Modified generalized p-value and confidence interval by Fisher s fiducial approach
- Resource Type
- Authors
- Ahmet Sezer; Berna Yazici; Evren Ozkip
- Source
- Hacettepe Journal of Mathematics and Statistics. 46:1-22
- Subject
- Heteroscedasticity
The Behrens-Fisher Problem
021103 operations research
Monte Carlo method
0211 other engineering and technologies
Inference
02 engineering and technology
General Medicine
Interval (mathematics)
Generalized Approach
Generalized p-value
01 natural sciences
Confidence interval
010104 statistics & probability
Sample size determination
Log-normal distribution
Statistics
Parametric Bootstrap Approach
Modified Fiducial Based Test
Lognormal Distribution
0101 mathematics
Mathematics
- Language
- ISSN
- 1303-5010
WOS: 000400349400015
In this study, we develop two simple generalized confidence intervals for the difference between means of two normal populations with heteroscedastic variances which is usually referred to as the Behrens-Fisher problem. The developed confidence intervals are compared with the generalized confidence interval in the literature. We also propose modified fiducial based approach using Fisher's fiducial inference for comparing the mean of two lognormal distributions and compare them with the other tests in the literature. A Monte Carlo simulation study is conducted to evaluate performances of the proposed methods under different scenarios. The simulation results indicate that the developed confidences intervals for the Behrens-Fisher problem have shorter interval lengths and they give better coverage accuracy in some cases. The modified fiducial based approach is the best to provide satisfactory results in respect to its type error and power in all sample sizes. The modified test is applicable to small samples and is easy to compute and implement. The methods are also applied to two real-life examples.