Fisher’s Fiducial Inference for Parameters of Uniform Distribution

Kefa Wu, Peiju Chang, Yaolan Ma, Tianxin Dong

College of Information and Computation, National University in the North, Yinchuan, China.
Office of Financial Affairs, Xi’an Jiaotong University, Xi’an, China.
Society of Old Scientist & Technicians, Xi’an Jiaotong University, Xi’an, China.

DOI: 10.4236/am.2013.44083                

Abstract

Fisher’s Fiducial Inference for the parameters of a totality uniformly distributed on [α, β] is discussed. The corresponding fiducial distributions are derived. The maximum fiducial estimators, fiducial median estimators and fiducial expect estimators of α and β are got. The problems about the fiducial interval, fiducial region and hypothesis testing are discussed. An example which showed that Neyman-Pearson’s confidence interval has some place to be improved is illustrated. An idea about deriving fiducial distribution is proposed.

Keywords

Fiducial Inference; Uniformly Distribution; Parameters; Fiducial Interval; Hypothesis Testing

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. A. Fisher, “Inverse Probability,” Proceedings of the Cambridge Philosophical Society, Vol. 26, 1930, pp. 528-535.
[2]	S. L. Zabell, “R. A. Fisher and the Fiducial Argument,” Statistical Science, Vol. 7, No. 3, 1992, pp. 369-387. doi:10.1214/ss/1177011233
[3]	J. C. Fan and K. F. Wu, “A Introduction of Statistical Inference,” Science Press, Beijing, 2001.
[4]	K. F. Wu, “The Relativity of Randomness and Fisher’s Fiducial Inference,” The 4th ICSA Statistical Conference, 1998, Kunming, Abstracts #88.