Optimum Test Procedures for the Mean of First Passage Time Distribution in Brownian Motion with Positive Drift (Inverse Gaussian Distribution)

Abstract

In this paper we discuss testing hypotheses and interval estimation for the mean of the first passage time distribution in Brownian motion with positive drift (inverse Gaussian distribution). Optimum test procedures and confidence intervals for both one-sided and two-sided cases are derived in their exact forms, which utilize the percentage points of standard normal and Student's t distributions. In thecase of an hypothesis with a two-sided alternative, it is shown that a uniformly most powerful (UMP) unbiased test is simply a two-tailed normal test if the nuisance parameter is known, and a two-tailed Student's t test if it is unknown.

KEY WORDS:

• Brownian Motion with Positive Drifl
• First Passage Time
• Inverse Gaussian
• UMP Unbiased Test
• Confidence Interval
• Failure-Data