The Statistical Inference Of Unknown Parameter In Two-parameter Exponential Distribution

Based on the theory of generalizedp-value and generalized confidence interval, generalizedstatistical inference for unknoun parameters in two-parameter exponential distribution are de-veloped.Firstly, this paper discusses the test on the equality of the unknown parameters of sev-eral two-parameter exponential distributions. A new generalized test variable is defined andthe generalizedp-value based on this generalized test variable is given. It is shown that theproposed generalizedp-value is invariant under the group of scale transformations. Simulationstudies show that the proposed approach based on the generalizedp-value to control type I errorprobability and power is quite satisfactory.Secondly, the statistical inference is developed for the ratio of expected lifetimes of twoindependently distributed two-parameter exponential distributions. A new generalized pivotquantity is defined and the generalized confidence interval of the ratio of expected lifetimes basedon this generalized pivot quantity is also given. Simulation studies show that compared to thoseof literature [21], our approach based on generalized confidence interval is more satisfactory interms of providing the intended coverage and expected lengths, especially for small samples.Lastly, the procedure for hypothesis testing and interval estimation for the common mean ofseveral two-parameter exponential distributions is presented. A new generalized pivot quantityand generalized test variable are constructed.The generalized confidence interval and proposedgeneralizedp-value of the common mean are given. Simulation studies show that the proposedapproach is quite satisfactory.