Conjecture Sur Les Familles Exponentielles

Authors: Idriss olivier BADO

in this article we will establish some properties of random variables and then we will propose a conjecture related to the exponential family. This conjecture seems interesting to me. Our results are based on the consideration of continuous random variables $X_{i}$ defined on the same space $\Omega$ and the same super-extra density law of parameter $\theta_{i} $ and canonique function $T$ Let $n\in \mathbb{N}^{*}$ Considering the random variable $J$ and $I$ a subsect of $\{1,2,..n\}$ such that : $ X_{J}=\inf_{i\in I}(X_{i})$ we show that : $$\forall i\in I:\mathbb{P}( J=i)=\frac{\theta_{i}\prod_{j\in I}c(\theta_{j})}{\sum_{j\in I}\theta_{j}}\int_{T(\Omega)}e^{-x}dx$$. We conjecture that if the density of $ X_{i}$ is $ c(\theta_{i})e^{-\theta_{i}T(x)}\mathbf{1}_{\Omega}(x)$ Hence $\exists h,r$ two functions h such that $$ \forall i\in I:\mathbb{P}( J=i)=\frac{r(\theta_{i})\prod_{j\in I}h(\theta_{j})}{\sum_{j\in I}r(\theta_{j})}\int_{T(\Omega)}e^{-x}dx$$

Comments: 5 Pages.

Download: PDF

Submission history

[v1] 2019-05-18 15:08:29

Unique-IP document downloads: 18 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus