Sequential testing of the size of an exponential sample

Abstract

The order statistics of a sample of unknown size n from an exponential distribution, with unknown mean, are observed sequentially. A sequential probability Ratio Test (SPRT) is obtained for discriminating between different values of n. An algorithm is given which enables the Average Sample Number (ASN) and Operating characteristic (OC) curves to be found exactly. A conservative approximation to the Average Time to Termination (ATT) of the test is derived. Examples given suggest that this test provides a useful reduction in the ATT compared to fixed sample size tests.

Keywords:

• Aroian' direct method
• censored sampling
• Jelinski-Moranda model
• linear pure death process
• sequential probability ratio test