse than that of gLISA. We find that all three missions achieve their best angular source reconstruction precision in the higher part of their accessible frequency band, with an error box better than ${10}^{-10}$ sr in the frequency band [${10}^{-1},10$] Hz when observing a monochromatic gravitational wave signal of amplitude $h_0={10}^{-21}$ that is incoming from a given direction. In terms of their reconstructed frequencies and amplitudes, TianQin achieves its best precision values in both quantities in the frequency band [${10}^{-2},4\times {10}^{-1}$] Hz, with a frequency precision ${\sigma }_{f_{gw}}=2\times {10}^{-11}$ Hz and an amplitude precision ${\sigma }_{h_0}=2\times {10}^{-24}$. gLISA matches these precisions in a frequency band slightly higher than that of TianQin, [$3\times {10}^{-2},1$] Hz, as a consequence of its smaller arm length. gLISA_d, on the other hand, matches the performance of gLISA only over the narrower frequency region, [$7\times {10}^{-1},1$] Hz, as a consequence of its higher acceleration noise at lower frequencies. The angular, frequency, and amplitude precisions as functions of the source sky location are then derived by assuming an average signal-to-noise ratio of 10 at a selected number of gravitational wave frequencies covering the operational bandwidth of TianQin and gLISA. Similar precision functions are then derived for gLISA_d by using the amplitudes resulting in the gLISA average SNR being equal to 10 at the selected frequencies. We find that, for any given source location, all three missions display a marked precision improvement in the three reconstructed parameters at higher gravitational wave frequencies. Full article

With the advent of large-scale electronic transportation, the construction of electric vehicle charging stations (EVCSs) has increased. The stochastic characteristic of the charging power of EVCSs leads to a risk of destabilization of the DC distribution network when there is a high degree of power electronification. Current deterministic stability analysis methods are too complicated to allow for brief descriptions of the effect of probabilistic characteristics of EVCSs on stability. This paper develops a probabilistic small-signal stability analysis method. Firstly, the probabilistic information of the system is obtained by combining the s-domain nodal impedance matrix based on the point estimation method. Then, the probability function of stability is fitted using the Cornish–Fisher expansion method. Finally, a comparison experiment using Monte Carlo simulation demonstrates that this method performs well in balancing accuracy and computational efficiency. The effects of line parameters and system control parameters on stability are investigated in the framework of probabilistic stability. This will provide a probabilistic perspective on the design of more complex power systems in the future. Full article

The structural health monitoring (SHM) of bridge infrastructure has become essential for ensuring safety, serviceability, and long-term functionality amid aging structures and increasing load demands. SHM leverages sensor networks to enable real-time data acquisition, damage detection, and predictive maintenance, offering a more reliable alternative to traditional visual inspection methods. A key challenge in SHM is optimal sensor placement (OSP), which directly impacts monitoring accuracy, cost-efficiency, and overall system performance. This review explores recent advancements in SHM techniques, sensor technologies, and OSP methodologies, with a primary focus on bridge infrastructure. It evaluates sensor configuration strategies based on criteria such as the modal assurance criterion (MAC) and mean square error (MSE) while examining optimisation approaches like the Effective Independence (EI) method, Kinetic Energy Optimisation (KEO), and their advanced variants. Despite these advancements, several research gaps remain. Future studies should focus on scalable OSP strategies for large-scale bridge networks, integrating machine learning (ML) and artificial intelligence (AI) for adaptive sensor deployment. The implementation of digital twin (DT) technology in SHM can enhance predictive maintenance and real-time decision-making, improving long-term infrastructure resilience. Additionally, research on sensor robustness against environmental noise and external disturbances, as well as the integration of edge computing and wireless sensor networks (WSNs) for efficient data transmission, will be critical in advancing SHM applications. This review provides critical insights and recommendations to bridge the gap between theoretical innovations and real-world implementation, ensuring the effective monitoring and maintenance of bridge infrastructure in modern civil engineering. Full article

In this article, we present a model for analyzing the co-occurrence count data derived from practical fields such as user–item or item–item data from online shopping platforms and co-occurring word–word pairs in sequences of texts. Such data contain important information for developing recommender systems or studying the relevance of items or words from non-numerical sources. Different from traditional regression models, there are no observations for covariates. Additionally, the co-occurrence matrix is typically of such high dimension that it does not fit into a computer’s memory for modeling. We extract numerical data by defining windows of co-occurrence using weighted counts on the continuous scale. Positive probability mass is allowed for zero observations. We present the Shared Parameter Alternating Tweedie (SA-Tweedie) model and an algorithm to estimate the parameters. We introduce a learning rate adjustment used along with the Fisher scoring method in the inner loop to help the algorithm stay on track with optimizing direction. Gradient descent with the Adam update was also considered as an alternative method for the estimation. Simulation studies showed that our algorithm with Fisher scoring and learning rate adjustment outperforms the other two methods. We applied SA-Tweedie to English-language Wikipedia dump data to obtain dense vector representations for WordPiece tokens. The vector representation embeddings were then used in an application of the Named Entity Recognition (NER) task. The SA-Tweedie embeddings significantly outperform GloVe, random, and BERT embeddings in the NER task. A notable strength of the SA-Tweedie embedding is that the number of parameters and training cost for SA-Tweedie are only a tiny fraction of those for BERT. Full article

This research focuses on the prediction and estimation problems for the generalized exponential distribution under Type-II censoring. Firstly, maximum likelihood estimations for the parameters of the generalized exponential distribution are computed using the EM algorithm. Additionally, confidence intervals derived from the Fisher information matrix are developed and analyzed alongside two bootstrap confidence intervals for comparison. Compared to classical maximum likelihood estimation, Bayesian inference proves to be highly effective in handling censored data. This study explores Bayesian inference for estimating the unknown parameters, considering both symmetrical and asymmetrical loss functions. Utilizing Gibbs sampling to produce Markov Chain Monte Carlo samples, we employ an importance sampling approach to obtain Bayesian estimates and compute the corresponding highest posterior density (HPD) intervals. Furthermore, for one-sample prediction and, separately, for the two-sample case, we provide the corresponding posterior distributions, along with methods for computing point predictions and predictive intervals. Through Monte Carlo simulations, we evaluate the performance of Bayesian estimation in contrast to maximum likelihood estimation. Finally, we conduct an analysis of a real dataset derived from deep groove ball bearings, calculating Bayesian point predictions and predictive intervals for future samples. Full article