User:OluyemiO

Oluyemi Oyeniran

I created my user page on this wikipedia site, I will like you to go through and give me feedback. Thank you.

Five things I learnt about Wikipedia

Five out of the numerous things I learnt about Wikipedia

1. Wikipedia is a free online multilingual encyclopaedia. The word Wikipedia (pronounced /ˌwɪkɪˈpidi.ə/ or /ˌwɪkiˈpidi.ə/ WIK-i-PEE-dee-ə) is a portmanteau from wiki (a technology for creating collaborative websites, from the Hawaiian word wiki, meaning "quick") and encyclopedia . It is unique in the sense that its content can be edit by any user(s) and probably that’s why there is so much criticism about the encycopedia.

2. Wikipedia is just a part of several wiki projects owned by a non profit organisation – Wikimedia Foundation Inc.. It has twelve major portals (introductory page for a given topic) that gives you information about almost anything or topic, which includes

• General reference,
• History and events,
• Philosophy and thinking,
• Culture and the arts,
• Mathematics and Logic,
• Religion and belief systems,
• Geography and places,
• Natural and physical sciences,
• Society and social sciences
• Health and fitness,
• People and self,
• Technology and applied sciences

3. Wikipedia operates on this major five pillars –

• Online encyclopedia,
• neutral point of view,
• free content that anyone can edit and distribute ,
• do not have firm rules,
• Wikipedians should interact in a respectful and civil manner

4. Wikimedia runs an annual conference for wikipedia and its sister projects - Wiktionary, Wikiquote, Wikibooks, Wikisource, Wikimedia Commons, Wikispecies, Wikinews, Wikiversity, Wikimedia Incubator and Meta-Wiki

5. The operation of Wikipedia depends on MediaWiki, a custom-made, free and open source wiki software platform written in PHP and built upon the MySQL database.

Some Complicated Math Formula

• A Copula

$B=\times _{i=1}^{n}[x_{i},y_{i}]\subseteq [0,1]^{n};$

$V_{C}\left(B\right):=\sum _{\mathbf {z} \in \times _{i=1}^{n}\{x_{i},y_{i}\}}(-1)^{N(\mathbf {z} )}C(\mathbf {z} )\geq 0;$

where the $N(\mathbf {z} )=\operatorname {card} \{k\mid z_{k}=x_{k}\}$. $V_{C}\left(B\right)$ is the so called C-volume of $B$.

• Sklar's Theorem

For the bivariate case, Sklar's theorem can be stated as follows. For any bivariate distribution function $H(x,y)$, let $F(x)=H(x,\infty )$ and $G(y)=H(\infty ,y)$ be the univariate marginal probability distribution functions. Then there exists a copula $C$ such that

$H(x,y)=C(F(x),G(y))\,$

(where we have identified the distribution $C$ with its cumulative distribution function). Moreover, if marginal distributions $F(x)$ and $G(y)$ are continuous, the copula function $C$ is unique. Otherwise, the copula $C$ is unique on the range of values of the marginal distributions.

To understand the density function of the coupled random variable $Y_{H}$ it should be noticed that $\operatorname {P} \left[Y_{H}\in [x,x+dx]\times [y,y+dy]\right]=H(x+dx,y+dy)-H(x+dx,y)-H(x,y+dy)+H(x,y)$.

Expectation reads $\operatorname {E} \left[g(X,Y)\right]=\int \int g(x,y)\mathrm {d} H(x,y)=\int \int g(F_{X}^{-1}(x),F_{Y}^{-1}(y))\mathrm {d} C(x,y)=\int _{0}^{1}\int _{0}^{1}g(F_{X}^{-1}(x),F_{Y}^{-1}(y)){\frac {\partial }{\partial x}}{\frac {\partial }{\partial y}}C(x,y)\mathrm {d} (x,y)$

• The Gaussian copula function is

$C_{\rho }(u,v)=\Phi _{\rho }\left(\Phi ^{-1}(u),\Phi ^{-1}(v)\right)$

where $u,v\in [0,1]$ and $\Phi$ denotes the standard normal cumulative distribution function.

Differentiating C yields the copula density function:

$c_{\rho }(u,v)={\frac {\varphi _{X,Y,\rho }(\Phi ^{-1}(u),\Phi ^{-1}(v))}{\varphi (\Phi ^{-1}(u))\varphi (\Phi ^{-1}(v))}}$

where

$\varphi _{X,Y,\rho }(x,y)={\frac {1}{2\pi {\sqrt {1-\rho ^{2}}}}}\exp \left(-{\frac {1}{2(1-\rho ^{2})}}\left[{x^{2}+y^{2}}-2\rho xy\right]\right)$

is the density function for the standard bivariate Gaussian with Pearson's product moment correlation coefficient ρ and $\varphi$ is the standard normal density.

Acknowledgment

• http://en.wikipedia.org/wiki/Main_Page
• http://en.wikipedia.org/wiki/Copula_(statistics)