Article
Mathematics, Applied
Saurabh L. Raikar, Rajesh S. Prabhu Gaonkar
Summary: This article presents a method for estimating the stress strength reliability of Weibull distribution and compares different estimation methods. The proposed method is validated through simulation studies and real-life applications.
Article
Multidisciplinary Sciences
R. Alshenawy, Hanan Haj Ahmad, Ali Al-Alwan
Summary: This paper discusses two prediction methods for predicting the non-observed units under progressive Type-II censored samples, and provides inference on the unknown parameters of the Marshall-Olkin model. Through simulation studies and evaluation on real data examples, the best prediction method is found.
Article
Materials Science, Ceramics
Serkan Nohut
Summary: This article investigates the effectiveness of three-parameter Weibull distribution function for fitting strength variation due to R-curve effect. It is found that the 3P-Weibull distribution function fits the strength distribution better than the 2P-Weibull distribution function for materials exhibiting R-curve behavior, especially when the crack resistance curve is steep and the Weibull modulus is high. Additionally, it is recommended to use at least 100 samples for reliable estimation when the material shows R-curve behavior.
CERAMICS INTERNATIONAL
(2021)
Article
Engineering, Civil
Liyang Xie, Ningxiang Wu, Xiaoyu Yang
Summary: This paper presents a new parameter estimation method for the three-parameter Weibull distribution. The method involves constructing a mapping from the random variable value and its corresponding cumulative distribution probability to the scale parameter. The proposed method outperforms the maximum likelihood method and the Weibull plot-based least squares method, as demonstrated by case studies.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Engineering, Industrial
Susumu Shuto, Takashi Amemiya
Summary: This study investigates the sequential Bayesian inference of the Weibull distribution parameters of system components using failure observations analyzed as censored data. The proposed method, Sequential Bayesian Inference with Optimized Prior Distribution (SBOPD), utilizes prior information and optimized initial prior distribution to estimate parameters more accurately and effectively at the preliminary stages of the system life cycle.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2022)
Article
Mathematics
Xiaowei Dong, Feng Sun, Fangchao Xu, Qi Zhang, Ran Zhou, Liang Zhang, Zhongwei Liang
Summary: This study effectively addressed the issue of multi-parameter estimation in the reliability analysis of electromechanical products by establishing a hybrid Weibull distribution model and designing an optimization algorithm.
Article
Engineering, Civil
Xiaoyu Yang, Liyang Xie, Bingfeng Zhao, Xiangwei Kong, Ningxiang Wu
Summary: This paper investigates the parameter estimation issue of the three-parameter Weibull distribution in the context of small sample size. The results show that by empirically determining the shape parameter and using an iterative method for estimating the location parameter and scale parameter, the parameters of the three-parameter Weibull distribution can be more accurately estimated than using the maximum likelihood method.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2022)
Article
Engineering, Industrial
Yogesh Mani Tripathi, C. Petropoulos, Mayank Kumar Jha
Summary: This paper considers the problem of estimating a stress-strength parameter under the assumption that both stress and strength variables follow independent lognormal distributions. The estimation and interval estimation of the parameter are obtained through methods such as maximum likelihood estimation and Bayesian estimation, and numerical comparisons and analysis of real data sets are conducted.
QUALITY TECHNOLOGY AND QUANTITATIVE MANAGEMENT
(2022)
Article
Multidisciplinary Sciences
Di Zhou, Xiao Zhuang, Hongfu Zuo
Summary: A novel parameter estimation method using CSAPSO algorithm is proposed in order to improve the parameter estimation accuracy of three-parameter Weibull distribution. Experimental results show that this method can achieve the best parameter estimation results in different scenarios.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2021)
Article
Energy & Fuels
Wenxin Wang, Kexin Chen, Yang Bai, Yu Chen, Jianwen Wang
Summary: This study accurately describes the characteristics of wind energy resources in suburbs using a new method of WPD estimation and the three-parameter Weibull distribution. Taking the month as the time scale can effectively capture the scattered and changing wind energy in suburbs.
Article
Green & Sustainable Science & Technology
Muhammad Sumair, Tauseef Aized, Muhammad Mahmood Aslam Bhutta, Farrukh Arsalan Siddiqui, Layba Tehreem, Abduallah Chaudhry
Summary: A new method for wind resource assessment based on the squared deviation of the first four moments of the Weibull Probability Distribution (WPD) is proposed in this study. The method is validated using a large dataset and found to be the best among all stations, making it suitable for wind resource assessment in different geographical regions worldwide.
Article
Engineering, Civil
Xiaoyu Yang, Liyang Xie, Jiaxin Song, Jianpeng Chen, Bingfeng Zhao, Yifeng Yang
Summary: In this paper, an optimal probability estimator for Weibull parameters is obtained through Monte Carlo simulations, and it is found to exhibit stronger robustness and higher accuracy compared to five commonly used estimators, especially in cases of small sample sizes. The recommended optimal probability estimator is the midpoint rank for LRE, MDE, and EIV in practical applications.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Engineering, Multidisciplinary
Yuxuan Wu, Hanyang Xie, Jyun-You Chiang, Gang Peng, Yan Qin
Summary: A new parameter estimation method is proposed for analyzing the strength data of glass fiber, which outperforms other competitors in obtaining reliable estimates. The method is validated through simulation results and application to real data sets, showing its suitability and effectiveness for analyzing glass fiber strength.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Environmental Sciences
Bulent Yaniktepe, Osman Kara, Ilyas Aladag, Cenk Ozturk
Summary: This study analyzes the wind measurement data in Osmaniye, Turkey to determine the wind characteristics and wind energy potential of the region. The suitability of the two-parameter Weibull distribution model is evaluated, and it was found that the modified maximum likelihood method is the most reliable. The graphical method performs the worst in comparison.
ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH
(2023)
Article
Thermodynamics
Yidong Wu, Nini Li, Yihan Liu, Liqun Tang, Wei Cao
Summary: The reliability assessment of fatigue life of automotive chassis parts is crucial for automobile safety. In this study, fatigue endurance tests were conducted on automotive half-axles, and a three-parameter Weibull distribution model was established to analyze the fatigue life distribution. A new parameter estimation method based on dual genetic algorithm was proposed, which improved the accuracy and iteration speed of parameter estimation, providing new ideas and theoretical basis for reliability assessment of mechanical components.
ADVANCES IN MECHANICAL ENGINEERING
(2022)
Article
Statistics & Probability
Jazaa S. Al-Mutairi, Mohammad Z. Raqab
STATISTICAL PAPERS
(2020)
Article
Statistics & Probability
Mohammad Z. Raqab, Omar M. Bdair, Manoj K. Rastogi, Fahad M. Al-aboud
Summary: In this paper, estimation of unknown parameters using frequentist and Bayesian approaches from a hybrid censored sample of a two parameter exponentiated half logistic distribution is considered. Various algorithms were used to obtain point estimators and confidence intervals for the shape and scale parameters, and data analyses on cancer patients' survival times were conducted. A numerical simulation study was carried out to evaluate the developed methods and conclusions on the findings were reported.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2021)
Article
Computer Science, Interdisciplinary Applications
M. S. Kotb, M. Z. Raqab
MATHEMATICS AND COMPUTERS IN SIMULATION
(2019)
Article
Engineering, Multidisciplinary
Mohammed S. Kotb, Mohammad Z. Raqab
APPLIED MATHEMATICAL MODELLING
(2019)
Article
Mathematics, Applied
Mohammad Z. Raqab, Laila A. Alkhalfan, Omar M. Bdair, Narayanaswamy Balakrishnan
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2019)
Article
Statistics & Probability
Mohammad Z. Raqab, Debasis Kundu, Fahimah A. Al-Awadhi
Summary: This study introduces a compound zero-truncated Poisson normal distribution and a four-parameter bivariate distribution with continuous and discrete marginals. It discusses estimation of unknown parameters using an EM type algorithm, and assesses the effectiveness of the algorithm through simulation experiments and analysis of a real data set.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2021)
Article
Statistics & Probability
Heba A. Almuzaini, Mohammad Z. Raqab
Summary: The performances of different point predictors of future record data are studied based on informative records from the two-parameter exponential distribution, with a focus on Pitman's measure of closeness. The best unbiased and conditional median predictors are found to be competitive in terms of Pitman closeness when compared to other predictors.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2022)
Article
Engineering, Multidisciplinary
Abduallah M. Almarashi, Ali Algarni, A. M. Daghistani, G. A. Abd-Elmougod, S. Abdel-Khalek, Mohammad Z. Raqab
Summary: This paper addresses the problem of comparative life tests under joint censoring samples from an exponential distribution with competing risks model, focusing on two causes of failure and units from two production lines censored under a hybrid progressive Type-I censoring scheme. Maximum likelihood estimation, different Bayes methods, asymptotic confidence intervals, and Bayes credible intervals are discussed, with a real data set analyzed for illustrative purposes. Theoretical results are evaluated and compared through Monte Carlo studies.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Statistics & Probability
Husam A. Bayoud, Mohammad Z. Raqab
Summary: This article investigates the joint Type-II progressive censoring scheme for two populations with lifetimes following Topp-Leone models, but with unknown parameters. Classical and Bayesian inferences are used to estimate the parameters, and Monte Carlo simulation is conducted to compare the performance of the methods.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2021)
Article
Automation & Control Systems
Mohammad Z. Raqab, Husam A. Bayoud, Guoxin Qiu
Summary: The information content of a random variable is studied in the field of information theory. The mean and variance of the information content are referred to as entropy and varentropy, respectively. This paper focuses on the varentropy of the inactivity time of a random variable, termed as past varentropy. Reliability properties associated with the past varentropy and the reversed hazard rate function are discussed. Lower and upper bounds for the past varentropy are provided. The varentropy is applied to the proportional reversed hazard rate model. Furthermore, an asymptotic distribution for the information content of the inactivity time is derived based on past entropy and varentropy.
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Mohammed A. Meraou, Noriah M. Al-Kandari, Mohammad Z. Raqab, Debasis Kundu
Summary: This paper introduces a new family of distributions, the compound zero-truncated Poisson exponential distribution, for analyzing skewed data. It proposes an algorithm for parameter estimation and considers a bivariate version of the model. Through simulation studies and analysis of real data, the performance and effectiveness of the proposed models are verified.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2022)
Article
Statistics & Probability
Omar M. Bdair, Mohammad Z. Raqab
Summary: The study focuses on predicting unobserved censored units from a mixture exponential distribution with unknown parameters, proposing different prediction methods and considering two scenarios of sample size. The parametric bootstrap-based prediction intervals are shown to be comparable in coverage probability and competitive in average length compared to other methods.
Article
Statistics & Probability
M. A. Meraou, N. M. Al-Kandari, M. Z. Raqab
Summary: In this article, a new compound zero-truncated Poisson gamma model is proposed and its mathematical properties are discussed. The model is shown to be convenient to implement and can be extended to a four-parameter bivariate model. Experiment results and analysis of real data demonstrate the flexibility of the proposed models.
JOURNAL OF STATISTICAL THEORY AND PRACTICE
(2022)
Article
Engineering, Multidisciplinary
Mohammad A. Amleh, Mohammad Z. Raqab
Summary: This paper investigates a simple step-stress model based on type-II censoring Weibull lifetimes, using KH model to develop Bayesian approaches for estimating model parameters and predicting future times to failure. The main goals of this work include parameter estimation and the study of posterior predictive density.
QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL
(2023)
Article
Statistics & Probability
R. Valiollahi, A. Asgharzadeh, M. Z. Raqab
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2019)
Article
Statistics & Probability
Antonio Di Noia, Gianluca Mastrantonio, Giovanna Jona Lasinio
Summary: Building on Dryden et al. (2021), this note presents the Bayesian estimation of a regression model for size-and-shape response variables with Gaussian landmarks, fitting into the framework of Bayesian latent variable models and potentially allowing for a highly flexible modeling framework.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Shuning Liu, Guangying Lv
Summary: This paper investigates the stability of stochastic differential equations with impulsive effects and provides sufficient conditions for obtaining stability. The research shows that impulse can stabilize stochastic differential equations.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Yuta Tanoue
Summary: In this study, we examine the properties of 9-subgaussian random variables, including inequalities, concentration inequalities, and the law of large numbers. We also discuss the characteristics of m-acceptable 9-subgaussian random variables.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
John Hughes
Summary: This article presents inferential methods for the binomial proportion in a unified way, as variations on a conjugate-Bayesian theme. An overlooked interval emerges as the best-performing approximate interval for small samples. This approach is simple, intuitive, and illuminating, and may hold pedagogical value for instructors of advanced courses on statistical inference.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Yunshi Gao
Summary: This paper studies the behavior of a particle systems on an Erdos-Renyi graph under large deviations and establishes the exponential equivalence between the systems and general interacting systems without random graphs. The results provide a foundation for the large deviations theory of particle systems.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
David Itkin
Summary: In this study, we examine a new family of distributions called Generalized Rank Dirichlet distributions on the ordered simplex. We investigate their properties and propose simulation algorithms for random variates. The results can be applied to model capital distribution in financial markets and ranked order statistics of weight vectors.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Mario Lefebvre
Summary: This passage describes the analytical solution method for an Ornstein-Uhlenbeck process with Poissonian jumps, considering both exponentially and uniformly distributed jumps.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Dongzhou Huang
Summary: This paper studies the sets of visit times to points on the plane by a standard two-dimensional Brownian motion. The concept of logarithmic scale Minkowski dimension is introduced as a tool for measuring these sets. It is proved that almost surely there exists a point x such that the logarithmic scale Minkowski dimension of the set of visit times to x is 1.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Terry J. Lyons, Vlad Margarint, Sina Nejad
Summary: In this paper, we study a one-dimensional stochastic differential equation obtained by performing a random time change of the backward Loewner dynamics in H. We show the convergence of this equation towards its stationary measure in the sense of random ergodic averages. The density formula of the stationary measure reveals a phase transition at W = 8, which coincides with the change in behavior of the SLEW trace. By using convergence in total variation, we identify families of random times on which the law of the arguments of points under the backward SLEW flow converges to a closed form expression measure.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Guangshuo Zhou, Fengjiao Du, Shengjun Fan
Summary: This paper proves a general invariant representation theorem for generators of general time interval backward stochastic differential equations, where the generator has a quadratic growth in the unknown variable z and satisfies some stochastic growth conditions in the unknown variable y. This result unifies and strengthens some known results.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Benito Pires
Summary: This article introduces an approach based on the energy function of Hopfield networks to obtain Lyapunov functions for a class of interacting reinforced stochastic processes. The method works for processes with finitely many 2-dimensional probability measures and can be applied to the study of the total stability of differential equations.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Yasuhito Nishimori
Summary: In this paper, we investigate the relation of hitting probabilities between two sets in Hunt processes, without considering spatial homogeneity. We claim that if the Hunt process satisfies the strong Feller property, then there is a certain relationship between the hitting probabilities of the two sets.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Nader Karimi, Erfan Salavati, Hirbod Assa, Hojatollah Adibi
Summary: This paper proposes a continuous time version of the speculative storage model for commodity prices and provides mathematical analysis and numerical algorithm verification for the model.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Offer Kella
Summary: The paper characterizes the independence of the minimum value and the events of the two independent random variables. It shows that the minimum value is independent if and only if both random variables are distributed according to the same increasing function of two independent random variables.
STATISTICS & PROBABILITY LETTERS
(2024)
Article
Statistics & Probability
Amites Dasgupta
Summary: We present Azuma-Hoeffding bounds for a class of urn models, which show exponentially decreasing probabilities of being away from the limit. The method involves relating the variables to linear combinations using eigenvectors of the replacement matrix, and introduces appropriate martingales. Some cases of repeated eigenvalues are also considered using cyclic vectors. Moreover, the strong convergence of proportions is proved as an application of these bounds.
STATISTICS & PROBABILITY LETTERS
(2024)
