It is a common and useful task in a web of trust to evaluate the trust value between two nodes using intermediate nodes. This is widely used when the source node has no experience of direct interaction with the target node or the direct trust is not reliable enough by itself. If trust is used to support decision-making, it is important to have not only an accurate estimate of trust, but also a measure of confidence in the intermediate nodes as well as the final estimated value of trust. The present paper thus aims to introduce a novel framework for integrated representation of trust and confidence using intervals which provides two operations of trust interval multiplication and summation.The former is used for computing propagated trust and confidence, whereas the latter provides a formula for aggregating different trust opinions. The properties of the two operations are investigated in details. This study also proposes a time-variant method that considers freshness, expertise level and two similarity measures in confidence estimation. The results indicate that this method is of more accuracy compared to the existing methods. In this regard, the results of experiments carried out on two well-known trust datasets are reported and analyzed, showing that the proposed method increases the accuracy of trust inference in comparison with the existing methods.

Improving return forecasting is very important for both investors and researchers in financial markets. In this study we try to aim this object by two new methods. First, instead of using traditional variable, gold prices have been used as predictor and compare the results with Goyal's variables. Second, unlike previous researches new machine learning algorithm called Deep learning (DP) has been used to improve return forecasting and then compare the results with historical average methods as bench mark model and use Diebold and Mariano’ s and West’ s statistic (DMW) for statistical evaluation. Results indicate that the applied DP model has higher accuracy compared to historical average model. It also indicates that out of sample prediction improvement does not always depend on high input variables numbers. On the other hand, when using gold price as input variables, it is possible to improve this forecasting capability. Result also indicate that gold price has better accuracy than Goyal's variable to predicting out of sample return.

Background and Objectives: When computing a confidence interval for a binomial proportion p, one must choose an exact interval that has a coverage probability of at least 1-α for all values of p. In this study, we compared the confidence intervals of Clopper-Pearson, Wald, Wilson, and double ArcSin transformation in terms of maintaining a constant nominal type I error.Methods: Simulations were used to compare four methods of estimating a confidence interval, including the Clopper-Pearson, Wald, Wilson, and double ArcSic. The data were generated from the binomial and Poison distribution with parameters p, n and m=np, 1000 were produced. Type I error of each method was calculated per simulation. The above methods were used to estimate confidence intervals in a meta-analysis study.Results: The results of the simulation study showed that double ArcSin keep confidence interval at [0,1], but for some proportion has high type I error or low coverage probability. The Clopper-Pearson interval guarantees that the coverage probability is always equal to or above the nominal confidence level for any fixed p.Conclusion: This study showed that confidence interval estimations the Clopper-Pearson than other methods of calculating the type I error fixed and smaller.

Data envelopment analysis (DEA) is a non-parametric technique to measuring the relative efficiency of decision-making units (DMU) that in this technique using of multiple input and multiple outputs is possible. In the DEA model efficiency of (DMU) calculate by making of appropriate linear programming models.In this paper we consider fuzzy DEA (FDEA) based on (1-a) statistical confidence interval and transform it to interval linear programming problem and solve theme's with Noor's method and a solution is present for the solve the problem in over the confidence interval (1-a) of level. We will use the new ranking method discussed in this paper to ordering DMU's. We will give example and solve them.

In this paper, we study the estimation problems for the two-parameter exponentiated Gumbel distribution based on lower record values. An exact confidence interval and an exact joint confidence region for the parameters are constructed. A simulation study is conducted to study the performance of the proposed confidence interval and region. Finally, a numerical example with real data set is given to illustrate the proposed procedures.

Application and interpretation of statistical significance of association are the basic and necessary principle in medical research. Traditionally, hypothesis testing and reporting p-values have been extensively utilized to quantify the statistical significance of observed results. The majority of published research that involves statistical inference seems to make exclusive use of hypothesis testing, and summarize their findings only to statistical significance. Most importantly, p-value fail to provide two crucial pieces of information: (1) the magnitude of an effect of interest, and (2) the precision of the estimate of the magnitude of that effect. Currently, most of the reputable journals no longer accept statistical significance alone; and there has been increasing attention focused on the Effect size index, confidence limits along with clinical significant. However, there is no single guideline for reporting statistical and clinical significance, and there are inconsistencies between journals. The aim of this paper is to provide a correct and integrated instruction for reporting statistical and clinical significance in medical sciences employing an estimation approach (reporting confidence interval).

An approach is proposed to construct fuzzy confidence intervals for unknown parameters in statistical models. In this approach, a family of confidence intervals of the unknown crisp parameter has been considered. Such confidence intervals are used to obtain a fuzzy confidence interval for the parameter of interest. The proposed approach benefits a wide range of confidence intervals to obtain a trapezoidal shaped fuzzy set of the parameter space as the fuzzy confidence interval for the parameter of interest. By using the resolution identity, it is shown that the constructed fuzzy confidence intervals are really fuzzy sets of the parameter space. Some numerical examples are provided to explain the approach in one-sided and two-sided fuzzy confidence intervals. Moreover, an application in health sciences is provided about the recovery time of olfactory and gustatory dysfunctions for COVID-19 patients.