MVP Exponential Distribution Test

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

MVP(E) =
(X - Xmin)2
s2

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.

  • One million simulations are taken from a theoretical exponential distribution.
  • The significance is obtained by taking the proportion observed in the simulations above the test statistic.
  • A two-tailed significance value is generated.
  • After 20,000 simulations, if no values, or all values, fall above the test statistic, the p-value is estimated to be zero.
  • The program provides an abort button, to stop the p-value generation.