Questions tagged [curved-exponential-family]

Let $X_1, X_2..., X_n$ follows iid negative exponential distribution with pdf $$f(x) = \frac{1}{\theta^2} \: e^{-\frac{(x-\theta)}{\theta^2}} \: \: I_{(x>\theta)} $$ I have to show whether the minimal sufficient statistic for this pdf is complete or…

Is there any example of curved exponential family with $T$ being a complete statistic? Here $T$ is the sufficient statistic.

I am reading about point estimation from Theory of Point Estimation by Lehmann and Casella (1999). I couldn't understand the following point mentioned in p.24, under the exponential family of distributions : An exponential family of distributions…