Complex and variable nature of the river sediment yield caused many problems in prediction of the long-term sediment yield and input into the reservoirs .sediment rating curves generally used to estimate the suspended sediment load of the river and drainage basin. Since the regression equations of the sediment rating curves obtained by logarithmic retransformation and little independent variable include in this equation they also overestimate or underestimate the true load of the rivers. In this research in order to improve and develop sediment yield estimation methods the estimates of 10 kind of sediment rating curves were compared with actual loads of 5 stations in different climate zones of the country by using accuracy and precision index .the results show that in estimating long term mean load of the selected periods the Linear-MVUE sediment rating curve has relatively high accuracy and precision comparing other kinds of sediment rating curves. In average, the accuracy index of this method is about 1.23 that is reasonable among other methods. Since this kind of sediment, rating curve uses different data characteristics and information it could be recommend for application in sediment yield estimation within acceptable confidence limits.

Some examples of absurd UNIFORMLY MINIMUM VARIANCE UNBIASED ESTIMATORs are discussed. Two reasons, argued in the literature, for having such ESTIMATORs are lack of enough information in the available data and property of UNBIASEDness. In this paper, accepting both of these views, we show that an appropriate choice of loss function using a general concept of UNBIASEDness leads to risk UNBIASED, admissible and reasonable ESTIMATORs. For this we extend the Rao-Blackwell theorem using a new way of defining UNBIASED ESTIMATOR.

In this paper, we show that the UNBIASED ESTIMATOR of the certion Parameter of the selected population does not exist. First, we give a new proof of this fact for the selected normal population. We then extend the result to some other distributions belonging to one-parameteric exponential family. Whenever an UNBIASED ESTIMATOR exists, it is shown to be a function of order statiscs.

This article examines statistical inference for R= P(Y<X) where X and Y are independent but not identically distributed Pareto of the first kind (Pareto (I)) random variables with same scale parameter but different shape parameters. The Maximum likelihood, UNIFORMLY MINIMUM VARIANCE UNBIASED and Bayes ESTIMATORs with Gamma prior are used for this purpose. Simulation studies which compare the ESTIMATORs are presented. Moreover, sensitivity of Bayes ESTIMATOR to the prior parameters is considered.

In this study, a simple generalization of the Lehmann-Scheffe theorem is proposed in cases where UMVUEs exist but a sufficiently complete statistics does not exist. Also, another method is introduced based on the group action. In this method, UMVUE for the unknown parameter is found using  a commutative and associative binary operation.  Finally, the motivation for using the words "completeness" and "UNBIASEDness" is expressed in such a way that completeness and UNBIASEDness are not characteristic of a statistic or its parametric form, but a family of distributions of a statistic, and deleting even one point of the parameter space may change the completeness.

In this paper, we propose a presmooth product-limit ESTIMATOR to draw statistical inference on the UNBIASED distribution function representing the population of interest. The strong consistency of the ESTIMATOR proposed is investigated. The finite sample performance of the proposed ESTIMATOR is evaluated using simulation studies. It is observed that the proposed ESTIMATOR exhibits greater efficiency in comparison with the alternative method in de Uñ a-Á lvarez (Test 11(1): 109– 125, 2002).

The ratio, product, and regression ESTIMATORs are commonly constructed based on conventional measures such as mean, median, quartiles, semi-interquartile range, semiinterquartile average, coefficient of skewness, and coefficient of kurtosis. In the case of the presence of outliers, these conventional measures lose their efficiency/performance ability and hence are less efficient as compared to those measures which performed efficiently in the presence of outliers. This study offers an improved class of ESTIMATORs for estimating the population VARIANCE using robust dispersion measures such as probability-weighted moments, Gini, Downton and Bickel, and Lehmann measures of an auxiliary variable. Bias, mean square error and MINIMUM mean square error of the suggested class of ESTIMATORs have been derived. Application with two natural data sets is also provided to explain the proposal for practical considerations. In addition, a robustness study is also carried out to evaluate the performance of the proposed ESTIMATORs in the presence of outliers by using environmental protection data. The results reveal that the proposed ESTIMATORs perform better than their competitors and are robust, not only in simple conditions but also in the presence of outliers.