User talk:Sunhong10

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Welcome to Wikipedia, Sunhong10! Thank you for your contributions. I am Vanjagenije and I have been editing Wikipedia for some time, so if you have any questions, feel free to leave me a message on my talk page. You can also check out Questions or type at the bottom of this page. Here are some pages that you might find helpful: Also, when you post on talk pages you should sign your name using four tildes ( ~ ); that will automatically produce your username and the date. I hope you enjoy editing here and being a Wikipedian!  Vanjagenije  (talk)  08:40, 30 July 2017 (UTC)
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Marshall–Olkin exponential distribution
You wrote: Let $$ \{E_B,B\subset \{1,2,\ldots,b\}\}$$ be a sequence of independent, exponentially distributed random variables, where $$ E_B $$ has mean $$ 1/\lambda_B $$. Let


 * $$ T_j=\min\{E_B:j\in B\},\ \ j=1,\ldots,b. $$

The joint distribution of $$ T=(T_1,\ldots,T_B) $$ is called the Marshall–Olkin exponential distribution with parameters $$ \{\lambda _B,B\subset \{1,2,\ldots,b\}\}$$.

So suppose b = 3. Then EB could be any of eight random variables corresponding to the eight sets $$ B \subset \{1,2,3\}:$$



\begin{align} E_\varnothing, E_{\{1\}}, E_{\{2\}}, E_{\{3\}}, E_{\{1,2\}}, E_{\{1,3\}}, E_{\{2,3\}}, E_{\{1,2,3\}} \end{align} $$ These are eight different exponential random variables. Then, for example

\begin{align} T_1 & = \min\{ E_{\{1\}}, E_{\{1,2\}}, E_{\{1,3\}}, E_{\{1,2,3\}} \} \\ T_2 & = \min\{ E_{\{2\}}, E_{\{1,2\}}, E_{\{2,3\}}, E_{\{1,2,3\}} \} \\ T_3 & = \min\{ E_{\{3\}}, E_{\{1,3\}}, E_{\{2,3\}}, E_{\{1,2,3\}} \} \\ \end{align} $$ Is that what you meant? At this point I wonder why, or whether, $$ E_\varnothing$$ is included at all, since it's not used in defining Ti.

Then you wrote: $$ (T_1,\ldots,T_B)$$. It appears this should have been $$ (T_1,\ldots,T_b) $$.

Could you add something to the article about the way in which this family of distributions arose in the firs place? Michael Hardy (talk) 15:13, 30 August 2017 (UTC)