مجله علوم آماری
سال شانزدهم شماره 2 (پیاپی 32، پاییز و زمستان 1401)

This paper considers series and parallel systems with independent and identically distributed component lifetimes. The reliability of these systems can be improved by using the reduction method. In the reduction method, system reliability is increased by reducing the failure rates of some of its components by a factor 0<ρ<1, called the equivalent reliability factor. Closed formulas are obtained for some reliability equivalence factors. In comparisons among the performance of the systems, these factors are helpful. We discuss that the reduction method can be considered as a particular case of the proportional hazard rates (PHR) model. Sufficient conditions for the relative aging comparison of the improved series and parallel systems under the PHR model and reduction method are also developed.

Although the multiple dependent state sampling (MDS) plan is preferred over the conditional plans due to the small size required, it is impossible to use it in a situation where the quality of manufactured products depends on more than one quality characteristic. In this study, to improve the performance of the mentioned method, S^T_{pk}-based MDS plan is proposed, which is applicable to inspect products with independent and multivariate normally distributed characteristics. The principal component analysis technique is used to develop an application of the proposed plan in the presence of dependent variables. Moreover, optimal values of plan parameters are obtained based on a nonlinear optimization problem. Findings indicate that compared to S^T_{pk}-based variable single sampling and repetitive group sampling plans, the proposed method is the best in terms of required sample size and OC curve. Finally, an industrial example is given to explain how to use the proposed plan.

This paper discusses the  Bayesian and E-Bayesian estimators in Burr type-XII model is discussed. The estimators are obtained based on type II censored data under the bounded reflected gamma loss function. The relationship between E-Bayesian estimators and their asymptotic properties is presented. The performance of the proposed estimators is evaluated using Monte Carlo simulation.

In this paper, the individual risk model of the insurance company with dependent claims is considered and assumes that the binary vector of random variables of claim sizes is independent. Also, they have a common joint distribution function. A recursive formula for infinite time ruin probability is obtained according to the initial reserve and joint probability density function of random variables of claim sizes using probability inequalities and the induction method. Some numerical examples and simulation studies are presented for checking the results related to the light-tailed bivariate Poisson, heavy-tailed Log-Normal and Pareto distributions. The results are compared for Farlie–Gambel–Morgenstern and bivariate Frank copula functions. The effect of claims with heavy-tailed distributions on the ruin probability is also investigated.

High interpretability and ease of understanding decision trees have made them one of the most widely used machine learning algorithms. The key to building efficient and effective decision trees is to use the suitable splitting method. This paper proposes a new splitting approach to produce a tree based on the T-entropy criterion for the splitting method. The method presented on three data sets is examined by 11 evaluation criteria. The results show that the introduced method in making the decision tree has a more accurate performance than the well-known methods of Gini index, Shannon, Tisalis, and Renny entropies and can be used as an alternative method in producing the decision tree.

In this paper, a new representation of the mean inactivity time of a coherent system with dependent identically distributed (DID) components is obtained. This representation compares the mean inactivity times of two coherent systems. Some sufficient conditions such that one coherent system dominates another system concerning ageing faster order in the reversed mean and variance residual life order are also discussed. These results are derived based on a representation of the system reliability function as a distorted function of the common reliability function of the components. Some examples are given to explain the results.

The Singular Spectrum Analysis (SSA) method is a powerful non-parametric method in the field of time series analysis and has been considered due to its features such as no need to stationarity assumptions or a limit on the number of collected observations. The main purpose of the SSA method is to decompose time series into interpretable components such as trend, oscillating component, and unstructured noise. In recent years, continuous efforts have been made by researchers in various fields of research to improve this method, especially in the field of time series prediction. In this paper, a new method for improving the prediction of singular spectrum analysis using Kalman filter algorithm in structural models is introduced. Then, the performance of this method and some generalized methods of SSA are compared with the basic SSA   using the root mean square error criterion. For this comparison, simulated data from structural models and real data of gas consumption in the UK have been used. The results of this study show that the newly introduced method is more accurate than other methods.

In this article, we consider the estimation of R{r,k}= P(X{r:n1} < Y{k:n2}), when the stress X and strength Y are two independent random variables from inverse Exponential distributions with unknown different scale parameters. R{r,k} is estimated using the maximum likelihood estimation method, and also, the asymptotic confidence interval is obtained. Simulation studies and the performance of this model for two real data sets are presented.

This paper suggests Liu-type shrinkage estimators in linear regression model in the presence of multicollinearity under subspace information. The performance of the proposed estimators is compared to Liu-type estimator in terms of their relative efficiency via a Monte Carlo simulation study and a real data set. The results reveal that the proposed estimators outperform better than the Liu-type estimator.

An important issue in many cities is related to crime events, and spatio–temporal Bayesian approach leads to identifying crime patterns and hotspots. In Bayesian analysis of spatio–temporal crime data, there is no closed form for posterior distribution because of its non-Gaussian distribution and existence of latent variables. In this case, we face different challenges such as high dimensional parameters, extensive simulation and time-consuming computation in applying MCMC methods. In this paper, we use INLA to analyze crime data in Colombia. The advantages of this method can be the estimation of criminal events at a specific time and location and exploring unusual patterns in places.

This article introduces a semiparametric multinomial logistic regression model to classify labeled configurations. In the regression model, the explanatory variable is the kernel function obtained using the power-divergence criterion. Also, the response variable was categorical and showed the class of each configuration. This semiparametric regression model is introduced based on distances defined in the shape space, and for this reason, the correct classification of shapes using this method has been improved compared to previous methods. ‎The performance of this model has been investigated in the comprehensive simulation study‎. ‎Two real datasets were analyzed using this article's method as an application‎. ‎Finally‎, ‎the method presented in this article was compared with the techniques introduced in the literature‎, ‎which shows the proper performance of this method in classifying configurations‎.

In this paper, a new integer-valued autoregressive process is introduced based on the discrete exponential-Weibull distribution to model integer-value time series data. Regarding the importance of discrete distributions in counting data modeling, the discrete counterpart of the exponential-Weibull distribution is introduced, and some of its statistical properties, such as survival function, hazard rate, moment generating function, skewness and kurtosis, are investigated. The Fisher dispersion, skewness and kurtosis indices show the flexibility and efficiency of the discrete Exponential-Weibull distribution in fitting different types of counting data. The discrete Exponential-Weibull distribution covers data fits with different dispersion characteristics (overdispersion, underdispersion and equidispersion), long right tail  (skewed to the right) and heavy-tailed. The model parameters are estimated using three approaches maximum conditional likelihood, minimum generalized conditional squares, and Yule-Walker. Finally, the efficiency and superiority of the process in fitting counts data of deaths due to COVID-19 disease are compared with other competing models.