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Can someone clarify if it is safe to declare that a distribution is not exponential if the mean and standard deviation are not equal, for example coefficient of variance, c < 1 and that it is exponential if c = 1.

The question is based on the argument that if this is indeed true then why are there so many tests out there that test the hypothesis?

Many thanks.

Alex
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Counter Example: $X \sim N(1,1)$

So, the answer is no. Just because a distribution's mean and standard deviation are identical it does not follow that the distribution is an exponential.

response
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  • Thankyou. However does it follow then that if the mean and standard deviation are not equal then categorically it is not exponentially distributed? – Alex Oct 24 '13 at 14:12
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    The answer is yes as long as the means and standard deviation are population measures and not based on sample data. – response Oct 24 '13 at 14:17
  • Agree. Many thanks. – Alex Oct 24 '13 at 14:19