Approximate Confidence Intervals for an Exponential Parameter from a Sequential Life Test.
MISSOURI UNIV-COLUMBIA DEPT OF STATISTICS
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A sequential life test for the exponential location parameter was given by Epstein and Sobel 1955. This sequential test may be modified by truncating the test at r sub 0 failures andor at total test time t. There may be a need or a desire to also estimate the parameter after the test decision, using the test data. Bryant and Schmee 1979 have given confidence intervals for the mean lifetime, theta, from a truncated sequential test scheme, using methods which depend heavily on numerical techniques using a computer. A more flexible approach is considered using a martingale inequality which was also given by Wald 1947 in another context. Interval estimates are found which are functions of a positive constant d which must be chosen less than an upper bound which is itself a function of the number of failures observed. It is suggested that d be chosen as a function of the sample path i.e., after the test is complete. The validity of the confidence coefficient comes into question if this posterior selection of d is employed. Simulation studies indicate that the resulting intervals are usually conservative.
- Statistics and Probability