Inferences on the Means of Two Log-Normal Distributions: A Computational Approach Test

In this article, we propose a novel approach for testing the equality of two log-normal populations using a computational approach test (CAT) that does not require explicit knowledge of the sampling distribution of the test statistic. Simulation studies demonstrate that the proposed approach can perform hypothesis testing with satisfying actual size even at small sample sizes. Overall, it is superior to other existing methods. Also, a CAT is proposed for testing about reliability of two log-normal populations when the means are the same. Simulations show that the actual size of this new approach is close to nominal level and better than the score test. At the end, the proposed methods are illustrated using two examples.     

A Risk-Based Method for Modeling Traffic Fatalities

We describe a risk-based analytical framework for estimating traffic fatalities that combines the probability of a crash and the probability of fatality in the event of a crash. As an illustrative application, we use the methodology to explore the role of vehicle mix and vehicle prevalence on long-run fatality trends for a range of transportation growth scenarios that may be relevant to developing societies. We assume crash rates between different road users are proportional to their roadway use and estimate case fatality ratios (CFRs) for the different vehicle-vehicle and vehicle-pedestrian combinations. We find that in the absence of road safety interventions, the historical trend of initially rising and then falling fatalities observed in industrialized nations occurred only if motorization was through car ownership. In all other cases studied (scenarios dominated by scooter use, bus use, and mixed use), traffic fatalities rose monotonically. Fatalities per vehicle had a falling trend similar to that observed in historical data from industrialized nations. Regional adaptations of the model validated with local data can be used to evaluate the impacts of transportation planning and safety interventions, such as helmets, seat belts, and enforcement of traffic laws, on traffic fatalities.     

Inferences on the ratio of two generalized variances: independent and correlated cases

Statistical inferences about the dispersion of multivariate population are determined by generalized variance. In this article, we consider constructing a confidence interval and testing the hypotheses about the ratio of two independent generalized variances, and the ratio of two dependent generalized variances in two multivariate normal populations. In the case of independence, we first propose a computational approach and then obtain an approximate approach. In the case of dependence, we give an approach using the concepts of generalized confidence interval and generalized p value. In each case, simulation studies are performed for comparing the methods and we find satisfactory results. Practical examples are given for each approach.     

Semi-doubly optimal concentric circles fitting with presence of heteroscedasticity

Previous studies focus on homogeneous and isotropic assumptions about the noisy data. Many methods have been developed recently for fitting concentric circles to data. In this paper, these statistical assumptions have been relaxed. To the best of our knowledge, only one iterative method has been recently developed. Due to its complexity, no such algorithm is available to compute the reliable maximum likelihood estimator (MLE). Accordingly, we have developed four new methods that outperform the existing methods including the orthogonal distance regression (ODR). We also discuss which of these methods is superior according to the four principles: statistical efficiency, accuracy, robustness, and computational efficiency. Numerical experiments on synthetic and real images have been conducted to validate our findings.     

On the $$L_p$$ norms of kernel regression estimators for incomplete data with applications to classification

We consider kernel methods to construct nonparametric estimators of a regression function based on incomplete data. To tackle the presence of incomplete covariates, we employ Horvitz–Thompson-type inverse weighting techniques, where the weights are the selection probabilities. The unknown selection probabilities are themselves estimated using (1) kernel regression, when the functional form of these probabilities are completely unknown, and (2) the least-squares method, when the selection probabilities belong to a known class of candidate functions. To assess the overall performance of the proposed estimators, we establish exponential upper bounds on the \(L_p\) norms, \(1\le p<\infty \), of our estimators; these bounds immediately yield various strong convergence results. We also apply our results to deal with the important problem of statistical classification with partially observed covariates.     

Optimal acceptance sampling policy considering Bayesian risks

In this paper, we propose a sampling policy considering Bayesian risks. Various definitions of producer's risk and consumer's risk have been made. Bayesian risks for both producer and consumer are proven to give better information to decision-makers than classical definitions of the risks. So considering the Bayesian risk constraints, we seek to find optimal acceptance sampling policy by minimizing total cost, including the cost of rejecting the batch, the cost of inspection, and the cost of defective items detected during the operation. Proper distributions to construct the objective function of the model are specified. In order to demonstrate the application of the proposed model, we illustrate a numerical example. Furthermore, the results of the sensitivity analysis show that lot size, the cost of inspection, and the cost of one defective item are key factors in sampling policies. The acceptable quality level, the lot tolerance proportion defective, and Bayesian risks also affect the sampling policy, but variations of acceptable quality level and producer Bayesian risks, for values more than a specified value, cause no changes in sampling policy.     

Bayesian and Robust Bayesian analysis under a general class of balanced loss functions

For estimating an unknown parameter θ, we introduce and motivate the use of balanced loss functions of the form L_{r, w, d0}(q, d)=wr(d₀, d)+ (1-w) r(q, d){L_{\rho, \omega, \delta_0}(\theta, \delta)=\omega \rho(\delta_0, \delta)+ (1-\omega) \rho(\theta, \delta)}, as well as the weighted version q(q) L_{r, w, d0}(q, d){q(\theta) L_{\rho, \omega, \delta_0}(\theta, \delta)}, where ρ(θ, δ) is an arbitrary loss function, δ ₀ is a chosen a priori “target” estimator of q, w ? [0,1){\theta, \omega \in[0,1)}, and q(·) is a positive weight function. we develop Bayesian estimators under L_{r, w, d0}{L_{\rho, \omega, \delta_0}} with ω > 0 by relating such estimators to Bayesian solutions under L_{r, w, d0}{L_{\rho, \omega, \delta_0}} with ω = 0. Illustrations are given for various choices of ρ, such as absolute value, entropy, linex, and squared error type losses. Finally, under various robust Bayesian analysis criteria including posterior regret gamma-minimaxity, conditional gamma-minimaxity, and most stable, we establish explicit connections between optimal actions derived under balanced and unbalanced losses.     

Determinants of Infant Mortality in Older ASEAN Economies

Infant mortality in the Association of Southeast Asian Nations (ASEAN) has been declining, yet disparities remain between the nations. This paper therefore explores the determinants of infant mortality in the older ASEAN-4 economies, Malaysia, Thailand, Indonesia and the Philippines using an Autoregressive Distributed Lag (ARDL) Error Correction Model framework. The key findings of the study are: First, there is evidence of long-run relationships among infant mortality, education, female fertility, income and access to healthcare. Second, the determinants of infant mortality vary between countries. Female fertility emerged as the main determinant of infant mortality in Malaysia, while access to healthcare matter for infant mortality in Indonesia, and to a lesser extent for the Philippines. The income effect is significant for reducing infant mortality in Malaysia, while female education is important for Indonesia and Thailand. Third, the speed of adjustment of infant mortality rate is comparatively low in ASEAN-4.     

The McDonald Gompertz distribution: Properties and applications

This article introduces a five-parameter lifetime model called the McDonald Gompertz (McG) distribution to extend the Gompertz, generalized Gompertz, generalized exponential, beta Gompertz, and Kumaraswamy Gompertz distributions among several other models. The hazard function of new distribution can be increasing, decreasing, upside-down bathtub, and bathtub shaped. We obtain several properties of the McG distribution including moments, entropies, quantile, and generating functions. We provide the density function of the order statistics and their moments. The parameter estimation is based on the usual maximum likelihood approach. We also provide the observed information matrix and discuss inferences issues. The flexibility and usefulness of the new distribution are illustrated by means of application to two real datasets.     

A note on the mean residual life of a coherent system with a cold standby component

In this paper, we investigate the effect of a cold standby component on the mean residual life (MRL) of a system. When the system fails, a cold standby component is immediately put in operation. We particularly focus on the coherent systems in which, after putting the standby component into operation, the failure of the system is due to the next component failure. For these systems, we define MRL functions and obtain their explicit expressions. Also some stochastic ordering results are provided. Such systems include k-out-of-n systems. Hence, our results extend some results in literature.