Enviado em 09/01/2015 - 11:10h
Antes de tudo , bom dia pessoal.
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\hline \
Distribuição & fdp & parâmetro & FGM & assimetria\\
\hline
Bernoulli & $p^k (1-p)^{1-k}$ & $p \in (0,1)$ & $q+pe^t$ & $\frac{1-2p}{\sqrt{pq}}$\\
\hline \
Binomial & ${n\choose k}p^k(1-p)^{n-k}$ & $p \in (0,1)$ & $(1-p + pe^t)^n \!$ & $\frac{1-2p}{\sqrt{np(1-p)}}$ \\
\hline
Geometrica & $(1 - p)^{k-1}\,p\!$ & $p \in (0,1)$ & $\frac{pe^t}{1-(1-p) e^t}\!$ & $\frac{2-p}{\sqrt{1-p}}\!$\\
\hline
Binomial negativa & ${k+r-1 \choose k}\cdot (1-p)^r p^k,\!$ & r$\geq$0, $p \in (0,1)$ & $\biggl(\frac{1-p}{1 - p e^t}\biggr)^{\!r}$ & $\frac{1+p}{\sqrt{pr}}$ \\
\hline
Poisson & $\frac{\lambda^k}{k!} e^{-\lambda}$ & $\lambda\geq$0, $k\geq$0 & $\exp(\lambda (e^{t} - 1))$ & $\lambda^{-1/2}$\\
\hline
Exponencial & $\mathrm \lambda e^{-\lambda x}$ & $\lambda\geq$1,x$\geq$0 & $\frac{\lambda}{\lambda-t}$ & 2\\
\hline
Normal & $\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}$ & $\mu\in$R , $\sigma^2\geq$0 & $\exp\{ \mu t + \frac{1}{2}\sigma^2t^2 \}$ & 0\\
\hline
Gama & $\frac{1}{\Gamma(k) \theta^k} x^{k \,-\, 1} e^{-\frac{x}{\theta}}$ & k$\geq$0, $\theta\geq$0 & $\scriptstyle (1 \,-\, \theta t)^{-k}$ & $\scriptstyle \frac{2}{\sqrt{k}}$ \\
\hline
Beta & $\frac{x^{\alpha-1}(1-x)^{\beta-1}}{ Beta(\alpha,\beta)}$ & $\alpha\geq$0, $\beta\geq$0 & $1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r} \right) \frac{t^k}{k!}$ & $\frac{2\,(\beta-\alpha)\sqrt{\alpha+\beta+1}}{(\alpha+\beta+2)\sqrt{\alpha\beta}}$\\
\hline
Uniforme & $\frac{1}{a-b}$, a$\leq$x$\geq$b & $-\infty < a < b < \infty$ &$\frac{\mathrm{e}^{tb}-\mathrm{e}^{ta}}{t(b-a)},\text{para }$ t $\neq$ 0 &0 \\
\hline
Chi-quadrado &$\frac{1}{2^{\frac{k}{2}}\Gamma\left(\frac{k}{2}\right)}\; x^{\frac{k}{2}-1} e^{-\frac{x}{2}}$ &k $\in$ N (graus de liberdade) &(1-2t)^{k/2}, t<1/2 & $\scriptstyle\sqrt{8/k}$ \\
\hline
Cauchy & $\frac{1}{\pi\gamma\,\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}\!$ & $\displaystyle$ x $\in$ ($-\infty$, $+\infty$)\! & não existe & indefinido \\
\hline
Log-Normal &$\frac{1}{x\sigma\sqrt{2\pi}}\ e^{-\frac{\left(\ln x-\mu\right)^2}{2\sigma^2}}$ &x $\in$ (0, $\infty$) &não está definida nos números reais & $(e^{\sigma^2}\!\!+2) \sqrt{e^{\sigma^2}\!\!-1}$ \\
\hline
Logistica &$\frac{e^{-\frac{x-\mu}{s}}} {s\left(1+e^{-\frac{x-\mu}{s}}\right)^2}\!$ &x $\in$ (0, $\infty$) &$e^{\mu t}\operatorname{B}(1-st, 1+st)$, st $\in$(-1,1) &0 \\
\hline
Pareto & $\frac{\alpha\,x_\mathrm{m}^\alpha}{x^{\alpha+1}}$, x$\ge x_m$ &$x \in [x_\mathrm{m}, +\infty$) &$\alpha(-x_\mathrm{m}t)^\alpha\Gamma(-\alpha,-x_\mathrm{m}t)$ &$\frac{2(1+\alpha)}{\alpha-3}\,\sqrt{\frac{\alpha-2}{\alpha}}$, $\alpha>3$ \\
\hline
Weibull &$\frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-(x/\lambda)^{k}}$, x$\geq$0 &$x \in [0, +\infty)\$ &$\sum_{n=0}^\infty \frac{t^n\lambda^n}{n!}\Gamma(1+n/k), \ k\geq$1 &$\frac{\Gamma(1+3/k)\lambda^3-3\mu\sigma^2-\mu^3}{\sigma^3}$ \\
\hline
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