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Statistical Hypothesis Testing with SAS and R by Dirk Taeger, Sonja Kuhnt

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Chapter 6

Exponential Distribution

The exponential distribution is typically used to model waiting times, for example, to model survival times of cancer patients or life times of machine components. Often these are waiting times between the events of a Poisson distribution. The exponential distribution is memoryless in the sense that the remaining waiting time at a specific time point is independent of the time which has already elapsed since the last event. The parameter c06-math-0001 can be seen as a constant failure rate (failures over a specific unit such as hours).

6.1 Test on the parameter of an exponential distribution

6.1.1 z-test on the parameter of an exponential distribution

Description: Tests if the parameter c06-math-0002 of an exponential distribution differs from a specific value c06-math-0003.
Assumptions:
  • Data are measured on an interval or ratio scale.
  • Data are randomly sampled from an exponential distribution.
  • The random variables c06-math-0004 are exponentially distributed with parameter c06-math-0005.
  • Let be the probability ...

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