Journal of Statistical Sciences

Geostatistical Survival Data Analysis with Bayesian Approach

Kiomars Motarjem

In some instances, the occurrence of an event can be influenced by its spatial location, giving rise to spatial survival data. The accurate and precise estimation of parameters in a spatial survival model poses a challenge due to the complexity of the likelihood function, highlighting the significance of employing a Bayesian approach in survival analysis. In a Bayesian spatial survival model, the spatial correlation between event times is elucidated using a geostatistical model. This article presents a simulation study to estimate the parameters of classical and spatial survival models, evaluating the performance of each model in fitting simulated survival data. Ultimately, it is demonstrated that the spatial survival model exhibits superior efficacy in analyzing blood cancer data compared to conventional models.

Stochastic Comparisons of ‎$(‎‎n-1)$-out-of-‎$‎n‎$‎‎ Systems with Additive Hazard Components under Random Shocks

Ghobad Saadat Kia

Often, reliability systems suffer shocks from external stress factors, stressing the system at random. These random shocks may have non-ignorable effects on the reliability of the system. In this paper, we provide sufficient and necessary conditions on components' lifetimes and their survival probabilities from random shocks for comparing the lifetimes of two $(n-1)$-out-of-$n$ systems in two cases: (i) when components are independent, and then (ii) when components are dependent.

Tsallis Entropy of the Lifetime of Coherent Systems and Its Properties

saeed toomaj

In this paper, the entropy characteristics of the lifetime of coherent systems are investigated using the concept of system signature. The results are based on the assumption that the lifetime distribution of system components is independent and identically distributed. In particular, a formula for calculating the Tsallis entropy of a coherent system's lifetime is presented, which is used to compare systems with the same characteristics. Also, bounds for the lifetime Tsallis entropy of coherent systems are presented. These bounds are especially useful when the system has many components or a complex structure. Finally, a criterion for selecting the preferred system among coherent systems based on the relative Tsallis entropy is presented.

Bayesian Analysis of Latent Variables in Spatial GLM Models with Stationary Skew Gaussian Random Field

Fatemeh Hosseini

The spatial generalized linear mixed models are often used, where the latent variables representing spatial correlations are modeled through a Gaussian random field to model the categorical spatial data. The violation of the Gaussian assumption affects the accuracy of predictions and parameter estimates in these models. In this paper, the spatial generalized linear mixed models are fitted and analyzed by utilizing a stationary skew Gaussian random field and employing an approximate Bayesian approach. The performance of the model and the approximate Bayesian approach is examined through a simulation example, and implementation on an actual data set is presented.

Estimating the Means of Two Sensitive Variables with a New Quantitative Randomized Response Method

Eisa Mahmoudi

Often, in sample surveys, respondents refused to answer some questions of a sensitive nature. Randomized response methods are designed not to reveal respondent confidentiality. In this article, a new quantitative randomized response method is introduced, and by conducting a series of simulation studies, we show that the proposed method is preferable to the cumulative and multiplicative methods. By using unbiased predictors, we estimate the covariance between two sensitive variables. In an experimental study using the proposed method, the average number of cheating and the average daily cigarette consumption of the Shahid Chamran University of Ahvaz students are estimated along with their variance, and an estimate for the covariance between them is provided.

Shrinkage Estimators in Semi-Parametric Heteroscedastic Hierarchical Models with Restricted Joint Empirical likelihood

Seyed Kamran Ghoreishi

In this paper, we first introduce semi-parametric heteroscedastic hierarchical models. Then, we define a new version of the empirical likelihood function (Restricted Joint Empirical likelihood) and use it to obtain the shrinkage estimators of the models' parameters in these models. Under different assumptions, a simulation study investigates the better performance of the restricted joint empirical likelihood function in the analysis of semi-parametric heterogeneity hierarchical models. Furthermore, we analyze an actual data set using the RJEL method.

Moving average modeling based on α-value of fuzzy random variables

Samira Taheri

In this paper, based on the concept of $alpha$-values of fuzzy random variables, the fuzzy moving average model of order $q$ is introduced. In this regard, first, the definitions of variance, covariance, and correlation coefficient between fuzzy random variables are presented, and their properties are investigated. In the following, while introducing the fuzzy moving average model of order $q$, this model's autocovariance and autocorrelation functions are calculated. Finally, some examples are presented for the obtained results.

Nonparametric Inference for Component Lifetime Distribution of Coherent Systems Based on Progressively Censored

adeleh fallah

‎In this paper‎, ‎non-parametric inference is considered for $k$-component coherent systems‎, ‎when the‎ ‎system lifetime data is progressively type-II censored‎. ‎In these coherent systems‎, ‎it is assumed that the‎ ‎system structure and system signature are known‎. ‎Based on the observed progressively type-II censored‎, ‎non-parametric confidence intervals are calculated for the quantiles of component lifetime distribution‎. ‎Also‎, ‎tolerance limits for component lifetime distribution are obtained‎. ‎Non-parametric confidence intervals for quantiles and tolerance limits are obtained based on two methods‎, ‎distribution function method and W mixed matrix method‎. ‎Two numerical‎ ‎example is used to illustrate the methodologies developed in this paper‎.

The Most Entropic Copula Based on Shannon Entropy and Blest's Measure and It's Application in Hydrology

Gholam Reza Mohtashami Borzadaran

Maximum entropy copula theory is a combination of copula and entropy theory. This method obtains the maximum entropy distribution of random variables by considering the dependence structure. In this paper, the most entropic copula based on Blest's measure is introduced, and its parameter estimation method is investigated. The simulation results show that if the data has low tail dependence, the proposed distribution performs better compared to the most entropic copula distribution based on Spearman's coefficient. Finally, using the monthly rainfall series data of Zahedan station, the application of this method in the analysis of hydrological data is investigated.

Autoregressive Modeling Based on the Support Function of Fuzzy Random Variables

Hossein Mohammadi

First, this article defines a meter between fuzzy numbers using the support function. Then, based on the support function, the concepts of variance, covariance, and correlation coefficient between fuzzy random variables are expressed, and their properties are investigated. Then, using the above concepts, the p-order fuzzy autoregressive model is introduced based on fuzzy random variables, and its properties are investigated. Finally, to explain the problem further, examples will be presented and compared with similar models using some goodness of fit criteria.

Robust Model-Based Clustering Using the Symmetric alpha-Stable Distribution for Measurement Error

Shaho Zarei

Model-based clustering is the most widely used statistical clustering method, in which heterogeneous data are divided into homogeneous groups using inference based on mixture models. The presence of measurement error in the data can reduce the quality of clustering and, for example, cause overfitting and produce spurious clusters. To solve this problem, model-based clustering assuming a normal distribution for measurement errors has been introduced. However, too large or too small (outlier) values of measurement errors cause poor performance of existing clustering methods. To tackle this problem {and build a stable model against the presence of outlier measurement errors in the data}, in this article, a symmetric $alpha$-stable distribution is proposed as a replacement for the normal distribution for measurement errors, and the model parameters are estimated using the EM algorithm and numerical methods. Through simulation and real data analysis, the new model is compared with the MCLUST-based model, considering cases with and without measurement errors, and the performance of the proposed model for data clustering in the presence of various outlier measurement errors is shown.

Fuzzy Order Statistics Based on α-Value and Some of Its Applications in Reliability

Mohammad Khanjari Sadegh

In this paper, fuzzy order statistics are expressed based on the concept of α-value, and some of its applications in reliability have been examined. For this purpose, if the lifetime distribution of the system components is known, some of the reliability criteria of the $i$th order statistic using the definition of a fuzzy random variable based on the α-value have been investigated. Also, if the lifetime distribution of the components is unknown or only the fuzzy observations of the lifetime of the components are available, the empirical distribution function of the fuzzy data is used to estimate the reliability based on ordinal statistics, and examples are provided to illustrate the results.