MVP Exponential Distribution Test

The MVP Test for Exponentiality, which assumes an unknown origin parameter, employs the following statistic:

MVP(E) =
(X - Xmin)2

The expected value of this test statistic is approximately one, for sampling from an exponential distribution. For most non-exponential distributions, the value will be much greater than one. Note though, a Chi-Square distribution, with one degree of freedom, will have an expected value less than one.

The significance (p-value) of this test is generated through simulations as follows.