Maximum Likelihood Estimation Method Research Articles

Fast and Robust Noise Background Modeling and Quasiperiodic Oscillation Detection for Astronomical Time Series

Spectrum with confidence levels is a commonly used method for quasiperiodic oscillation (QPO) detection, but it is prone to yield false positives for two reasons: poor choice and/or biased modeling of the null hypothesis (or noise background). Motivated by this, we propose a new time-domain maximum-likelihood estimation method, which can quickly and accurately estimate the noise background free from background trends, spectra peaks, and even QPOs. Our method provides a wide range of candidate stochastic models (e.g., conventional first-order autoregressive, power law, generalized Gauss–Markov, Matérn, and damped random walk), some of which have not been considered previously. Some pitfalls (e.g., detrending) in previous QPO detections are also correctly processed to minimize the false detections. Along with the multitaper method and wavelet, we revisit QPO detection in the X-ray emission from the active galaxies RE J10341+396 and 1H 0707-495, and point out why the significance levels of the QPO at ∼2.6 × 10−4 Hz would be different in previous detections and reduced if the whole observation duration is considered. Our algorithm can be easily extended to other branches of astrophysics and beyond.

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online.

A New Extension of Topp-Leone Distribution (NETD) Using Generalized Logarithmic Function

Study’s Excerpt New Extension of Topp-Leone Distribution (NETD), derived using a generalized logarithm function, expanding the Topp-Leone family of distributions, is introduced. Mathematical properties of the NETD, including its quantile function, moments, Renyi entropy, and order statistics were investigated. The model demonstrates superior goodness-of-fit over existing models across four real-world datasets. Full Abstract In this study, we introduce a novel statistical model termed the New Extension of Topp-Leone Distribution (NETD), constructed using a generalized logarithm function. The derivation of the cumulative density function (CDF) and the probability density function (PDF) for this new distribution is thoroughly detailed. A validity test was conducted to confirm the legitimacy of the proposed NETD, and the results affirm that it is indeed a valid probability distribution. We investigate several key mathematical and statistical properties of the NETD, including the quantile function, moments, Renyi entropy, probability-weighted moments, and order statistics. These properties provide a comprehensive understanding of the distribution's behaviour and characteristics. To estimate the parameters of the NETD, we applied the Maximum Likelihood Estimation (MLE) method, which is known for its efficiency and asymptotic properties. The flexibility, versatility, and performance of the NETD were evaluated using four diverse real-world datasets. Through the application of model selection criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Corrected Akaike Information Criterion (CAIC), and Hannan-Quinn Information Criterion (HQIC), we demonstrated that the NETD exhibits superior goodness-of-fit compared to existing variants of the Topp-Leone distribution. Our findings suggest that the NETD is a robust and adaptable distribution, capable of effectively modelling a wide range of empirical data. This new extension not only broadens the applicability of the Topp-Leone family of distributions but also enhances the toolkit available for statistical analysis and modelling in various fields.

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

A New Lifetime Distribution and its Application to Cancer Data

Introduction: Recently, researchers have introduced new generated families of univariate lifetime distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution or compounding two distributions to get more flexibility in fitting data in different areas such as medical sciences, environmental sciences, and engineering. The addition of parameter(s) has been proven useful in exploring tail properties and for improving the goodness-of-fit of the family of the proposed distributions. Methods:A new Three-Parameter Weibull-Generalized Gamma distribution which provides more flexibility in modeling lifetime data is developed using a two-component mixture of Weibull distribution (with parameters θ and λ) and Generalised Gamma distribution (with parameters α=4,θ and λ). Some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, moment generating function, Renyi entropy and order statistics are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study is performed to examine the performance of the maximum likelihood estimators of the parameters. Results: Real life applications of the proposed distribution to two cancer datasets are presented and its fit was compared with the fit attained by some existing lifetime distributions to show how the Three-Parameter Weibull-Generalized Gamma distribution works in practice Conclusion: The results suggest that the proposed model performed better than its competitors and it’s a useful alternative to the existing models.

The Two Component Generalized Finite Erlang Mixture and its Properties and Special Cases

This research proposes the construction of a two-component generalized finite Erlang mixture with four parameters. Three distinct cases of this mixture are presented, differing in their mixing weights and corresponding component probability (Erlang) distributions. Special cases of these mixtures, including the one-, two-, and three-parameter finite Erlang mixtures, have also been derived. The statistical properties examined for these mixtures include the distribution function, survival function, hazard function, moment generating function, raw and central moments, mean, variance, coeffcient of skewness, coeffcient of kurtosis, and order statistics. Parameter estimation for the finite Erlang mixtures was conducted using both the method of moments and maximum likelihood estimation. Furthermore, the 4-parameter mixed Erlang distributions were applied to a real dataset on the relief times of patients receiving an analgesic, to evaluate their goodness of fit. The results demonstrate the potential of these mixtures to provide robust modeling for empirical data, suggesting their applicability in various statistical and practical contexts.

Association of crop commercialization and rural households' multidimensional poverty using targeted maximum likelihood estimation

Recent evidence shows the highest prevalence of multidimensional poverty in the world. To alleviate poverty, Ethiopia is investing in stimulating agricultural commercialization for poverty reduction, driving sustainable economic growth, and creating jobs. Therefore, this study investigated the causal relationship between crop commercialization and multidimensional poverty across Ethiopian rural households using the Ethiopia Socioeconomic Survey 2018/19 data, which included 1129 crop commercialized and 1585 completely subsistence rural households. Moreover, this study also examined the causal effect of crop commercialization on the multidimensional poverty mediated by mobile phone ownership status. The study used the double robust method of the augmented inverse probability of treatment weighted (AIPTW) and targeted maximum likelihood estimation (TMLE) methods. The result showed that crop commercialization has an association with multidimensional poverty. Specifically, the TMLE with a default super learner model estimates were the most precise and suggest that the prevalence of risk of being multidimensionally poor among rural households who were crop commercialized is 12.2 % lower than for those who were completely subsistence households. Thus, it is important to have more robust policies like crop commercialization to target rural multidimensional poverty reduction. Moreover, the controlled direct effect estimation analyses showed that crop-commercialized rural households reduced the adjusted risk of multidimensional poverty by; 12 % for those who owned mobile phones and 7.8 % for those who did not. To ensure sustainable livelihoods for rural multidimensional poor households, it is necessary to have a multidisciplinary policy intervention to promote crop commercialization through the spread of mobile phones in rural areas.

Evaluation of Wolbachia infection in Aedes aegypti suggests low prevalence and highly heterogeneous distribution in Medellín, Colombia

Dengue virus, transmitted mainly by Aedes aegypti mosquitoes, is a significant public health challenge in tropical and subtropical countries, with an incidence that is growing at an alarming rate. The release of Wolbachia-carrying mosquitoes has been suggested as a strategy to reduce the incidence of multiple arboviruses. In Medellín, Colombia, large-scale releases of Wolbachia-infected Ae. aegypti mosquitoes were performed between 2017 and 2022 by the World Mosquito Program to facilitate population replacement. In this study, we evaluated the prevalence and distribution of Wolbachia-infected Ae. aegypti two years after completion of these releases. We conducted the sampling across 19 communes in Medellín, using 416 ovitraps to collect Ae. aegypti eggs from epidemiological weeks 26 to 41 in 2023. Upon hatching the collected eggs, we identified and pooled adult female Ae. aegypti for DNA extraction. Subsequently, we conducted PCR assays for the detection of Wolbachia infection in these mosquitoes. We used maximum likelihood estimation (MLE) and Bayesian methods to estimate the prevalence of Wolbachia infection, while using QGIS to analyze spatial distribution of infection in the region. A total of 774 female Ae. aegypti mosquitoes from 182 pools were evaluated. We detected Wolbachia in 33.5 % of pools, with an estimated individual minimum infection rate of 9.5 % and a maximum of 33.2 %. The prevalence varied significantly across communes, with the highest rates observed in the northeastern and southwestern areas. Spatial analysis revealed a highly heterogeneous island-like distribution of Wolbachia across Medellín with a few hotspots. The observed Wolbachia prevalence in this work was lower than previously reported. We suspect a decline in the prevalence of Wolbachia-infected Ae. aegypti mosquitoes in Medellín following the completion of their release.

A bivariate dependent degradation model based on artificial neural network supported stochastic process and Copula function

AbstractIn order to use the high ability of the artificial neural network (ANN) in data fitting, this paper introduces an ANN in stochastic process to describe the mean function for degradation modeling. Due to the fact that the existing method cannot handle the bivariate dependent degradation conditions, a bivariate dependent degradation model based on Copula function and ANN‐supported stochastic processes is proposed. Considering the random effects caused by individual difference, it is assumed that the unknown parameters in the stochastic processes and Copula functions are randomly distributed. Based on the maximum likelihood and moment estimation methods, a related statistical inference method for ANN training and parameter estimation is developed to use the bivariate dependent degradation model. An actual fatigue crack dataset is used to demonstrate the validity of the proposed method. The obtained results show that the dependent relationship between two degradation indicators should not be neglected, and it can be efficiently handled by the proposed method. Furthermore, the proposed degradation model can provide reliability and degradation intervals with enough precision due to the fact that it considers the random effects caused by individual difference.

Estimation and inference of multi-effect generalized geographically and temporally weighted regression models

Geographically and temporally weighted regression (GTWR) models have been an effective tool for exploring spatiotemporal heterogeneity of regression relationships. However, they cannot effectively model such response variables that follows discrete distributions. In this study, we first extend the distributions of response variables to one-parameter exponential family of distributions and formulate generalized geographically and temporally weighted regression (GGTWR) models with their unilaterally temporally weighted maximum likelihood estimation method. Furthermore, we propose so-called multi-effect GGTWR (MEGGTWR) models in which spatiotemporally varying, constant, temporally varying, and spatially varying coefficients may simultaneously be included to reflect different effects of explanatory variables. A coefficient-average-based estimation method is suggested to calibrate MEGGTWR models and a generalized likelihood ratio statistic based test is formulated to identify the types of coefficients. Simulation studies are then conducted to assess the performance of the proposed estimation and inference methods with the impact of multicollinearity among explanatory variables also examined. The results show that the estimation method for MEGGTWR models can accurately estimate various types of coefficients and the test method is of valid type I error and satisfactory power. Finally, the relationship between childhood hand, foot, and mouth disease cases and climate factors is analyzed by the proposed models with their estimation and inference methods and some interesting spatiotemporal patterns are uncovered.

Copula-based analysis of dependent current status data with semiparametric linear transformation model.

This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example.

Drive sustainable business performance with humane entrepreneurship, knowledge management: the mediation of sustainable business advantage and sustainable business model innovation

PurposeThis study evaluates the important role of humane entrepreneurship (HE) on sustainable business advantage (SBA) and sustainable business performance (SBP) by exploring the mediating role of sustainable business model innovation (SBMI) under the influence of knowledge management (KM) in small and medium-sized enterprises (SMEs). Encouraging businesses to implement a combination of KM and HE facilitates the implementation of SBMI that brings value to businesses, communities and the environment in emerging economies.Design/methodology/approachThis study uses an empirical quantitative research method using primary information based on data collected by questionnaires. The study sample resulted in 424 valid responses (66.77% response rate). The target audience of the study is middle and senior managers in SMEs. This study aims to perform structural modeling analysis with the maximum likelihood estimates method to examine structural relationships.FindingsThis study found a positive relationship between KM and HE to SBMI. At the same time, SBMI plays an important role for businesses to achieve SBA and SBP. Similarly, a positive relationship was also found between HE to SBA and SBP. And SBA strongly promotes SMEs to achieve SBP. In addition, the mediating role of SBMI and SBA is clarified to have a positive impact between HE–SBP and SBMI–SBP. HE plays an important role in motivating businesses to innovate sustainable business models, making it easier to gain sustainable competitive advantages, thereby bringing sustainable business results.Practical implicationsThis research helps SMEs realize the importance of KM and HE in SBMI. At that time, SMEs take advantage of internal and external information sources and innovate their business models based on HE mechanisms. Applying HE mechanisms will allow businesses to innovate their business models by combining concerns between stakeholders and the social environment for sustainable development. Therefore, businesses will achieve their SBA toward SBP.Originality/valueThe present literature shows that there are few empirical studies on the mechanism mediating SBMI in the relationship between HE and SBP; and SBA in the link between SBMI and SBP. In addition, the impact of KM and HE on SBMI is also very important in the current context. The study's findings could have huge implications for entrepreneurs and senior managers in SMEs in emerging economies. Help them realize the importance of KM and HE for SBMI, thereby building strategic perspectives that help businesses achieve sustainable competitive advantages and increase SBP for businesses.

Long-Term Dynamic Effect of Body Mass Index on Adverse Cardiovascular Outcomes with the Targeted Maximum Likelihood Estimation Method: Results from the KNOW-CKD Study

Long-Term Dynamic Effect of Body Mass Index on Adverse Cardiovascular Outcomes with the Targeted Maximum Likelihood Estimation Method: Results from the KNOW-CKD Study

Some Properties of the Cosine Lomax Distribution with Applications

This paper introduces a new trigonometric distribution, named the Cosine Lomax (CLM) distribution. This distribution is a combination of the Lomax distribution and the Cosine-G family of distributions. Among the many mathematical moments, moment-generating function, incomplete moments, and the quantile function. We try to determine the model parameters using the maximum likelihood estimation method. Simulation studies evaluate the effectiveness of maximum likelihood estimators using bias and root mean square error. We applied the CLM distribution to two real-world datasets and tested for consistency using the Akaike information criterion, the consistent AIC, the Hannan-Quinn information criterion, the Bayesian information criterion, the Kolmogorov-Smirnov p-value, Cramer Von-Mises, and Andersen-Darling. The CLM model fared better when compared to the following distributions: Lomax, Inverse Lomax, Inverse Weibull, Burr Type X, Rayleigh, and Exponential, as well as measures of data set fit.

Efficient approximation of global population dynamic models through statistical inference using local data

Biological growth curves are pivotal in predicting natural growth across disciplines, typically analyzed using nonlinear least squares or maximum likelihood methods. Bhowmick et al. (2014) introduced the interval-specific rate of parameters (ISRP) for growth equations, improving the estimation of relative growth rate (RGR) and model selection accuracy. Despite its effectiveness, computing these model-specific RGR estimates involves complex calculations and lacks explicit expressions for many nonlinear models. Also, for highly nonlinear models and non-monotonic data where the parameters are non-linearly related, the computation of interval estimates is almost impossible and may suffer from significant approximation errors. So, the need for a more efficient computation method for ISRP remains a significant challenge in growth studies. In this article, we propose a computational approach to obtain interval estimates of parameters based on the maximum likelihood estimation method. The likelihood function is maximized using the data on smaller intervals. Our study underscores the importance of an efficient ISRP computation technique, providing a more stable, unbiased, and normally distributed estimator. The most important advantage is that it can be implemented using existing optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. Both simulation studies and real data analysis have been carried out to validate the proposed estimation process. Additionally, its applicability to non-monotonic growth profiles and its robustness in handling highly non-linear growth equations highlight its versatility. We also developed a web application GpEM-R which is freely available for researchers and practitioners to analyze growth data.

Multi-Stress Accelerated Degradation Testing Reliability Assessment of LED Lamp Beads Considering Generalized Coupling

Due to the complex operating environment of LED lamp beads (hereinafter referred to as LED), the test method that only considers the action of multiple stresses alone ignores the mutual influence between stresses, making it difficult to accurately obtain the life indicators of LEDs, resulting in a large deviation in the theoretical life results. In this regard, this paper proposes a multi-stress accelerated degradation evaluation method considering generalized coupling and conducts an accelerated degradation test (ADT) to evaluate the life of LEDs. We identified three stress sources and designed five new high-gradient ADTs. Through experimental data, we found that the three stress sources are strongly coupled on this LED. Then, a generalized coupling maximum likelihood estimation method (MLE) for the entire sample was constructed, and the particle swarm algorithm was used to solve the parameters. Finally, the life of this LED was evaluated based on the experimental data. The results show that the life of the LED considering multiple-stress coupling is within 6.5% of the historical life scatter point, which is more in line with the actual working environment.

Timeliness-aware rumor sources identification in community-structured dynamic online social networks

Identifying rumor sources in online social networks (OSNs) plays a crucial role in controlling the spread of rumors and mitigating their damage. However, the community structure of OSNs and timeliness of rumors increase the complexity of accurately characterizing rumor-spreading behavior, making it extremely challenging to identify the source of rumor in OSNs. Conventional studies on rumor source identification often overlook the community structure of OSNs and timeliness of rumors. This paper proposes a rumor sources identification framework that take these two aspects into consideration. First, we transfer the snapshots of a dynamic OSN into a community-structured dynamic OSN through 4 meticulously designed phases. Second, instead of considering a constant influence of rumors in traditional techniques, we introduce a time-varying dynamic propagation parameter to quantify the timeliness of rumor, and apply the propagation parameter to establish a microscopic rumor spreading model. This process addresses the issue of modeling the timeliness of rumor. Third, we adopt sensor-based observation techniques to collect the propagation information of rumor, and a hybrid sensor deployment strategy is designed to improve the efficiency of information collection. Fourth, we propose an algorithm for identifying single and multiple rumor sources in community-structured dynamic OSN, this algorithm initiates with the utilization of some criteria to analyze the gathered propagation information and estimate the suspicious communities that harbor the source of rumors. Subsequently, it applies maximum likelihood estimation method within each community to determine the ultimate source of the rumor. Experimental results on real-world and synthetic networks indicate that our method can accurately identify the real rumor sources. To the best of our knowledge, the proposed method is the first that can be used to identify rumor sources in community-structured dynamic OSNs.

Iterative maximum-likelihood estimation algorithm for clock offset and skew correction in UWB systems assisted by 5G NR multipath

High-precision location services such as unmanned driving, indoor navigation, and mine positioning have been benefiting significantly with the breakthroughs in Fifth-Generation (5G) technology. This paper proposes a collaborative Time of Flight (TOF) measurement framework for 5G New Radio (NR) in Release 17 and Ultra-Wideband (UWB). The method proposed improves the positioning accuracy by tackling the issues of UWB clock offset and clock skew. To this end, we have designed an innovative correction algorithm that effectively utilizes 5G multipath measurement and Timing Error Group (TEG) identifiers. The algorithm employs a low-complexity iterative maximum likelihood estimation (MLE) method to accurately estimate error parameters and calibrate UWB TOF measurement results. Simulation results show that this algorithm significantly enhances positioning precision and robustness. It reduces positioning error by 24 % and 35 % compared to the baseline algorithm in two representative scenarios. These improvements make it suitable for UWB systems in real-time and complex environments.

Exploring a new two-parameter Archimedean copula: the Gumbel-Joe copula

In this article, we introduce a novel Archimedean copula constructed from a unique strict generator function. It can be described as a two-parameter unification of the well-established Gumbel-Barnett and Joe copulas. The first part is devoted to its formulation, as well as those of the corresponding density, the conditional copula, and the Kendall distribution function. Additionally, graphical representations are included to elucidate their shape behavior under various parameter configurations. In a second part, we examine some of its notable properties, with emphasis on correlation characteristics. Practical applications are discussed in the last part. In particular, we employ the maximum likelihood estimation method to determine the unknown parameters involved based on data and conduct a simulation study to demonstrate the effectiveness of this approach. Additionally, we analyze a dataset to provide practical illustrations of copula behavior and potential.

Global Probabilistic Forecasting for Multiple Tight Gas Wells Using Deep Autoregressive Networks

Summary Traditional methods for forecasting production rate, such as Arps, analytical techniques, and recurrent neural network (RNN)–based deep learning, are mainly point prediction techniques developed within the framework of single-well forecasting. These methods often face limitations stemming from single-well historical production data and model assumptions, hindering their ability to consider the influence of development patterns of other production wells within the block on the target well. In addition, they struggle to predict the multiple production rate time series simultaneously and often fail to quantify uncertainty in predictions or adequately exploit extensive relevant historical production data. To tackle these challenges, we propose a model based on the deep autoregressive recurrent neural network (DeepAR), leveraging related multiwell production rate data to enable global modeling and probabilistic forecasting. This model incorporates dynamic covariate and static categorical variable data, integrating Bayesian inference and using gradient descent algorithms and maximum likelihood estimation methods to derive a comprehensive historical-future production probability evolution pattern shared across multiple wells. Leveraging data from 943 tight gas wells, a comprehensive evaluation of the DeepAR model’s performance was undertaken, encompassing the comparison of prediction accuracy with long short-term memory (LSTM), classification prediction, cold-start prediction, and single-well multitarget prediction scenarios, summarizing the applicability conditions for each. The research findings highlight that DeepAR integrates the acquired comprehensive production probability evolution pattern with specific production historical data of the target well to formulate a “comprehensive + specific” production probability prediction approach, resulting in improved stability and accuracy. On average, DeepAR demonstrates a 58.79% reduction in normalized deviation (ND) compared to the LSTM model, showcasing enhanced stability, particularly in scenarios involving frequent well shut-ins and openings. Moreover, DeepAR can learn static categorical features, with the classification model resulting in a 27.15% reduction in the ND compared to the unclassified model. Furthermore, DeepAR adeptly addresses the challenge of limited data availability, achieving cold-start prediction and facilitating multitarget single-well training and prediction while considering the interdependency among multiple variables over time and effectively mitigating the issue of missing auxiliary variables during the prediction phase. This study contributes to a broader understanding of production forecasting and analysis of production dynamics methods from a big data perspective.