Sevil Bacanli

Fuzzy approach of group sequential test for binomial case

The aim of this study is to present the fuzzy statistics into group sequential test when response variable has binomial case. Confidence intervals for fuzzy parameter estimation in group sequential test procedure is applied to construct the related fuzzy test statistic with the help of Buckley’s approach with r-cuts. Afterwards, this present study is completed with a numerical application to real data. Finally it is concluded that the fuzzy approach is also applicable for group sequential tests when response variable has binomial case.

Hypothesis testing for the mean of inverse Gaussian distribution using α-cuts

In this study, we modify the method proposed by Buckley to testing statistical hypothesis for the mean of an inverse Gaussian distribution. In order to obtain fuzzy test statistic, we use confidence intervals by the help of

Horvitz-Thomson Ratio Type Estimator in Estimating Population Mean

\alpha

Fuzzy approach for group sequential test

α-cuts. Then the method is applied to test the hypothesis for the mean of inverse Gaussian distribution when the scale parameter is known. Also a comparison is made between the fuzzy and non-fuzzy test procedure for the inverse Gaussian distribution.

Power Comparisons for Group Sequential Tests with Nonparametric Statistics in Case of Nonproportional Hazards

In this article, a group sequential test (GST) of non-parametric statistics for survival data is briefly reviewed. An asymptotic joint distribution of the test statistics, obtained after each interim analysis, is given to illustrate the applicability of the critical values of the GST procedures. It should be noted that censored observations are generally seen in survival data. Therefore, if one makes power calculations irrespective of censoring, reliable results may not be achieved, due to the lack of information about the censoring structure. A wide simulation study, covering different censoring rates and tied observations, is conducted to make the power comparisons under various scenarios. The simulation results are interpreted and compared with the results obtained by using power analysis and sample size (PASS) software.

A group sequential test for the inverse Gaussian mean

This study proposes Horvitz-Thompson ratio estimators for the population mean by using the ratio estimators based on regression estimator which is presented in Kadilar and Cingi [1]. Mean square error (MSE)of the proposed Horvitz-Thompson ratio type estimators are obtained and compared with ratio estimators which are presented by Bacanli and Kadilar [2]. The theoretical results are supported by a numerical illustration.The findings demonstrate that the proposed Horvitz-Thompson ratio estimators are more efficient than the estimators of Bacanli and Kadilar [2].

A Post-Stratified Randomized Response Model for Proportion

In this study, the group sequential test is suggested for the mean direction parameter of the von Mises distribution when the concentration parameter is known and unknown. An application of the proposed test is illustrated by using a medical data of the patients, who were complained about internal rotation angles of the shoulder and treated in a rehabilitation and physical therapy center in Eskisehir, Turkey. It is shown that the results of the study demonstrate that the group sequential test can provide a great advantage not only for linear data but also for circular data in terms of sample size.

Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing

Buckleys approach (Buckley (2004), (2005), (2006)) uses sets of confidence intervals by taking into consideration both of the uncertainty and impreciseness of concepts that produce triangular shaped fuzzy numbers for the estimator. This approach produces fuzzy test statistics and fuzzy critical values in hypothesis testing. In addition, the sample size is fixed for this test. When data comes sequentially, however, it is not suitable to study with a fixed sample size test. In such cases, sequential and group sequential tests are recommended. Unlike a sequential test, a group of sequential test provides substantial savings in sample and enables us to make decisions as early as possible. This intends paper to combine the benefits of group sequential test and Buckleys approach using α-cuts. It attempts to show that using α-cuts can be used within the group sequential tests. To illustrate the test more explicitly a numerical example is also given.