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
 * 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
$$B=\times_{i=1}^{n}[x_i,y_i]\subseteq [0,1]^n;$$
 * A Copula


 * $$ V_{C}\left( B\right):=\sum_{\mathbf z\in \times_{i=1}^{n}\{x_i,y_i\}} (-1)^{N(\mathbf z)} C(\mathbf z)\ge 0;$$

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 $$B$$.

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
 * Sklar's Theorem


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

(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)