# Questions tagged [exponential-family]

A set of distributions (eg, normal, $\chi^2$, Poisson, etc) that share a specific form. Many of the distributions in the exponential family are standard, workhorse distributions in statistics, w/ convenient statistical properties.

368 questions
Filter by
Sorted by
Tagged with
112 views

• 431
1 vote
54 views

1 vote
44 views

• 349
1 vote
45 views

286 views

### Asymptotic normality of MLE

We know under regularity conditions the MLE is asymptotically normal. Usually, it is said that in practice it's hard to check these assumptions. However, I wondered whether we can claim that these ...
• 140
1 vote
135 views

### How to prove that von mises distribution belongs to exponential family?

Can anyone help me prove this, I'm not able to simplify the distribution to find the sufficient statistics, log normalizer, etc.
• 11
211 views

### Finding UMVUE of difference of exponentals

Let $X_1, \ldots, X_n$ be a sample from an exponential distribution with p.d.f. $f(x; \theta) = \theta e^{-\theta x}$ for $x > 0$ where $\theta > 0$ is an unknown parameter. I would like to find ...
40 views

### How can write the probability density function of generalized exponential distribution as exponential family?

I want to use GAM method and generalized exponential distribution for response variable. I know GAM method is a generalized GLM method and the distribution of response variable must be in exponential ...
207 views

• 1,096
### How is this implied by the properties of the exponential, gamma, and $\chi^2$ distributions?
Let's say we have the random variables $X_1, \dots, X_p$. Furthermore, say that these random variables are a random sample from a PDF of the form f_\tau (x) = \begin{cases} \tau x^{\tau-1}, & 0 ...