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This article provides a new estimator of the exponential mean life which makes use of a preliminary test of hypothesis on the scale parameter for certain life test situations where a guess of the parameter value is available from past studies. Expressions for the bias and mean square error of the proposed estimator are derived. Generalization of this result to a class of weighted estimators is also considered. [ABSTRACT FROM AUTHOR]

In many studies there is believed to be a trend in a categorical variate with a continuous variate. Often in these cases it is desired to test for the trend using k groups farmed from the continuous variable. This article is concerned with the grouping problem where the goal is essentially to maximize the asymptotic efficiency of the test. Optimal classes are given for k = 2, 3, 4, 5 and 6 for the uniform, normal and exponential distributions. Also, the number of groups to use and the "robustness" of the optimal grouping are investigated. It is noted that the "mathematical problem" in determining the optimal classes appears in other studies; a rationale for this is presented. [ABSTRACT FROM AUTHOR]

Statistical properties of the bivariate exponential distribution are investigated. Maximum likelihood and method of moments type estimates are obtained and compared with the estimates given by Arnold. The method of moments type estimates are easy to compute and highly efficient, whereas the maximum likelihood estimates are computationally inconvenient. The problem of testing for correlation in the bivariate exponential distribution is also investigated. [ABSTRACT FROM AUTHOR]