In this paper, we propose a simple dynamic model for supply and demand of labor based on domestically trained workforce and internationally trained workers acquired by immigration. The economy of a country may be divided into certain distinct sectors. The state variable of the system model is given by the number of workers in each sector as a function of time. It is clear that over-intake of new immigrants will lead to unemployment, while any shortage of the workforce will lead to economic downturn. We use the dynamic model proposed in this paper to develop an optimal strategy for immigration and workforce management to ensure sustained economic growth and stability. We prove existence of optimal policies subject to workforce availability constraints. Further, we present necessary conditions of optimality whereby one can determine such policies. Simulation results are presented illustrating the concepts.

Empirical likelihood is a nonparametric way of statistical inference which makes use of the effectiveness of nonparametric as well as likelihood approaches. We develop empirical likelihood (EL) and Jackknife empirical likelihood (JEL) ratio tests for decreasing mean residual life (DMRL). The asymptotic properties of empirical and jackknife empirical log likelihood ratio statistics are studied. We have performed a Monte Carlo simulation study to compare the performance of the proposed test. Finally, the proposed method is illustrated through three real data sets.

With changes in the fertility patterns, the earlier developed demographic models fall short in imitating the changes that occur with respect to both time and geographic locations. Models providing a good fit for the classical fertility patterns prove to be inadequate in case of distorted patterns, whereas those useful for distorted data prove to be inefficient and can have poor predictive performance for traditional curves. In this paper, a logistic distribution is taken as a base and new models are proposed for modelling these gradual changes in the age-specific fertility rates. The work consists of differentiating between the pre-modal and the post-modal variability and explores Bayesian techniques to deal with such problems. To show the relevance of the models in current scenario, the real life age-specific fertility rate data of three countries, namely Denmark, India, and Ireland, having different age-specific fertility rate shapes for different years are considered and the posterior samples are generated for further analysis using the Metropolis algorithm. The proposed models are found compatible and satisfactory results are obtained for their respective usages. Finally, the proposed models are compared using some model comparison tools and the best among the proposed models is suggested.

A guaranteed annuity option (GAO) converts an insured’s fund value into a life annuity subject to a guaranteed minimum rate at the policy’s maturity. This type of insurance product is contingent on policyholder’s survival, and it is therefore sensitive to both investment and longevity risks. An adequate quantification of the impact of the underlying variables, including their correlation, in the pricing methodology is necessary to ensure the issuer’s solvency. A pricing framework for GAO that addresses the stochasticity and correlation of these two risks is considered. In comparison to previous approaches of GAO valuation, this proposed method directly evaluates the conditional expectation without resorting to any probability measure changes. We provide an accessible parameter estimation and examination of GAO’s sensitivity to the parameters of the combined models. The accuracy of our estimated parameters is verified and an empirical demonstration making use of actual mortality and financial data are included.

This paper aims to estimate the model parameter of a k-out-of-n load-sharing system under a progressive censoring scheme. In such a system, n identical components with lifetimes following an exponential distribution. The system functions as long as at least k components are operational. When a component fails, its load is redistributed among the surviving components, increasing their failure rates. Such systems are known as load-sharing systems (LSS). We estimate the model parameters under both classical and Bayesian frameworks. In the classical approach, Maximum Likelihood Estimation (MLE) and Maximum Product Spacing (MPS) methods are employed, with asymptotic confidence intervals derived for both. For the Bayesian framework, we use noninformative priors to obtain Bayes estimates and construct the Highest Posterior Density (HPD) intervals. A Monte Carlo simulation study is presented to compare the performance of these estimation methods. Furthermore, real data is used to validate the proposed methodologies, demonstrating the effectiveness of the approaches. The results show that the methods perform well under progressive censoring, providing reliable parameter estimates for load-sharing systems.

This paper extends the quadratic transmuted distribution (QTD) by Shaw and Buckley (2009) to improve flexibility in modeling diverse datasets. By relaxing the parameter constraints of QTD, we introduce the adaptive quadratic transmuted distribution (AQTD), which allows for a wider parameter range, enhancing data fitting. The study examines AQTD’s statistical properties, including parameter estimation and potential applications. We also propose the adaptive quadratic transmuted exponential (AQTE) distribution for exponential-type data and the mixed Poisson AQTE (MPAQTE) model, which combines AQTE with the Poisson distribution for better count data modeling. We assess these models with six datasets and find MPAQTE generally outperforms MPQTE, especially for Belgian claim frequency, random digit errors, and European red mites datasets. MPAQTE also provides the best fit for the Turkish claim frequency dataset, with a chi-square value of 2.6406, outperforming Poisson and Negative Binomial models. AIC and BIC values for MPAQTE and other distributions were similar, with Poisson performing worst. We also propose an adaptive cubic transmuted distribution for future research.

This article considers the Bayes analysis of the Weibull regression model when a number of covariates are involved in the model. Considering appropriate prior distributions for the model parameters and independent Laplace priors for the regression coefficients, the Bayes analysis is performed using the Gibbs sampler algorithm. Both empirical Bayes and hierarchical Bayes approaches are used to deal with the shrinkage parameter involved in the Laplace prior. Since the final objective is variable selection, the article uses Bayesian least absolute selection and shrinkage operator for the same. A comparison of the full model with the reduced model is done using a few important Bayesian tools. Finally, the numerical illustration is provided using both simulated and a real data set of comprehensive Micro-Ribonucleic acid profiling of nasopharyngeal carcinoma specimens. It may be noted that such an analysis might be useful in a variety of fields, including medical research, reliability analysis and several other experiments involving time to event data.

An economic order quantity (EOQ) model for items with an exponential demand rate and a three-parameter Weibull distribution deterioration is presented in this article. The model is developed and analyzed under the assumption of quasi-partial backlogging, meaning that when a product is in low supply, a sizable portion of consumers are ready to wait for it to become available once more. The deterministic exponential demand rate shows an expedited growth in demand. A rising function of time describes the instantaneous rate of deterioration. In order to derive the model, we provide straightforward analytically tractable approaches, and we give a real-world example to show how to solve the problem. Sensitivity analysis is carried out to demonstrate how various model parameters affect the optimal values of the policy variables in the model.

In this paper, we study a class of SEIRI epidemic dynamical models with a general nonlinear incidence rate representing the transfer from susceptible class to infected class. Besides we incorporate a relapse rate and an isolation rate. Throughout the paper, Lyapunov’s stability tools are used to establish the global stability for both disease-free and endemic equilibriums depending on reproduction number value R 0 and isolation rate. Finally, numerical simulations are presented to illustrate and explain our theoretical results.

In this article, the lower k-record values arising from a generalized exponential distribution is considered. The best linear unbiased estimators for the location and scale parameters of generalized exponential distribution are considered with known shape parameter. The marginal best linear unbiased predictor of future lower k-record value and the joint best linear unbiased predictor of a pair of future lower k-record values are derived. Finally, real datasets are considered to compare the efficiencies of the proposed predictors developed here.