<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/f5bc037a-6b9c-49f9-b621-0514b8db65a2/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls17 wsb"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls17 wsb">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls17 wsb"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls17 wsb">Estatística Aplicada - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls17 wsb"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls17 wsb">DISTRIBUIÇÃO GAMA </div><div class="t m0 x1 h6 y8 ff4 fs3 fc1 sc0 ls17 wsb">Função gama </div><div class="t m0 x1 h7 y9 ff2 fs4 fc0 sc0 ls17 wsb">Seja <span class="ff5 ws0">\ue7d9<span class="_0 blank"> </span>\u2208 \u211d<span class="fs5 ls0 v1">\ueb3e</span></span>. </div><div class="t m0 x3 h8 ya ff5 fs4 fc0 sc0 ls17 ws1">\u0393<span class="v2">(</span><span class="ls1">\ue7d9<span class="ls2 v2">)</span></span><span class="ws2">=<span class="_1 blank"> </span>\uedb1<span class="_2 blank"> </span>\ue754 <span class="fs5 ws3 v1">\uec08 \ueb3f\ueb35</span><span class="wsb"> \ue741<span class="_3 blank"> </span><span class="fs5 ws4 v1">\ueb3f\uebeb </span> \ue740\ue754</span></span></div><div class="t m0 x4 h9 yb ff5 fs5 fc0 sc0 ls17">\uebb6</div><div class="t m0 x5 ha yc ff5 fs5 fc0 sc0 ls3">\ueb34<span class="ff2 fs4 ls17 wsb v3"> </span></div><div class="t m0 x1 h8 yd ff2 fs4 fc0 sc0 ls17 wsb">Resultado: <span class="ff5 ls4">\ue7c1<span class="ls17 ws1 v2">(</span><span class="ls5">\ue74a<span class="ls2 v2">)</span><span class="ls6">=<span class="ls17 ws1 v2">(</span><span class="ls17 ws5">\ue74a \u2212 1<span class="ws1 v2">)</span></span></span></span>\ue7c1<span class="ls17 ws1 v2">(</span><span class="ls17 ws5">\ue74a<span class="_4 blank"> </span>\u2212 1<span class="ls7 v2">)</span><span class="ls6">=</span><span class="ws1 v2">(</span>\ue74a \u2212 1<span class="ws1 v2">)</span><span class="wsb">!<span class="_5 blank"> </span> ,<span class="_5 blank"> </span> \ue74a<span class="_1 blank"> </span>\u2208<span class="_1 blank"> </span>\u2124<span class="fs5 ls0 v1">\ueb3e</span></span></span></span> </div><div class="t m0 x1 h6 ye ff4 fs3 fc1 sc0 ls17 wsb">Função gama modificada<span class="_6 blank"> </span> </div><div class="t m0 x1 h7 yf ff2 fs4 fc0 sc0 ls17 wsb">Seja <span class="ff5 ws0">\ue7d9<span class="_0 blank"> </span>\u2208 \u211d<span class="fs5 ls0 v1">\ueb3e</span></span>. <span class="_7 blank"> </span><span class="ff5 ls8 v4">\u0393</span><span class="ff5 ws1 v5">(<span class="ls1 v6">\ue7d9</span>)</span></div><div class="t m0 x6 hb y10 ff5 fs4 fc0 sc0 ls9">\ue7da<span class="fs5 lsa v7">\uec08</span><span class="ls17 ws2 v8">=<span class="_1 blank"> </span>\uedb1<span class="_2 blank"> </span>\ue754 </span><span class="fs5 ls17 ws6 v9">\uec08 \ueb3f<span class="_8 blank"></span>\ueb35 <span class="fs4 wsb va"> \ue741<span class="_3 blank"> </span></span><span class="ws7">\ueb3f<span class="_8 blank"></span>\uec09\uebeb <span class="fs4 wsb va"> \ue740\ue754</span></span></span></div><div class="t m0 x7 h9 y11 ff5 fs5 fc0 sc0 ls17">\uebb6</div><div class="t m0 x8 ha y12 ff5 fs5 fc0 sc0 lsb">\ueb34<span class="ff2 fs4 ls17 wsb v3"> </span></div><div class="t m0 x1 hc y13 ff2 fs4 fc0 sc0 ls17 wsb"> </div><div class="t m0 x1 hc y14 ff2 fs4 fc0 sc0 ls17 wsb">Útil pra mostrar que a densidade integra 1 e para o cálculo da esperança <span class="_8 blank"></span>e variância. </div><div class="t m0 x1 h6 y15 ff4 fs3 fc1 sc0 ls17 wsb">Distribuição gama </div><div class="t m0 x1 h7 y16 ff2 fs4 fc0 sc0 ls17 wsb">Seja <span class="ff5 lsc">\ue73a</span> v.a contínua. <span class="ff5 lsc">\ue73a</span> tem distribuição gama se sua densidade é da forma: </div><div class="t m0 x9 h7 y17 ff5 fs4 fc0 sc0 ls17">\ue742</div><div class="t m0 xa hd y18 ff5 fs5 fc0 sc0 lsd">\uebd1<span class="fs4 ls17 ws1 vb">(<span class="lse v6">\ue754</span><span class="ls7">)<span class="ls6 v6">=</span></span><span class="v6">\uf250<span class="ls9 vc">\ue7da</span></span></span><span class="lsf vd">\uec08</span><span class="fs4 ls17 wsb ve"> \ue754<span class="_9 blank"> </span></span><span class="ls17 ws6 vd">\uec08<span class="_6 blank"></span>\ueb3f\ueb35 </span><span class="fs4 ls17 wsb ve"> \ue741<span class="_9 blank"> </span></span><span class="ls17 wsb vd">\ueb3f\uec09 \uebeb</span></div><div class="t m0 xb hb y19 ff5 fs4 fc0 sc0 ls4">\ue7c1<span class="ls17 ws1 v2">(</span><span class="ls1">\ue7d9<span class="ls10 v2">)</span><span class="ls17 wsb v8"> ,<span class="_5 blank"> </span> \ue754<span class="_1 blank"> </span>\u2265<span class="_1 blank"> </span>0</span></span></div><div class="t m0 xc h7 y1a ff5 fs4 fc0 sc0 ls17 wsb">0 ,<span class="_5 blank"> </span> <span class="ff6">caso contrário </span></div><div class="t m0 xd he y17 ff6 fs4 fc0 sc0 ls17 wsb"> </div><div class="t m0 x1 h7 y1b ff2 fs4 fc1 sc0 ls17 wsb">Notação: <span class="ff5 fc0 ws8">\ue73a<span class="_0 blank"> </span>\u223c<span class="_4 blank"> </span>\ue729\ue73d\ue749\ue73d<span class="_6 blank"> </span>(\ue7d9<span class="_9 blank"> </span>, \ue7da<span class="_6 blank"></span>)</span><span class="fc0"> </span></div><div class="t m0 x1 hc y1c ff2 fs4 fc1 sc0 ls17 wsb"> </div><div class="t m0 x1 h8 y1d ff2 fs4 fc1 sc0 ls17 wsb">Esperança: <span class="ff5 fc0 ls11">\ue727<span class="ls17 ws1 v2">[</span><span class="lsc">\ue73a<span class="ls2 v2">]</span><span class="ls12">=<span class="fs5 ls17 vf">\uec08</span></span></span></span></div><div class="t m0 xe h9 y1e ff5 fs5 fc0 sc0 ls13">\uec09<span class="ff2 fs4 fc1 ls17 wsb v10"> </span></div><div class="t m0 x1 hc y1f ff2 fs4 fc1 sc0 ls17 wsb"> </div><div class="t m0 x1 h7 y20 ff2 fs4 fc1 sc0 ls17 wsb">Variância: <span class="ff5 fc0 ws9">\ue738\ue73d\ue74e<span class="_6 blank"></span>(\ue73a<span class="_6 blank"></span>) =<span class="_a blank"> </span><span class="fs5 vf">\uec08</span></span></div><div class="t m0 xf h9 y21 ff5 fs5 fc0 sc0 ls14">\uec09<span class="fs6 ls15 v11">\uec2e</span><span class="ff2 fs4 fc1 ls17 wsb v10"> </span></div><div class="t m0 x1 hf y22 ff3 fs3 fc1 sc0 ls17 wsb">Distribuição exponencial \u2013 Caso particular da dis<span class="_6 blank"> </span>tribuição gama<span class="ff2"> </span></div><div class="t m0 x1 h8 y23 ff2 fs4 fc0 sc0 ls16 wsb">Se <span class="ff5 ls17 wsa">\ue73a \u223c \ue729\ue73d\ue749\ue73d<span class="_9 blank"> </span>(\ue7d9<span class="_0 blank"> </span>= 1,<span class="_b blank"> </span>\ue7da<span class="_6 blank"></span>)</span><span class="ls17">, então <span class="ff5 wsa">\ue73a<span class="_0 blank"> </span>\u223c \ue727\ue754\ue74c<span class="ws1 v2">(</span><span class="ls9">\ue7da</span><span class="ws1 v2">)</span></span>. </span></div><div class="t m0 x1 h10 y24 ff2 fs0 fc0 sc0 ls17 wsb"> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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