R. A. Fisher's fiducial inference has been the subject of many discussions and controversies ever since he introduced the idea during the 1930's. The idea experienced a bumpy ride, to say the least, during its early years and one can safely say that it eventually fell into disfavor among mainstream statisticians. However, it appears to have made resurgence recently under the label of generalize...

Generalized logistic distribution, as the generalized form of symmetric plays an important role in reliability analysis. This article focuses on statistical inference for stress–strength parameter R=P(Y<X) distribution with same and different scale parameters. Firstly, we use frequentist method to construct asymptotic confidence intervals, adopt constructing point estimators well intervals. ...

We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or Weyl-Heisenberg group as it is often called)). We also obtain a number of results concerning the structure of the Clifford Group proper (i.e. the group consisting just of the unitary operators which normalize the...

A real-valued fiducial process is a process in the probabilistic sense, but the probability distributions are not defined on Borel sets. The adjective ‘fiducial’ indicates that a group acts on the observation spaces and the probability distributions are defined on the smaller σ-algebra of group-invariant Borel sets. Since a different group action determines a different σ-algebra, the group is a...

Construction of confidence intervals for a variance component corresponding to the random factor in mixed linear models with two variance components is considered. At first, attention is drawn to an approximate confidence interval suggested by El-Bassiouni (1994), which is an extension of the well known Williams-Tukey interval. Though the stated interval has some nice properties, it is not very...

In this paper we derive general formulae suitable for Monte Carlo computation of conditional expectations of functions of a random vector given a sufficient statistic. The problem of direct sampling from the conditional distribution is considered in particular. It is shown that this can be done by a simple parameter adjustment of the original statistical model, provided the model has a certain ...