Exponential Distribution GARP vs. Wiki

[OHe1274]

Hello

I am a little bit confused with regards to the formulas for the exponential distribution incl:
-moments
-PDF / CDF
-VaR / ES

In GARP materials (book2, p. 39) the exponential is described with a mean of:
E[Y] = b
wheras wikipedia and also BT says:
E[Y] = 1/lambda

Same holds for other moments etc.
I could imagine that wikipedia holds the correct interpretation
but I don't get why GARP uses a complete other definition for the exponential.

Does anybody have an idea? Am I missing something?


Thanks in advance and regards
Oliver

 

[OHe1274]

..short update, both notations seem to be equivalent i.e. just substitute lambda = 1/beta

 

[yelan376]

Great observation, Oliver. This confusion is super common because the exponential distribution has two parameterizations. GARP typically uses the scale parameter (β), while academic texts and Wikipedia often use the rate parameter (λ).

They’re reciprocals: β = 1/λ. So, the formulas for mean, variance, PDF, CDF, etc., all stay consistent once you substitute accordingly.