Point Estimates Of Parameters Research Articles

Sparsify dynamically expandable network via variational dropout

This paper develops a new method for lifelong learning referred to as Sparsify Dynamically Expandable Network (SDEN) via Variational Dropout, which explores a sparse model while preserving the performance. Dynamically Expandable Network (DEN) can learn a sequence of tasks via performing network retraining, network expansion by adding only the necessary neurons, and network split to effectively prevent semantic drift in an online manner. To overcome point estimation of parameters in DEN, Bayesian Compression for DEN is developed under the Bayesian framework. However, this method demands more time for model training and testing. To improve the model efficiency, we propose SDEN under the efficient sparse learning framework. We validate our SDEN in the lifelong learning scenarios with multiple frequently used benchmarks, on which it can obtain comparable classification accuracy, and less training and testing time compared with the comparison methods. Furthermore, our method can also learn a more sparse network structure which means fewer network parameters.

A new cosine-based approach for modelling the time-to-event phenomena in sports and engineering sectors

Data analysis through probability-based methods plays an important role in decision-making in all spheres of life. Probability-based approaches lead to productive decision-making under uncertainty. To date, several probability distributions have been formulated that are characterized in different ways and successfully applied in various fields. Most of these probability distributions are studied by adding many additional parameters, typically from one to eight. There is the very least number of available distributional methodologies that are devised without inducing new parameters. In this integrated research piece of work, we provide a new cosine-adaptive method that is developed without considering any new parameters. We call the proposed method the weighted cosine-K family of distributions. Focusing on the proposed method, a new probability model is developed that is named the weighted cosine-Weibull (WC-Weibull) distribution. Some quartile-based characteristics along with estimators of the WC-Weibull distribution are derived. For the parameters of the WC-Weibull distribution, the point estimators are derived. The assessment of point estimators of the WC-Weibull distribution's parameters is provided through a simulation study. Finally, the utility of the WC-Weibull distribution is demonstrated by considering time-to-event phenomena in sports and the engineering sectors. Considering four statistical criteria, it has been shown that the WC-Weibull distribution is an efficient and optimal model for time-related facts (or events) in sports and engineering fields.

Relative bioavailability study of ticagrelor in healthy subjects under fasting conditions

Objectives: This is a randomized, single-dose, two-period, two-sequence, and crossover study to evaluate the bioequivalence (BE) profiles of two formulations of ticagrelor 90 mg, under fasting conditions. Materials and Methods: The plasma concentrations of ticagrelor were measured using a validated liquid chromatography mass spectrometry method. Enrolled for the study were 30 healthy adult volunteers (21 males and 9 females). All completed the study. The two formulations of ticagrelor were considered bioequivalent if a 90% confidence interval (CI) fell within 80.00–125.00% for Cmax and AUC0-t. Tolerability and safety were assessed throughout the study. Results: The pharmacokinetic (PK) parameters were similar between the test product (T) Clenosan® and reference product (R) Brilinta® under fasting conditions (90% CI for all PK parameters fell within 80.00–125.00%). The 90% CI of the test/reference ratios of log-transformed PK parameter point estimates were Cmax: 95.49% (87.99– 103.62%) and AUC0-t: 103.20% (97.52–109.21%), respectively. Conclusion: Our results demonstrated BE between the test and reference drug products of oral ticagrelor in healthy subjects under fasting conditions.

Adaptive suboptimal control of some discrete-time plants with nonstochastic bounded disturbances

This paper deals with the adaptive suboptimal control of linear, discrete-time, time-invariant, minimum phase, scalar plants in the presence of nonstochastic bounded unmeasurable disturbances whose upper and lower bounds, which may be asymmetric, are assumed to be unknown a priori. Additional assumption is that an order of the difference equation describing the plant is known a priori. The distinguishing feature of the problem stated in this paper is that neither bounds on the unmeasured disturbances, nor bounds on an allowable region to which the unknown plant parameters belong are assumed to be known a priori. To solve this problem, adaptation procedures for the point and membership set estimation are utilized. The standard recursive procedure with adjustable dead zone is employed in order to derive the point estimates of unknown plant parameters together with the point estimate of time-invariant disturbance component. The size of this dead zone depends on the previous point estimate of the bounds on the time-varying disturbance component and also on a fixed suboptimality index chosen by the designer. The estimates generated by the point estimation procedure are directly exploited to derive the adaptive control law. The main idea advanced in this paper is that, instead of unknown a priori membership set of these parameters, their peculiar hypothetical a posteriori membership sets are designed via the use of the measured system’s signals together with the current point estimate of bounds on the time-varying disturbance component. Contrary to the usual membership set estimation approach, this set is updated if only it is discovered that the unknown parameter vector does not belong in reality to this set. To this end, a remarkable property of the point estimation procedure is utilized. Such an approach makes it possible to reconstruct this set and to update the previous estimate of the bounds on the time-varying disturbance component. The finite convergence of the adaptation procedures and also the ultimate boundedness of system’s signals are established. To demonstrate an efficiency of the adaptive controller and support the theoretical study, simulation results are presented.

Non-informative Bayesian estimation in dispersion models

The estimation of parameters for a distribution function is a significant and prominent field within statistical inference. This particular problem holds great relevance in various domains, including industries, stock markets, image processing, and reliability studies. There are two recognized approaches to estimation: point estimation and interval estimation, also known as confidence intervals. In this study, our primary focus lies in the point estimation of parameters associated with an exponential dispersion distribution function. In this process, we consider one of the parameters as a random variable that requires estimation. To tackle this, we adopt a Bayesian inference approach utilizing a one-parameter dispersion distribution. We explore non-informative priors, such as uniform and Jeffrey's priors, and provide evidence of the effectiveness of our method through simulation studies.

Based Copula Reliability Estimation with Stress-Strength Model for Bivariate Stress under Progressive Type II Censoring

This study investigates the dependence between stress and component strength in a stress–strength model with bivariate stresses by incorporating a specialized Archimedean copula, specifically the 3-dimensional Clayton copula. Diverging from prior research, we consider a scenario where two stresses simultaneously influence the component strength, enhancing the realism of our model. Initially, dependent parameter estimates were obtained through moment estimation. Subsequently, maximum likelihood estimation and Bayesian estimation were employed to acquire point and interval estimates for the model parameters. Finally, numerical simulations and real-world data analysis were conducted to validate the accuracy and practicality of our proposed model. This research establishes a foundation for further exploration of general dependence structures and multi-component stress–strength correlation issues.

Statistical inference of the Birnbaum-Saunders model using adaptive progressively hybrid censored data and its applications

<abstract><p>Lately, the Birnbaum-Saunders distribution has gained a lot of attention, mainly due to its different density shapes and the non-monotonicity property of its failure rates. This work considered some estimation issues for the Birnbaum-Saunders distribution using adaptive progressive Type-Ⅱ hybrid censoring. Point and interval estimations were performed employing both conventional and Bayesian methodologies. In addition to estimating the model parameters, we obtained point and interval estimates for the reliability and hazard rate functions. We looked at the method of maximum likelihood as a classical approach, and its asymptotic traits were employed to obtain approximate confidence ranges. From a Bayesian point of perspective, we considered the squared error loss function to obtain the point estimates of the various parameters. The Bayes and highest posterior density credible intervals were additionally determined. For the complex form of the posterior distribution, Bayes estimates and credible intervals were computed by sampling from the posterior distribution through the Markov chain Monte Carlo procedure. For assessing the performance of all of these estimators, a Monte Carlo simulation was employed. Several statistical standards were applied to check the effectiveness of various estimates for multiple levels of censoring with small, moderate, and large sample sizes. Finally, two scenarios for applications were given in order to highlight the usefulness of the supplied approaches.</p></abstract>

Extrapolating Metal (Cu, Ni, Zn) Toxicity from Individuals to Populations Across Daphnia Species Using Mechanistic Models: The Roles of Uncertainty Propagation and Combined Physiological Modes of Action.

Mechanistic effect modeling is a promising tool to improve the ecological realism of environmental risk assessment. An open question for the mechanistic modeling of metal toxicity is whether the same physiological mode of action (PMoA) could be assumed for closely related species. The implications of various modeling choices, such as the use of parameter point estimates and assumption of simplistic toxicodynamic models, are largely unexplored. We conducted life-table experiments with Daphnia longispina, Daphnia magna, and Daphnia pulex exposed to the single metals Cu, Ni, and Zn, and calibrated toxicokinetic-toxicodynamic (TKTD) models based on dynamic energy budget theory. We developed TKTD models with single and combined PMoAs to compare their goodness-of-fit and predicted population-level sensitivity. We identified the PMoA reproduction efficiency as most probable in all species for Ni and Zn, but not for Cu, and found that combined-PMoA models predicted higher population-level sensitivity than single-PMoA models, which was related to the predicted individual-level sensitivity, rather than to mechanistic differences between models. Using point estimates of parameters, instead of sampling from the probability distributions of parameters, could also lead to differences in the predicted population-level sensitivity. According to model predictions, apical chronic endpoints (cumulative reproduction, survival) are conservative for single-metal population effects across metals and species. We conclude that the assumption of an identical PMoA for different species of Daphnia could be justified for Ni and Zn, but not for Cu. Single-PMoA models are more appropriate than combined-PMoA models from a model selection perspective, but propagation of the associated uncertainty should be considered. More accurate predictions of effects at low concentrations may nevertheless motivate the use of combined-PMoA models. Environ Toxicol Chem 2024;43:338-358. © 2023 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Statistical inference for the step-stress model with competing risks from the Kumaraswamy distribution under progressive type-II censoring

In reliability and life analysis, the accelerated life test is frequently used because it can reduce cost and obtain additional reliability and lifetime information. In addition, when a unit fails in a life test, there are often two or more risk factors related to the cause of the failure. In this article, we consider the inference from a step-stress-accelerated life test with competing risks using progressive type-II censored data. Based on the assumption that the parameters affected by stress follow a log-linear model with the stress level, the proportional hazard model with the Kumaraswamy distribution is established. The point estimation of the unknown parameters is derived using maximum likelihood and Bayesian methods. Accordingly, the logarithmic asymptotic confidence and the highest posterior density credible intervals are derived and constructed. Moreover, the algorithm for multi-parameter sampling and simulation technology based on this model is given. Simulation results show that the proposed methods have good performance. In light of the estimates of the parameters, the estimated reliability function under normal conditions can be expressed, and its images under different methods are drawn. Last, a real dataset and a set of simulated data are presented for illustrative purposes.

Exact confidence intervals for population growth rate, longevity and generation time

By quantifying key life history parameters in populations, such as growth rate, longevity, and generation time, researchers and administrators can obtain valuable insights into its dynamics. Although point estimates of demographic parameters have been available since the inception of demography as a scientific discipline, the construction of confidence intervals has typically relied on approximations through series expansions or computationally intensive techniques. This study introduces the first mathematical expression for calculating confidence intervals for the aforementioned life history traits when individuals are unidentifiable and data are presented as a life table. The key finding is the accurate estimation of the confidence interval for r, the instantaneous growth rate, which is tested using Monte Carlo simulations with four arbitrary discrete distributions. In comparison to the bootstrap method, the proposed interval construction method proves more efficient, particularly for experiments with a total offspring size below 400. We discuss handling cases where data are organized in extended life tables or as a matrix of vital rates. We have developed and provided accompanying code to facilitate these computations.

The predictability of daily rainfall during rainy season over East Asia by a Bayesian nonhomogeneous hidden Markov model

AbstractPrecipitation plays a significant role in human society and the environment, and how large‐scale climatic features influence precipitation has obtained worldwide attention. The nonhomogeneous hidden Markov model (NHMM) is a typical method to downscale large‐scale climatic elements to the regional level for many hydrologic applications. The traditional NHMM using point estimates of parameters has the risk to have no solutions for parameter estimation, but the Bayesian‐NHMM provides a Bayesian method to estimate parameters and avoids the risk. In this study, the suitability of the Bayesian‐NHMM in East Asia is evaluated. Two typical regions (i.e., the Yangtze River basin and the Zhujiang River basin in China) dominated by different climates were chosen to check model performance. Results show that: (1) the model could divide rainy‐season precipitation into several hidden states, whose variation is correspondent to the variability of monsoon and flux moisture transportation; (2) the model captures seasonality and inter‐annual variation of precipitation amount and also wet days during rainy season well in both river basins. These results suggest that the model could improve the prediction of daily precipitation in East Asia, which in turn could help many regions with similar climatic conditions worldwide to supervise floods and droughts.

Inference and optimal design of accelerated life test using the geometric process for power rayleigh distribution under time-censored data

In this paper, a new extension of the standard Rayleigh distribution called the Power Rayleigh distribution (PRD) is investigated for the accelerated life test (ALT) using the geometric process (GP) under Type-I censored data. Point estimates of the formulated model parameters are obtained via the likelihood estimation approach. In addition, interval estimates are obtained based on the asymptotic normality of the derived estimators. To evaluate the performance of the obtained estimates, a simulation study of 4, 5 and 6 levels of stress is conducted for ALT in different combinations of sample sizes and censored times. Simulation results indicated that point estimates are very close to their initial true values, have small relative errors, are robust and are efficient for estimating the model parameters. Similarly, the interval estimates have small lengths and their coverage probabilities are almost converging to their 95% nominated significance level. The estimation procedure is also improved by the approach of finding optimum values of the acceleration factor to have optimum values for the reliability function at the specified design stress level. This work confirms that PRD has the superiority to model the lifetimes in ALT using GP under any censoring scheme and can be effectively used in reliability and survival analysis.

Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution

Monitoring life-testing trials for a product or substance often demands significant time and effort. To expedite this process, sometimes units are subjected to more severe conditions in what is known as accelerated life tests. This paper is dedicated to addressing the challenge of estimating the power hazard distribution, both in terms of point and interval estimations, during constant- stress partially accelerated life tests using progressive first failure censored samples. Three techniques are employed for this purpose: maximum likelihood, two parametric bootstraps, and Bayesian methods. These techniques yield point estimates for unknown parameters and the acceleration factor. Additionally, we construct approximate confidence intervals and highest posterior density credible intervals for both the parameters and acceleration factor. The former relies on the asymptotic distribution of maximum likelihood estimators, while the latter employs the Markov chain Monte Carlo technique and focuses on the squared error loss function. To assess the effectiveness of these estimation methods and compare the performance of their respective confidence intervals, a simulation study is conducted. Finally, we validate these inference techniques using real-life engineering data.

Bayesian Analysis for Dependent Progressively Censored Weibull Competing Risks Using Copulas

In many reliability studies, the experimental units may fail due to one of several causes of failure. It is usually assumed that the competing risks of failure are independent. In many practical situations, however, the interpretation of the failure modes makes the assumption of independence unreasonable. Copulas are considered an effective tool for modeling the dependence structure among the multiple competing risks. This paper presents Bayesian analysis of progressively Type-II censored dependent competing risks data using copulas. The analysis is performed under the assumption of binomial progressive random removals and Weibull failure times, where unit failure occurs due to only one of the competing risks. Bayesian point and interval estimates of the unknown parameters are derived using different Archimedean copulas with non-conjugate prior distributions. A simulation study is carried out to assess the performance of the proposed techniques under different dependence structures. A real data set is analyzed for illustrative purposes.

Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data

The present study focuses on estimating the stress–strength parameter when the parent distribution is the alpha power exponential model and the available data are progressively Type-II censored. As a starting point, the usual maximum likelihood approach is applied to obtain point and interval estimates of the model parameters, as well as the stress–strength parameter. Another competing strategy employed in this paper is the maximum product of spacing method, which may be thought of as a rival to the maximum likelihood method. The product of spacing approach is used to obtain point and interval estimates for the various parameters. The asymptotic properties of both methods are used to obtain interval estimates of the model parameter and the stress–strength parameter, and the variance of the stress–strength parameter is approximated using the well-known delta method. Two parametric bootstrap confidence intervals are provided based on the suggested classical estimation procedures. A simulation study is also used to assess the performance of various point and interval estimations. For illustrative purposes, the proposed methods are applied to two real data sets, one for the kidney patients’ recurrence times to infection and the other for breaking the strength of jute fibers.

Analysis of generalized inverted exponential competing risks model in presence of partially observed failure modes

In reliability engineering or medical studies, failure of units or individuals may occurring due to several failure modes which is known by competing risks model. In this paper, we have adopted a competing risks model under consideration that, the failure time has generalized inverted exponential distribution (GIED) and the failure modes are independent and partially observed. Under type-II progressive censoring scheme (type-II PCS), the experiment is designed as a quite popular scheme for collecting data specially, for a highly reliable product. The point estimates of the model parameters are formulated under classical approach (maximum likelihood and bootstrap) and Bayesian approach with respect to the symmetric squared error loss function. Also, the approximate confidence intervals under a large sample theory, bootstrap technique’s and Markov chain Monte Carlo method (MCMC) are constructed. The estimators are assessed and compared with building the simulation study. Analysis a set of type-II PCS competing risks mortality data for illustration purpose.

Analysis of WE Parameters of Life Using Adaptive-Progressively Type-II Hybrid Censored Mechanical Equipment Data

A new two-parameter weighted-exponential (WE) distribution, as a beneficial competitor model to other lifetime distributions, namely: generalized exponential, gamma, and Weibull distributions, is studied in the presence of adaptive progressive Type-II hybrid data. Thus, based on different frequentist and Bayesian estimation methods, we study the inferential problem of the WE parameters as well as related reliability indices, including survival and failure functions. In frequentist setups, besides the standard likelihood-based estimation, the product of spacing (PS) approach is also taken into account for estimating all unknown parameters of life. Making use of the delta method and the observed Fisher information of the frequentist estimators, approximated asymptotic confidence intervals for all unknown parameters are acquired. In Bayes methodology, from the squared-error loss with independent gamma density priors, the point and interval estimates of the unknown parameters are offered using both joint likelihood and the product of spacings functions. Because a closed solution to the Bayes estimators is not accessible, the Metropolis–Hastings sampler is presented to approximate the Bayes estimates and also to create their associated highest interval posterior density estimates. To figure out the effectiveness of the developed approaches, extensive Monte Carlo experiments are implemented. To highlight the applicability of the offered methodologies in practice, one real-life data set consisting of 30 failure times of repairable mechanical equipment is analyzed. This application demonstrated that the offered WE model provides a better fit compared to the other eight lifetime models.

Production Facilities Safety Assessment According to the Maximum Values of Machines Reliability

Introduction. At the stage of designing technical devices and performing appropriate strength calculations of metal structures, sufficiently large reserves of strength are taken, which, theoretically, exclude any failures of parts. In fact, the machines work with frequent failures. Of interest are undiagnosed failures that lead to a critical decrease in safety, especially at hazardous production facilities. It is assumed that the previously applied approaches of selective determination of the maximum (minimum) reliability value, based on point estimates of the distribution parameters of the two-parameter Weibull law, lead to an overestimation of the calculated indicators of the probability of failure-free operation, i.e. underestimation of risk. Therefore, the work objective is to consider an approach to assessing the risk of operating production facilities in a situation of accidental occurrence of dangerous and undiagnosed failures in systems.Materials and Methods. Methods for technical devices safety assessment based on probability theory were used in the work, and the probability of machine failure was determined based on the well-known method of reliability theory. This method consists in calculating and constructing distribution functions of random variables (load-bearing capacity and loading) that influence the occurrence of failure. The level of increase in the reliability index was determined, leading to frequent unpredictable failures of technical devices (machines) and a decrease in the safety of their operation.Results. The signs of inconsistency of strength calculations based on overestimated safety margins, which in theory exclude failures of parts and machines in general, are identified and substantiated. A new approach to risk assessment of operating production facilities in a situation of accidental occurrence of dangerous and undiagnosed failures by safety systems has been developed and implemented. An algorithm for determining the three parameters of Weibull's law for a population based on sample data has been developed. The resource distribution densities of the boom of the single-bucket excavator EK-14 are constructed. The recommendations are given to increase the probability of failure-free operation to 0.9989.Discussion and Conclusion. The results of the conducted research allow us to substantiate a new approach to risk assessment of operating production facilities in the event of dangerous and undiagnosed failures of basic parts by safety systems, leading to negative consequences.

Classical and Bayesian Inference for the Kavya–Manoharan Generalized Exponential Distribution under Generalized Progressively Hybrid Censored Data

This manuscript focuses on the statistical inference of the Kavya–Manoharan generalized exponential distribution under the generalized type-I progressive hybrid censoring sample (GTI-PHCS). Different classical approaches of estimation, such as maximum likelihood, the maximum product of spacing, least squares (LS), weighted LS, and percentiles under GTI-PHCS, are investigated. Based on the squared error and linear exponential loss functions, the Bayes estimates for the unknown parameters utilizing separate gamma priors under GTI-PHCS have been derived. Point and interval estimates of unknown parameters are developed. We carry out a simulation using the Monte Carlo algorithm to show the performance of the inferential procedures. Finally, real-world data collection is examined for illustration purposes.

Statistical Inference on the Entropy Measures of Gamma Distribution under Progressive Censoring: EM and MCMC Algorithms

Studying the ages of mobile phones is considered one of the most important things in the recent period in the field of shopping and modern technology. In this paper, we will consider that the ages of these phones follow a gamma distribution under progressive first-failure (PFF) censoring. All of the unknown parameters, as well as Shannon and Rényi entropies, were estimated for this distribution. The maximum likelihood (ML) approach was utilized to generate point estimates for the target parameters based on the considered censoring strategy. The asymptotic confidence intervals of the ML estimators (MLEs) of the targeted parameters were produced using the normal approximation to ML and log-transformed ML. We employed the delta method to approximate the variances of the Shannon and Rényi functions to obtain their asymptotic confidence intervals. Additionally, all parameter estimates utilized in this study were determined using the successful expectation–maximization (EM) method. The Metropolis–Hastings (MH) algorithm was applied to construct the Bayes estimators and related highest posterior density (HPD) credible intervals under various loss functions. Further, the proposed methodologies were contrasted using Monte Carlo simulations. Finally, the radio transceiver dataset was analyzed to substantiate our results.