Can a two parameter Weibull Distribution be written as an exponential family form?

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Hi guys, I was wondering whether the two parameter Weibull Distribution belongs to a exponential family?

Answers (1)

John BG
John BG on 27 Mar 2017
makedist generates exactly the same points when the setting
Weibull a = Exponential mu
a:scale b:shape
pd1=makedist('Weibull','a',2,'b',2) % a:scale b:shape
plot(y,'r');grid on
hold all
pd2=makedist('Weibull','a',2,'b',1) % a:scale b:shape
pd3=makedist('Exponential','mu',2) % a:scale b:shape
y2 blue and y3 black are completely overlapped.
ans =
if you find these lines useful would you please mark my answer as Accepted Answer?
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thanks in advance for time and attention
John BG
  1 Comment
Keqiao Li
Keqiao Li on 28 Mar 2017
Hi John, thank you for your answer. Your answer is quite useful. But since Weibull distribution can be reduced to exponential distribution, this is because the shape parameter is "1" and a = mu? Is this the only condition when Weibull distribution can be considered as a exponential family (not just exponential distribution)?

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