This paper addresses the problem of estimating unknown parameters of the inverted exponentiated Rayleigh distribution within the context of accelerated life testing. We consider lifetime data observed through step-stress and type-I hybrid censoring, and incorporate the cumulative exposure model assumptions to establish connections between the distribution at various stress levels. We then write the associated likelihood function based on the observed data and derive maximum likelihood estimators for the distribution's unknown parameters. Furthermore, employing a Bayesian approach, we initially adopt gamma priors and compute posterior distributions for the parameters. These posterior distributions are then utilized to calculate Bayesian estimates using the squared error loss function. To assess the performance of maximum likelihood and Bayesian estimates, we conduct a simulation study under various scenarios, considering both non-informative and informative priors. We also evaluate interval estimates and coverage percentages under both classical and Bayesian approaches. Finally, for illustrative purposes, we analyze two real data sets, demonstrating the practical application of our proposed methodology.

ABSTRACTIn this paper, we consider the problem of estimating the unknown parameters of a generalized half‐normal (GHN) distribution when lifetime data are observed from accelerated life test (ALT) experiments in the presence of hybrid censoring. To relate the lifetime of products under different stress levels, we make use of a cumulative exposure model (CEM), and obtain maximum likelihood estimates using a numerical approach and stochastic expectation–maximization (SEM) algorithm. We further obtain the expected Fisher information matrix, and use it to compute associated confidence interval estimates for the unknown parameters of the distribution. The expected Fisher information matrix is also used to select the optimal time to conduct an experiment based on three considered optimality criteria. Next, we consider independent and conditional gamma priors and obtain the associated posterior distributions for the unknown parameters. We then make use of samples generated from the posterior distributions using importance sampling and the MH algorithm to compute the Bayesian estimates under the squared error loss function. Furthermore, the highest associated posterior density interval estimates are also computed. Finally, we conduct a simulation study to evaluate the efficiency of the suggested approaches in various situations and analyze a real data set for illustration purposes.

Accelerated life test experiments are valuable for studying highly reliable units, as they aim to quickly generate failure lifetime data for statistical analysis. The complexity of statistical analysis for accelerated failure lifetime data increases when the data are observed under censoring schemes. In this paper, we consider the Birnbaum-Saunders distribution under step-stress accelerated life testing when data are observed with hybrid censoring. We first obtain maximum likelihood estimates and their corresponding interval estimates, assuming that lifetimes follow the cumulative exposure model across various stress levels. Additionally, we calculate Bayesian estimates and their associated highest posterior density interval estimates under a squared error loss function. Finally, we conduct a simulation study to evaluate the effectiveness of the proposed methods across various scenarios and illustrate their application using two real datasets.

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni-modal hazard rates. In this paper, we address the problem of discriminating among these statistical distributions to consider a more appropriate lifetime model. We first consider the complete samples and make use of the maximized log-likelihood approach for choosing the correct model. We also obtain the expressions for logarithmic of defined test statistics, and associated asymptotic distributions. We then extend our discussion based on the observed sample in the presence of some censoring. We perform a simulation study in both cases to compare the probabilities of correct selection. Furthermore, for a given probability of correct selection and user-specified protection level, we present a discussion to determine the minimum sample size required to discriminate among the three lifetime models. Finally, two real data sets are analyzed to illustrate the proposed methodology. In our findings, we observed that model parameters and methods of estimating unknown parameters play very important roles in the discrimination process, and sample size and the proportion of censoring become key factors to ensure a high probability of selecting a correct model.

The log-normal and the log-logistic distributions are two of the most commonly used distributions for studying positively skewed lifetime data. Both the distributions share number of interesting properties, and for a certain range of parameters their cumulative and hazard functions can also be similar in nature. However, selecting a more appropriate distribution and discriminating among them for a given data to best fit is an important issue. Further, when the data are observed in the presence of some censoring scheme the problem becomes more challenging. In this paper, we address the problem of selecting a more appropriate distribution by discriminating based on the random samples drawn in the presence of type-II censoring. We consider the difference of the maximized log-likelihood functions, and compute the asymptotic distribution of the discrimination statistic. We further propose a modified discriminating approach, and compute the probabilities of correct selection to check the performance of the discrimination procedure. Finally, simulation study is conducted, and two real data sets are analysed for the illustration purpose.

Accelerated life test experiments aim to generate lifetime data in a short time for the further statistical analysis, and are very useful when the units under experiment are highly reliable. Statistical analysis for lifetime data observed from accelerating life testing in presence of some censoring becomes a challenging task. In this paper, we consider lognormal distribution under a simple step-stress model in the presence of hybrid censoring. We assume that the lifetimes follow the cumulative exposure model, and first obtain maximum likelihood estimates and their associated interval estimates using various methods. We then compute Bayes estimates and associated highest posterior interval estimates under squared error loss function. To observe the effectiveness of the proposed methods under the different situations, we conduct a simulation study.

This paper considers the problems of estimation and prediction when lifetime data following Poisson-exponential distribution are observed under type-I hybrid censoring. For both the problems, we compute point and associated interval estimates under classical and Bayesian approaches. For point estimates in the problem of estimation, we compute maximum likelihood estimates using Newton-Raphson, Expectation-Maximization and Stochastic Expectation-Maximization algorithms under classical approach, and under Bayesian approach we compute Bayes estimates with the help of Lindley and importance sampling technique under informative and non-informative priors using symmetric and asymmetric loss functions. The associated interval estimates are obtained using the Fisher information matrix and Chen and Shao method respectively under classical and Bayesian approaches. Further, the predictive point estimates and associated predictive interval estimates are computed by making use of best unbiased and conditional median predictors under classical approach, and Bayesian predictive and associated Bayesian predictive interval estimates in the problem of prediction. We analysis real data set, and conduct Monte Carlo simulation study for the comparison of various proposed methods of estimation and prediction. Finally, a conclusion is given.

Natural language processing (NLP) has recently gained much attention for representing and analyzing human language computationally. It has spread its applications in various fields such as machine translation, email spam detection, information extraction, summarization, medical, and question answering etc. In this paper, we first distinguish four phases by discussing different levels of NLP and components of Natural Language Generation followed by presenting the history and evolution of NLP. We then discuss in detail the state of the art presenting the various applications of NLP, current trends, and challenges. Finally, we present a discussion on some available datasets, models, and evaluation metrics in NLP.

In this paper, we consider the problems of Bayesian estimation and prediction for lognormal distribution under progressive Type-II censored data. We propose various non-informative and informative priors for the unknown lognormal parameters and compute the Bayes estimates under squared error loss function. Importance sampling technique and OpenBUGS are taken into consideration for the computational purpose. Further, we predict lifetimes of both censored and future samples under one- and two-sample prediction frameworks. We also compute the corresponding Bayes predictive bounds. A simulation study is conducted to compare the performance of proposed estimates and a real data set is analyzed to illustrate applications of this study. Finally, a conclusion is presented.

This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.

SYNOPTIC ABSTRACT This article deals with problems of estimation and prediction under classical and Bayesian approaches when lifetime data following a lognormal distribution are observed under type-I progressive hybrid censoring. We first obtain maximum likelihood estimates, Bayes estimates, and corresponding interval estimates of unknown lognormal parameters. We then develop predictors to predict censored observations and construct prediction intervals. Further, we analyze two real data sets and conduct a simulation study to compare the performance of proposed methods of estimation and prediction. Finally, optimal censoring schemes are constructed under cost constraints and a conclusion is presented.

In this article, we consider the problem of estimation and prediction on unknown parameters of a Lomax distribution when the lifetime data are observed in the presence of progressively type-I hybrid censoring scheme. In the classical scenario, the Expectation–Maximization (EM) algorithm is utilized to derive the maximum likelihood estimates (MLEs) for the unknown parameters and associated confidence intervals. Under the Bayesian framework, the point estimates of unknown parameters with respect to different symmetric, asymmetric and balanced loss functions are obtained using Tierney–Kadane’s approximation and Markov Chain Monte Carlo (MCMC) technique. Also, the highest posterior density (HPD) credible intervals for the parameters are reckoned using importance sampling procedure. Simulation experiments are performed to compare the different proposed methods. Further, the predictive estimates of censored observations and the corresponding prediction intervals are also provided. One real-life data example is presented to illustrate the derived results.

In this paper, we consider the problem of estimating unknown parameters of an inverse Weibull distribution when it is known that samples are progressive type-I interval censored. We propose an EM algorithm to obtain maximum likelihood estimates and mid point estimates. For comparison purpose Bayes estimates are also obtained under the square error loss function. A simulation study is conducted to access the performance of the proposed estimators and recommendations are made on the basis of simulation results. A real data set is also analyzed in detail for an illustration purpose. Finally, by making use of expected Fisher information matrix various inspection times and optimal censoring schemes are obtained.

SYNOPTIC ABSTRACT This article addresses the problems of estimation and prediction when the lifetime data following Poisson-Exponential distribution are observed under type-II censoring. We obtain maximum likelihood estimates and associated interval estimates under a classical approach, and Bayes estimates using various loss functions and associated highest posterior density interval estimates. Maximum likelihood estimates are obtained using the Newton-Raphson method and Expectation Maximization (EM) algorithm, and Bayes estimates are computed using importance sampling and Lindley approximation. We also compute shrinkage preliminary test estimates based on maximum likelihood and Bayes estimates. Further, we provide inference on the censored observations by making use of best unbiased and condition median predictors under a classical approach, and predictive estimates under the Bayesian paradigm using importance sampling. The associated predictive interval estimates are also obtained using different methods. Finally, we conduct a simulation study to compare the performance of all the proposed methods of estimation and prediction, and analyze a real data set for illustration purpose.

In today's world of computers, any kind of information can be made available within few clicks for different endeavors. The information may be tampered by changing the statistical properties and can be further used for criminal activities. These days, Cyber crimes are happening at a very large scale, and possess big threats to the security of an individual, firm, industry and even to developed countries. To combat such crimes, law enforcement agencies and investment institutions are incorporating supportive examination policies, procedures and protocols to address the complete investigation process. The paper entails a detailed review of several cyber crimes followed by various digital forensics processes involved in the cyber crime investigation. Further various digital forensics tools with detail explanation are discussed with their advantages, disadvantages, challenges, and drawbacks. A comparison among all the selected tools is also presented. Finally the paper recommends the need of training programs for the first res ponder and judgement of signature based image authentication.

This paper deals with the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian approaches when samples are observed under progressive type-I interval censoring. Under classical approach we employ the stochastic expectation maximization algorithm to obtain maximum likelihood estimators for the unknown parameters and also compute associated interval estimates. Further under Bayesian approach we obtain Bayes estimators with respect to different symmetric, asymmetric and balanced loss functions. In this regard we use Tierney-Kadane and Metropolis-Hastings (MH) algorithm. For illustration purpose we analyse a real data set and conduct a Monte Carlo simulation study to observe the performance of the proposed estimators. Finally we present a discussion on inspection times and optimal censoring.

In this paper we consider the problems of estimation and prediction when observed data from a lognormal distribution are based on lower record values and lower record values with inter-record times. We compute maximum likelihood estimates and asymptotic confidence intervals for model parameters. We also obtain Bayes estimates and the highest posterior density (HPD) intervals using noninformative and informative priors under square error and LINEX loss functions. Furthermore, for the problem of Bayesian prediction under one-sample and two-sample framework, we obtain predictive estimates and the associated predictive equal-tail and HPD intervals. Finally for illustration purpose a real data set is analyzed and simulation study is conducted to compare the methods of estimation and prediction.

This paper addresses the problem of double and group acceptance sampling plans for an inverse Weibull distribution based on truncated life test. We consider quality parameter of the test units based on median lifetime and obtain the design parameters such as sample size and acceptance number. These plans are obtained under the consumer’s risk and the producer’s risk simultaneously involved at a certain confidence level. We present a simulation study to support the proposed methods and a comparison between single and double acceptance sampling plans is made. A real data set is also analyzed to illustrate the implementation of the proposed sampling plans. Further, the situation under which the proposed samplings plans can also be used for other percentiles points is discussed. Finally a conclusion is presented.

Objectives: This paper presents an up-to-date overview of research performed in the Virtual Reality (VR) environment ranging from definitions, its presence in the various fields, and existing market players and their projects in the VR technology. Further an attempt is made to gain an insight on the psychological mechanism underlying experience in using VR device. Methods: Our literature survey is based on the research articles, analysis of the projects of various companies and their findings for different areas of interest. Findings: In our literature survey we observed that the recent advances in virtual reality enabling technologies have led to variety of virtual devices that facilitate people to interact with the digital world. In fact in the past two decades researchers have tried to integrate reality and VR in the form of intuitive computer interface. Improvements: This has led to variety of potential benefits of VR in many applications such as News, Healthcare, Entertainment, Tourism, Military and Defence etc. However despite the extensive research efforts in creating virtual system environments it is yet to become apparent in normal daily life.