Annals of Data Science最新文献

In this study, a competing risk model was developed under a generalized progressive hybrid censoring scheme using a generalized inverted exponential distribution. The latent causes of failure were presumed to be independent. Estimating the unknown parameters is performed using maximum likelihood (ML) and Bayesian methods. Using the Markov chain Monte Carlo technique, Bayesian estimators were obtained under gamma priors with various loss functions. ML estimate was used to create confidence intervals (CIs). In addition, we present two bootstrap CIs for the unknown parameters. Further, credible CIs and the highest posterior density intervals were constructed based on the conditional posterior distribution. Monte Carlo simulation is used to examine the performance of different estimates. Applications to real data were used to check the estimates and compare the proposed model with alternative distributions.

Epidemiology, the aspect of research focusing on disease modelling is date intensive. Research epidemiologists in different research groups played a key role in developing different data driven model for COVID-19 and monkeypox. The requirement of accessing highly accurate data useful for disease modelling is beneficial but not without having challenges. Currently, the task of data acquisition is executed by select individuals in different research groups. This approach experiences the drawbacks associated with getting permission to access the desired data and inflexibility to change data acquisition goals due to dynamic epidemiological research objectives. The presented research addresses these challenges and proposes the design and use of dynamic intelligent crawlers for acquiring epidemiological data related to a given goal. In addition, the research aims to quantify how the use of computing entities enhances the process of data acquisition in epidemiological related studies. This is done by formulating and investigating the metrics of the data acquisition efficiency and the data analytics efficiency. The use of human assisted crawlers in the global information networks is found to enhance data acquisition efficiency (DAqE) and data analytics efficiency (DAnE). The use of human assisted crawlers in a hybrid configuration outperforms the case where manual research group member efforts are expended enhancing the DAqE and DAnE by up to 35% and 99% on average, respectively.

The stress–strength model is a basic tool used in evaluating the reliability ( R = P(Y < X)). We consider an expression for R where the random variables X and Y denote strength and stress, respectively. The system fails only if the stress exceeds the strength. We aim to study the effect of the dependency between X and Y on R. We assume that X and Y follow Weibull distributions and their dependency is modeled by a copula with the dependency parameter ( theta ). We compute R for Farlie–Gumbel–Morgenstern (FGM), Ali–Mikhail–Haq (AMH), Gumbel’s bivariate exponential copulas, and for Gumbel–Hougaard (GH) copula using a Monte-Carlo integration technique. We plot the graph of R versus (theta ) to study the effect of dependency on R. We estimate R by plugging in the estimates of the marginal parameters and of ( theta ) in its expression. The estimates of the marginal parameters are based on the marginal likelihood. The estimates of (theta ) are obtained from two different methods; one is based on the conditional likelihood and the other is based on the method of moments using Blomqvist’s beta. Asymptotic distribution of both the estimators of R is obtained. Finally, analysis of real data set is also performed for illustrative purposes.

This paper presents a study on a new family of distributions using the Weibull distribution and termed as Modi-Weibull distribution. This Modi-Weibull distribution is based on four parameters. To understand the behaviour of the distribution, some statistical characteristics have been derived, such as shapes of density and distribution function, hazard function, survival function, median, moments, order statistics etc. These parameters are estimated using classical maximum likelihood estimation method. Asymptotic confidence intervals for parameters of Modi-Weibull distribution are also obtained. A simulation study is carried out to investigate the bias, MSE of proposed maximum likelihood estimators along with coverage probability and average width of confidence intervals of parameters. Two applications to real data sets are discussed to illustrate the fitting of the proposed distribution and compared with some well-known distributions.

Logistic distribution (LogDis) is frequently used in many different applications, such as logistic regression, logit models, classification, neural networks, physical sciences, sports modeling, finance and health and disease studies. For instance, the distribution function of the LogDis has the same functional form as the derivative of the Fermi function that can be used to set the relative weight of various electron energies in their contributions to electron transport. The LogDis has wider tails than a normal distribution (NorDis), so it is more consistent with the underlying data and provides better insight into the likelihood of extreme events. For this reason the United States Chess Federation has switched its formula for calculating chess ratings from the NorDis to the LogDis. The outcomes of many real-life experiments are sequences of record-breaking data sets, where only observations that exceed (or only those that fall below) the current extreme value are recorded. The practice demonstrated that the widely used estimators of the scale and location parameters of logistic record values, such as the best linear unbiased estimators (BLUEs), have some defects. This paper investigates the shrinkage estimators of the location and scale parameters for logistic record values using prior information about their BLUEs. Theoretical and computational justifications for the accuracy and precision of the proposed shrinkage estimators are investigated via their bias and mean square error (MSE), which provide sufficient conditions for improving the proposed shrinkage estimators to get unbiased estimators with minimum MSE. The performance of the proposed shrinkage estimators is compared with the performances of the BLUEs. The results demonstrate that the resulting shrinkage estimators are shown to be remarkably efficient.

Classification is a fundamental problem in statistics and data science, and it has garnered significant interest from researchers. This research proposes a new classification algorithm that builds upon two key improvements of the Bayesian method. First, we introduce a method to determine the prior probabilities using fuzzy clustering techniques. The prior probability is determined based on the fuzzy level of the classified element within the groups. Second, we develop the probability density function using Vine Copula. By combining these improvements, we obtain an automatic classification algorithm with several advantages. The proposed algorithm is presented with specific steps and illustrated using numerical examples. Furthermore, it is applied to classify image data, demonstrating its significant potential in various real-world applications. The numerical examples and applications highlight that the proposed algorithm outperforms existing methods, including traditional statistics and machine learning approaches.

The objectives of this study are to propose a new two-parameter lifespan distribution and explain some of the most essential properties of that distribution. Through the course of this investigation, we will be able to achieve both of these objectives. For the aim of assessment, research is carried out that makes use of simulation, and for the same reason, a variety of various approaches are studied and taken into account for the purpose of evaluation. Making use of two separate data collections enables an analysis of the adaptability of the suggested distribution to a number of different contexts. The risk exposure in the context of asymmetric bimodal right-skewed precipitation data was further defined by using five essential risk indicators, such as value-at-risk, tail-value-at-risk, tail variance, tail mean–variance, and mean excess loss function. This was done in order to account for the right-skewed distribution of the data. In order to examine the data, several risk indicators were utilized. These risk indicators were used in order to achieve a more in-depth description of the risk exposure that was being faced.

In data analysis, change point problems correspond to abrupt changes in stochastic mechanisms generating data. The detection of change points is a relevant problem in the analysis and prediction of time series. In this paper, we consider a class of conjugate prior distributions obtained from conditional specification methodology for solving this problem. We illustrate the application of such distributions in Bayesian change point detection analysis with Poisson processes. We obtain the posterior distribution of model parameters using general bivariate distribution with gamma conditionals. Simulation from the posterior are readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

This work concerns the effective personalized prediction of longitudinal biomarker trajectory, motivated by a study of cancer targeted therapy for patients with chronic myeloid leukemia (CML). Continuous monitoring with a confirmed biomarker of residual disease is a key component of CML management for early prediction of disease relapse. However, the longitudinal biomarker measurements have highly heterogeneous trajectories between subjects (patients) with various shapes and patterns. It is believed that the trajectory is clinically related to the development of treatment resistance, but there was limited knowledge about the underlying mechanism. To address the challenge, we propose a novel Bayesian approach to modeling the distribution of subject-specific longitudinal trajectories. It exploits flexible Bayesian learning to accommodate complex changing patterns over time and non-linear covariate effects, and allows for real-time prediction of both in-sample and out-of-sample subjects. The generated information can help make clinical decisions, and consequently enhance the personalized treatment management of precision medicine.

In this article, a reliability test plan under time truncated life test is considered for the logistic Rayleigh distribution ((mathcal {LRD})). A brief discussion over statistical properties and significance of the (mathcal {LRD}) is placed in this present study. Larger the value of median—better is the quality of the lot is considered as quality characteristic for the proposed reliability test plan. Minimum sample sizes are placed in tabular form for different set up of specified consumer’s risk. Also operating characteristics ((mathcal{O}mathcal{C})) values are shown in tabular forms for the chosen set up and discussed the pattern of (mathcal{O}mathcal{C}) values. A comparative analysis of the present study with some other reliability test plans is discussed based on the sample sizes. As an illustration, the performance of the proposed plan for the (mathcal {LRD}) is shown through real-life examples.