On the boundary crossing problem in memoryless models

Abstract

The joint Laplace transform of the two sided boundary crossing stopping rule is known for the negative exponential model only under certain conditions. In this paper we eliminate the need for such conditions. Our results also apply to the boundary crossing problem for the geometric models. We further illustrate how the results can be used to obtain the distribution for the multidimensional boundary crossing stopping rules under the memoryless models.

Keywords

• Average run length
• exponential model
• geometric model
• SPRT
• cusum
• sequential analysis
• waiting times

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