Location Parameters Of Exponential Distributions Research Articles

Sample Size Determination for Two-Stage Multiple Comparisons for Exponential Location Parameters with the Average

In this paper, the design constant is determined based on a criterion of probability of correct detection for a given deviation of k location parameters from the average being at least γ for the two-stage multiple comparisons for location parameters of exponential distributions when scale parameters are unequal. All required values for determining the design constant and then the total sample size for a two-stage procedure are listed in tables for practical use. For illustrative purposes, two examples are given to demonstrate the sample size determination for this two-stage procedure.

Shrinkage estimation for the difference between exponential guarantee time parameters

This paper studies the shrinkage estimation for the difference between location parameters of exponential distributions when it is suspected but uncertain whether the two parameters are equal. A pre-test estimator and a shrinkage estimator after pre-test are proposed. Both the suboptimal levels of significance for the pre-test estimator in a special case and suboptimal values of shrinkage coefficients for the shrinkage estimator are obtained based on a regret function.

Testing Homogeneity of Uniform Scale Distributions against Two-Sided and One-Sided Alternatives

Abstract Consider the model where Xij, i = 1, 2, …, k; j = 1, …, n i are independent uniform random variables with scale parameter θ i > 0. Test H 0: θl = ··· = θ k versus H 2: not H 0. Also consider the alternative H 1: θl ≤ ··· ≤ θ k . For H 0 versus H 2 and n i = n, we obtain a complete class of constant-size permutation invariant tests and show that each test in the class is unbiased. The likelihood ratio test and others are in this class. For H 0 versus H 1 we obtain a complete class of constant-size tests based on a set of variables that is a transformation of the sufficient statistics. Again we show that each test in the class is unbiased. The likelihood ratio test is in this class. We derive the exact and asymptotic distribution of the likelihood ratio test. All results also hold for testing homogeneity of location parameters of exponential distributions. This latter case is of considerable practice importance in reliability.