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Suppose that we have a random sample from one-parameter Rayleigh distribution‎. ‎In classical methods‎, ‎we estimate the interesting parameter based on the sample information and‎ ‎with usual estimators‎. ‎Sometimes in practice‎, ‎the researcher has some information about the unknown‎ ‎parameter in the form of a guess value‎. ‎This guess is known as nonsample information‎. ‎In this case‎, ‎linear shrinkage estimators are introduced‎ ‎by combining nonsample and sample information which have smaller risk than usual estimators in the vicinity of‎ ‎guess and true value‎. ‎In this paper‎, ‎some shrinkage testimators are introduced using different methods based on‎ ‎vicinity of guess value and true parameter and their risks are computed under the entropy loss function‎. ‎Then‎, ‎the performance of‎ ‎shrinkage testimators and the best linear estimator is calculated via the relative efficiency of them‎. ‎Therefore‎, ‎the results are applied for the type-II censored data.

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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.

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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.

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In the time series analysis, we may encounter situations where some elements of the model are imprecise quantities. One of the most common situations is the inaccuracy of the underlying observations, usually due to measurement or human errors. In this paper, a new fuzzy autoregressive time series model based on the support vector machine approach is proposed. For this purpose, the kernel function has been used for the stability and flexibility of the model, and the constraints included in the model have been used to control the points. In order to examine the performance and effectiveness of the proposed fuzzy autoregressive time series model, some goodness of fit criteria are used. The results were based on one example of simulated fuzzy time series data and two real examples, which showed that the proposed method performed better than other existing methods.