Sequential estimation is used where the total sample size is not fix and the problem cannot solve with this fixed sample
size. Sequentially estimating the mean in an exponential distribution (one and two parameter), is an important
problem which has attracted attentions from authors over the years. These largely addressed an exponential distribution
involving a single or two parameters. In this paper, two stage sampling, which introduced by Mukhopadhyay
and Zacks (2007), is employed to estimate linear combinations of the location and scale parameters of a negative
exponential distribution (two parameter) with bounded quadratic risk function. Furthermore some simulation results
are provided.

‎In this paper we propose a utility function and obtain the Bayese stimate and the optimum sample size under this utility function‎. ‎This utility function is designed especially to obtain the Bayes estimate when the posterior follows a gamma distribution‎. ‎We consider a Normal with known mean‎, ‎a Pareto‎, ‎an Exponential and a Poisson distribution for an optimum sample size under the proposed utility function‎, ‎so that minimizes the cost of sampling‎. ‎In this process‎, ‎we use Lindley cost function in order to minimize the cost‎. ‎Here‎, ‎because of the complicated form of computation‎, ‎we are unable to solve it analytically and use the mumerical methids to get the optimum sample size.

The Area under the ROC Curve (AUC) is a common index for evaluating the ability of the biomarkers for classification. In practice, a single biomarker has limited classification ability, so to improve the classification performance, we are interested in combining biomarkers linearly and nonlinearly. In this study, while introducing various types of loss functions, the Ramp AUC method and some of its features are introduced as a statistical model based on the AUC index. The aim of this method is to combine biomarkers in a linear or non-linear manner to improve the classification performance of the biomarkers and minimize the experimental loss function by using the Ramp AUC loss function. As an applicable example, in this study, the data of 378 diabetic patients referred to Ardabil and Tabriz Diabetes Centers in 1393-1394 have been used. RAUC method was fitted to classify diabetic patients in terms of functional limitation, based on the demographic and clinical biomarkers. Validation of the model was assessed using the training and test method. The results in the test dataset showed that the area under the RAUC curve for classification of the patients according to the functional limitation, based on the linear kernel pf biomarkers was 0.81 and with a kernel of the radial base function (RBF) was equal to 1.00. The results indicate a strong nonlinear pattern in the data so that the nonlinear combination of the biomarkers had higher classification performance than the linear combination.

Whenever approximate and initial information about the unknown parameter of a distribution is available, the shrinkage estimation method can be used to estimate it. In this paper, first, the E-Bayesian estimation of the parameter of an inverse Rayleigh distribution under the general entropy loss function is obtained. Then, the shrinkage estimate of the inverse Rayleigh distribution parameter is investigated using the guess value. Also, using Monte Carlo simulations and a real data set, the proposed shrinkage estimation is compared with the UMVU and E-Bayesian estimators based on the relative efficiency criterion.