Journal of Statistical Sciences

New Bounds for Fractional Mean-Square Stochastic Integrals

Hamzeh Agahi

This paper presents new bounds for the left and right fractional mean-square stochastic integrals based on convex stochastic processes. Then a range is proposed that includes a linear combination of the left and right fractional mean-square stochastic integrals. Finally, the previous results presented in this subject are improved.

Construction a Non-parametric Prediction Model for Spatial Random Field Using Projection Theorem

Mehdi Omidi

Identifying the best prediction of unobserved observation is one of the most critical issues in spatial statistics. In this line, various methods have been proposed, that each one has advantages and limitations in application. Although the best linear predictor is obtained according to the Kriging method, this model is applied for the Gaussian random field. The uncertainty in the distribution of random fields makes researchers use a method that makes the nongaussian prediction possible. In this paper, using the Projection theorem, a non-parametric method is presented to predict a random field. Then some models are proposed for predicting the nongaussian random field using the nearest neighbors. Then, the accuracy and precision of the predictor will be examined using a simulation study. Finally, the application of the introduced models is examined in the prediction of rainfall data in Khuzestan province.

Stochastic Comparisons of Parallel and Series Systems Comprising Multiple-Outlier Scale Components

Ebrahim Amini Seresht

This paper discusses stochastic comparisons of the parallel and series systems comprising multiple-outlier scale components. Under uncertain conditions on the baseline reversed hazard rate, hazard rate functions and scale parameters, the likelihood ratio, dispersive and mean residual life orders between parallel and series systems are established. We then apply the results for two exceptional cases of the multiple-outlier scale model: gamma and Pareto multiple-outlier components to illustrate the found results.

Estimation of Past Entropy in Length-Biased Data

Anis Iranmanesh

In this article, we propose two non-parametric estimators for the past entropy based on length-biased data, and the strong consistency of the proposed estimators is proved. In addition, some simulations are conducted to evaluate the performance of the proposed estimators. Based on the results, we show that they have better performance in a different region of the probability distribution for length-biased random variables.

Estimation and Prediction for the Poisson-Exponential Distribution Based on Records and Inter-Record Times: A Comparative Study

Seyed Mohamad Taghi Kamel MirMostafaee

In this paper, estimation and prediction for the Poisson-exponential distribution are studied based on lower records and inter-record times. The estimation is performed with the help of maximum likelihood and Bayesian methods based on two symmetric and asymmetric loss functions. As it seems that the integrals of the Bayes estimates do not possess closed forms, the Metropolis-Hastings within Gibbs and importance sampling methods are applied to approximating these integrals. Moreover, the Bayesian prediction of future records is also investigated. A simulation study and an application example are presented to evaluate and show the applicability of the paper's results and also to compare the numerical results when the inference is based on records and inter-record times with those when the inference is based on records alone.

The Efficiency of Some Shrinkage Estimators for Shape Parameter of the Pareto-Rayleigh Distribution

Einolah Deiri

In most practical cases, to increase parameter estimation accuracy, we need an estimator with the least risk. In this, contraction estimators play a critical role. Our main purpose is to evaluate the efficiency of some shrinkage estimators of the shape parameter of the Pareto-Rayleigh distribution under two classes of shrinkage estimators. In this research, the purpose estimators' efficiency will be compared with the unbiased estimator obtained under the quadratic loss function. The relationship between these two classes of shrinkage estimators was examined, and then the relative efficiency of the proposed estimators was discussed and concluded via doing a Monte Carlo simulation.

Some Stochastic Orderings Among (n-1)-out-of-n Systems from Scale Components

Ghobad Barmalzan

This paper discusses the hazard rate order of the fail-safe systems arising from two sets of independent multiple-outlier scale distributed components. Under certain conditions on scale parameters in the scale model and the submajorization order between the sample size vectors, the hazard rate ordering between the corresponding fail-safe systems from multiple-outlier scale random variables is established. Under certain conditions on the Archimedean copula and scale parameters, we also discuss the usual stochastic order of these systems with dependent components.

Multivariate Outlier Detection Based on Depth-Based Outlyingness Function

Sakineh Dehghan

The concept of data depth has provided a helpful tool for nonparametric multivariate statistical inference by taking into account the geometry of the multivariate data and ordering them. Indeed, depth functions provide a natural centre-outward order of multivariate points relative to a multivariate distribution or a given sample. Since the outlingness of issues is inevitably related to data ranks, the centre-outward ordering could provide an algorithm for outlier detection. In this paper, based on the data depth concept, an affine invariant method is defined to identify outlier observations. The affine invariance property ensures that the identification of outlier points does not depend on the underlying coordinate system and measurement scales. This method is easier to implement than most other multivariate methods. Based on the simulation studies, the performance of the proposed method based on different depth functions has been studied. Finally, the described method is applied to the residential houses' financial values of some cities of Iran in 1397.

Robust Empirical Bayes Small Area Estimation with Symmetric α-Stable Distribution for Error Components

Shaho Zarei

The most widely used model in small area estimation is the area level or the Fay-Herriot model. In this model, it is typically assumed that both the area level random effects (model errors) and the sampling errors have a Gaussian distribution. However, considerable variations in error components (model errors and sampling errors) can cause poor performance in small area estimation. In this paper, to overcome this problem, the symmetric α-stable distribution is used to deal with outliers in the error components. The model parameters are estimated with the empirical Bayes method. The performance of the proposed model is investigated in different simulation scenarios and compared with the existing classic and robust empirical Bayes methods. The proposed model can improve estimation results, in particular when both error components are normal or have heavy-tailed distribution.

Optimization Problem in Series Systems with Random Number of Components from the Family of Power Series Distributions

Jafar Ahmadi

In this paper, the lifetime model based on series systems with a random number of components from the family of power series distributions has been considered. First, some basic theoretical results have been obtained, which have been used to optimize the number of components in series systems. The average lifetime of the system, the cost function, and the total time on test have been used as an objective function in optimization. The issue has been investigated in detail when the lifetimes of system components have Weibull distribution, and the number of components has geometric, logarithmic, or zero-truncated Poisson distributions. The results have been given analytically and numerically. Finally, a real data set has been used to illustrate the obtained results.

Modeling of Continuous-Count and Continuous-Ordinal Mixed Longitudinal Bivariate Inflated Responses with Possibility of Non Random Missingness

Ehsan Bahrami Samani

One of the most frequently encountered longitudinal studies issues is data with losing the appointments or getting censoring. In such cases, all of the subjects do not have the same set of observation times. The missingness in the analysis of longitudinal discrete and continuous mixed data is also common, and missing may occur in one or both responses. Failure to pay attention to the cause of the missing (the mechanism of the missingness) leads to unbiased estimates and inferences. Therefore, in this paper, we investigate the mechanism of nonignorable missing in set-inflated continuous and zero-inflation power series, as well as the continuous and k-inflated ordinal mixed responses. A full likelihood-based approach is used to obtain the maximum likelihood estimates of the parameters of the models. In order to assess the performance of the models, some simulation studies are performed. Two applications of our models are illustrated for the American's Changing Lives  survey, and the Peabody Individual Achievement Test  data set.

A Suggestion for Using Ranked Set Sampling in Household Expenditure and Income Survey

Roshanak Aliakbari Saba

The ranked set sampling method uses the ranking information of the units to provide a more representative sample of the population to the survey designers. The sampling distribution is closer to the actual distribution of the population. In this article, to ensure the effectiveness of ranked set sampling in extensive surveys conducted to prepare official statistics, we intend to use this sampling method to improve the efficiency of key estimates of household expenditure and income survey of the Statistics Center of Iran. The results show that using ranked set sampling to design household expenditure and income surveys can improve the efficiency of key estimates of the study, provided that the ranking variable used has a high correlation with the main variables of the study. Obviously, in the absence of a suitable and available variable for ranking the units, the information of the sampling frame can be used to construct a ranking variable correlated with the key variables of the survey.

Introducing a Stationary Skew-Gaussian Random Field

Omid Karimi

The Gaussian random field is commonly used to analyze spatial data. One of the important features of this random field is having essential properties of the normal distribution family, such as closure under linear transformations, marginalization and conditioning, which makes the marginal consistency condition of the Kolmogorov extension theorem. Similarly, the skew-Gaussian random field is used to model skewed spatial data. Although the skew-normal distribution has many of the properties of the normal distribution, in some definitions of the skew-Gaussian random field, the marginal consistency property is not satisfied. This paper introduces a stationery skew-Gaussian random field, and its marginal consistency property is investigated. Then, the spatial correlation model of this skew random field is analyzed using an empirical variogram. Also, the likelihood analysis of the introduced random field parameters is expressed with a simulation study, and at the end, a discussion and conclusion are presented.

Introduce a Survival Model with Spatial Skew Gaussian Random Effects and its Application in Covid-19 Data Analysis

Kiomars Motarjem

The prevalence of Covid-19 is greatly affected by the location of the patients. From the beginning of the pandemic, many models have been used to analyze the survival time of Covid-19 patients. These models often use the Gaussian random field to include this effect in the survival model. But the assumption of Gaussian random effects is not realistic. In this paper, by considering a spatial skew Gaussian random field for random effects and a new spatial survival model is introduced. Then, in a simulation study, the performance of the proposed model is evaluated. Finally, the application of the model to analyze the survival time data of Covid-19 patients in Tehran is presented.