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In this paper, four approaches are presented to the problem of fitting a linear regression model in the presence of spatially misaligned data. These approaches are plug-in method‎, ‎simulation‎, ‎regression calibration and maximum likelihood‎. In the first two approaches‎, ‎with modeling the correlation between the explanatory variable, prediction of explanatory variable is determined at sites corresponding to response variable. Then the model is fitted using the predictions as a covariate in regression model. It is shown that this creates Berkson error and this error leads to bias in estimation of the slope of regression model. To adjust the bias, regression calibration approach is provided. In the maximum likelihood approach, misaligned data is used directly, and the regression model parameters are estimated. In fact, it is not required to predict explanatory variable at sites corresponding to response. Unfortunately, the maximum likelihood estimator properties can not be accurately assessed due to lack of analytical form. In a simulation study, the performance of all these approaches is assessed under several spatial models for explanatory variable. It is observed that regression calibration can significantly reduce the bias of slope of regression line compared to other methods. Moreover, Nominal coverage of confidence interval of slope of regression line is notable by this method.

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In many diverse scientific fields, the measurements are directions. For instance, a biologist may be measuring the
direction of flight of a bird or the orientation of an animal. A series of such observations is called ”directional
data”. Since a direction has no magnitude, these can be conveniently represented as points on the circumference of
a unit circle centered at the origin or as unit vectors connecting the origin to these points. Because of this circular
representation, such observations are also called circular data. In this paper, circular data will be introduced at first
and then it is explained how to calculate the mean direction, dispersion and higher moments. The solutions to many
directional data problems are often not obtainable in simple closed analytical forms. Therefore, computer softwares
is essential to use these methods. At the end of this paper, the CircStat’s package has been used to analyze data sets
in R and Matlab softwares.

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Methods for small area estimation have been received great attention in recent years due to growing demand for
reliable small area estimation that are needed in development planings, allocation of government funds and marking
business decisions. The key question in small area estimation is how to obtain reliable estimations when sample
size is small. When only a few observations(or even no observation) are available from a given small area, small
sample sizes lead to undesirably large standard errors. The only possible solution to the estimation problem is to
borrow strength from available data sets. This is accomplish by using appropriate linking models (included explicit
and implicit models) to increas the effect of sample size for estimation. The generalized linear mixed models and
the empirical best linear unbiased predictor, are extensively used to estimate reliable mean of small areas. In this
article,first we introduce the small area estimation.Then, to obtain reliable small area estimations we introduce the
Fay-Herriot model as a special case of the generalized linear mixed model. Finally, in an Simulation study we use
Iran 1382 agricultural census data to estimate orange production in Fars cities (small areas) in the year 1382 based
on Fay-Herriot model.

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In the analysis of Bernoulli's variables, an investigation of the their dependence is of the prime importance. In this paper, the distribution of the Markov logarithmic series is introduced by the execution of the first-order dependence among Bernoulli variables. In order to estimate the parameters of this distribution, maximum likelihood, moment, Bayesian and also a new method which called the expected Bayesian method (E-Bayesian) are employed. In continuation, using a simulation study, it is shown that the expected Bayesian estimator out performed over the other estimators.

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In this paper, we first define longitudinal-dynamic heteroscedastic hierarchical  normal  models. These models can be used to fit longitudinal data in which the dependency structure is constructed through a dynamic model rather than observations. We discuss different methods for estimating the hyper-parameters. Then the corresponding estimates for the hyper-parameter that causes the association in the model will be presented. The comparison among various  empirical estimators  is illustrated through a simulation study. Finally, we apply our methods to a  real dataset.

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In this paper, first, the generalized lambda distribution and the characteristics of this distribution are introduced. The concept of resistance stress is fully explained and the reliability of a system from the perspective of resistance stress is examined. Also, the mathematical form of the resistance stress parameter in the generalized lambda distribution has been calculated. The estimation of the parameters has been investigated by the moments method‎‎ and ‎for different parameters values the graph of generalized lambda distribution is drawn ‎‎and resistance stress parameter calculated. With a real example the application of the results is illustrated.‎‎