{"id":1973,"date":"2026-10-08T09:05:34","date_gmt":"2026-10-08T08:05:34","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-gama\/"},"modified":"2026-10-08T09:05:34","modified_gmt":"2026-10-08T08:05:34","slug":"calculadora-distribuicao-gama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-gama\/","title":{"rendered":"Calculadora da distribui\u00e7\u00e3o gama"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Calcule probabilidades, densidade e momentos da distribui\u00e7\u00e3o gama<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"1973\" data-favorite-title=\"Distribui\u00e7\u00e3o gama\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-gama\/\" data-favorite-excerpt=\"Calcule a densidade, a probabilidade acumulada e da cauda, a probabilidade de intervalo, m\u00e9dia, vari\u00e2ncia e moda da distribui\u00e7\u00e3o gama. Informe o par\u00e2metro de forma k, a escala \u03b8 e um valor ou intervalo.\" aria-label=\"Adicionar aos favoritos\" data-favorite-icon=\"icon icon-wpcalc-distribution-histogram\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-gama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-1973\" data-post=\"1973\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Par\u00e2metro de forma<\/label><div class=\"term\">k<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"parmetro_de_forma\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 2\" min=\"0.01\" value=\"2\"\/><small id=\"calc-info-1\">Forma k: controla o formato da curva. k = 1 d\u00e1 a distribui\u00e7\u00e3o exponencial; k inteiro d\u00e1 a distribui\u00e7\u00e3o Erlang (tempo de espera at\u00e9 o k-\u00e9simo evento).<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Par\u00e2metro de escala<\/label><div class=\"term\">\u03b8<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"parmetro_de_escala\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 3\" min=\"1.0E-9\" value=\"3\"\/><small id=\"calc-info-2\">Escala \u03b8 na mesma unidade de x. Deve ser maior que 0.<\/small><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">O que calcular<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"o_que_calcular\"><option value=\"point\" selected>Em um \u00fanico valor x<\/option><option value=\"interval\">Em um intervalo [a, b]<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-4\">Valor<\/label><div class=\"term\">x<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"valor\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 4\" min=\"0\" value=\"4\"\/><small id=\"calc-info-4\">O valor x no qual avaliar (na mesma unidade de \u03b8).<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">Limite inferior<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"limite_inferior\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 3\" min=\"0\" value=\"3\"\/><small id=\"calc-info-5\">In\u00edcio do intervalo.<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">Limite superior<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"limite_superior\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 9\" min=\"0\" value=\"9\"\/><small id=\"calc-info-6\">Fim do intervalo; deve ser maior que o limite inferior.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"1973\">Calcular<\/button><button type=\"reset\">Redefinir<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calcular automaticamente<\/label><small>Se ativado, o resultado \u00e9 atualizado automaticamente quando voc\u00ea altera qualquer valor.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Resultados da distribui\u00e7\u00e3o gama<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Densidade no valor<\/span><span class=\"result-term\">f(x)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Probabilidade acumulada P(X \u2264 x)<\/span><span class=\"result-term\">F(x)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Probabilidade da cauda superior P(X &gt; x)<\/span><span class=\"result-term\">S(x)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Probabilidade no intervalo P(a \u2264 X \u2264 b)<\/span><span class=\"result-term\">P(a\u2264X\u2264b)<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>M\u00e9dia<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"unidades de \u03b8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Vari\u00e2ncia<\/span><\/span><span class=\"field-value\" id=\"result-6\" data-unit=\"unidades de \u03b8\u00b2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-7\"><span class=\"field-title\"><span>Moda (valor mais prov\u00e1vel)<\/span><\/span><span class=\"field-value\" id=\"result-7\" data-unit=\"unidades de \u03b8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-8\"><span class=\"field-title\"><span>Como funciona e interpreta\u00e7\u00e3o<\/span><\/span><span class=\"field-value\" id=\"result-8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copiar link para este c\u00e1lculo<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Deixar um coment\u00e1rio<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"1973\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">O que voc\u00ea achou deste resultado?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Curti <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">\u00datil <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confuso <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Decepcionado <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Impreciso <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>F\u00f3rmula da distribui\u00e7\u00e3o gama<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">F\u00f3rmula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ f(x) = \\frac{x^{k-1} e^{-x\/\\theta}}{\\Gamma(k)\\,\\theta^k}, \\qquad F(x) = P\\!\\left(k, \\frac{x}{\\theta}\\right), \\quad x \\ge 0 \\\\ \\mu = k\\theta, \\qquad \\sigma^2 = k\\theta^2, \\qquad \\text{moda} = (k-1)\\theta \\ \\text{para } k \\ge 1 \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(k\\) \u2014 par\u00e2metro de forma, \\(k &gt; 0\\); controla o formato da curva<\/li>\n<li>\\(\\theta\\) \u2014 par\u00e2metro de escala, \\(\\theta &gt; 0\\), na mesma unidade de \\(x\\)<\/li>\n<li>\\(\\Gamma(k)\\) \u2014 a fun\u00e7\u00e3o gama, que generaliza o fatorial (\\(\\Gamma(n) = (n-1)!\\) para inteiros)<\/li>\n<li>\\(P(k, x\/\\theta)\\) \u2014 a fun\u00e7\u00e3o gama incompleta inferior regularizada, que fornece a FDA<\/li>\n<\/ul>\n<p>A primeira linha define a densidade de probabilidade e a fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada da distribui\u00e7\u00e3o gama com parametriza\u00e7\u00e3o por escala; a segunda linha traz a m\u00e9dia, a vari\u00e2ncia e a moda. A probabilidade de um intervalo \u00e9 \\(P(a \\le X \\le b) = F(b) - F(a)\\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Distribui\u00e7\u00e3o gama \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> o tempo de espera de um sistema segue uma distribui\u00e7\u00e3o gama com forma \\(k = 2\\) e escala \\(\\theta = 3\\) horas. Encontre a densidade, a probabilidade acumulada e a probabilidade da cauda superior em \\(x = 4\\) horas.<\/p>\n<p>\\[ f(4) = \\frac{4^{1} e^{-4\/3}}{\\Gamma(2)\\cdot 3^2} = \\frac{4 \\cdot 0{,}2636}{1 \\cdot 9} \\approx 0{,}1172 \\]<\/p>\n<p>Como \\(k\\) \u00e9 inteiro, a FDA tem forma fechada: \\(F(x) = 1 - e^{-x\/\\theta}\\left(1 + x\/\\theta\\right)\\):<\/p>\n<p>\\[ F(4) = 1 - e^{-4\/3}\\left(1 + \\tfrac{4}{3}\\right) = 1 - 0{,}2636 \\cdot 2{,}3333 \\approx 0{,}3849 \\]<\/p>\n<p>\\[ P(X &gt; 4) = 1 - F(4) \\approx 0{,}6151 \\]<\/p>\n<p><strong>Resultado:<\/strong> \\(f(4) \\approx 0{,}1172\\) por unidade, \\(P(X \\le 4) \\approx 0{,}3849\\) (38,49%), \\(P(X &gt; 4) \\approx 0{,}6151\\) (61,51%). A m\u00e9dia \u00e9 \\(k\\theta = 6\\) horas, a vari\u00e2ncia \u00e9 \\(k\\theta^2 = 18\\) e a moda \u00e9 \\((k-1)\\theta = 3\\) horas.<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Informe o <strong>par\u00e2metro de forma<\/strong> \\(k\\). Ele deve ser positivo; \\(k = 1\\) resulta na distribui\u00e7\u00e3o exponencial e valores inteiros de \\(k\\) d\u00e3o a distribui\u00e7\u00e3o de Erlang.<\/li>\n<li>Informe o <strong>par\u00e2metro de escala<\/strong> \\(\\theta\\), um n\u00famero positivo na mesma unidade dos seus dados.<\/li>\n<li>Escolha <strong>o que calcular<\/strong>: \u201cEm um \u00fanico valor x\u201d ou \u201cEm um intervalo [a, b]\u201d.<\/li>\n<li>Para um \u00fanico valor, informe o <strong>valor<\/strong> \\(x \\ge 0\\). A calculadora devolve a densidade, a probabilidade acumulada \\(P(X \\le x)\\), a probabilidade da cauda superior \\(P(X &gt; x)\\), al\u00e9m da m\u00e9dia, da vari\u00e2ncia e da moda.<\/li>\n<li>Para um intervalo, informe o <strong>limite inferior<\/strong> \\(a\\) e o <strong>limite superior<\/strong> \\(b\\) (com \\(b &gt; a\\)). Voc\u00ea obt\u00e9m \\(P(a \\le X \\le b)\\) junto com as densidades e os valores acumulados nos dois extremos.<\/li>\n<li>Consulte o painel \u201cComo funciona e interpreta\u00e7\u00e3o\u201d para uma leitura em linguagem simples dos seus n\u00fameros.<\/li>\n<\/ol>\n<h2>O que \u00e9 a distribui\u00e7\u00e3o gama?<\/h2>\n<p>A distribui\u00e7\u00e3o gama \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua para grandezas positivas \u2014 tempos de espera, totais de sinistros de seguro, volumes de chuva, tempos de vida \u00fatil. Ela tem dois par\u00e2metros: a forma \\(k\\), que determina o formato geral da curva, e a escala \\(\\theta\\), que a estica ou comprime ao longo do eixo x. O resultado \u00e9 uma fam\u00edlia extremamente flex\u00edvel: para \\(k\\) pequeno, a densidade \u00e9 fortemente assim\u00e9trica \u00e0 direita, com pico pr\u00f3ximo de zero; para \\(k\\) grande, ela se torna quase sim\u00e9trica e em forma de sino.<\/p>\n<p>A distribui\u00e7\u00e3o tem uma interpreta\u00e7\u00e3o natural como tempo de espera. Se eventos ocorrem aleatoriamente a uma taxa m\u00e9dia constante (um <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-de-poisson\/\">processo de Poisson<\/a>), o tempo total at\u00e9 o \\(k\\)-\u00e9simo evento segue uma distribui\u00e7\u00e3o gama com forma \\(k\\) e escala \\(\\theta\\) igual ao tempo m\u00e9dio entre eventos. Com \\(k = 1\\), ela se reduz \u00e0 <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-exponencial\/\">distribui\u00e7\u00e3o exponencial<\/a> (a espera por um \u00fanico evento); com \\(k\\) inteiro, ela \u00e9 chamada de distribui\u00e7\u00e3o de Erlang.<\/p>\n<p>Interpretar os resultados \u00e9 simples. A densidade \\(f(x)\\) mostra o qu\u00e3o prov\u00e1veis s\u00e3o valores pr\u00f3ximos de \\(x\\), por unidade de medida. A probabilidade acumulada \\(F(x)\\) \u00e9 a chance de um valor no m\u00e1ximo igual a \\(x\\), e a cauda superior \\(S(x) = 1 - F(x)\\) \u00e9 a chance de ultrapassar \\(x\\) \u2014 muitas vezes a grandeza de interesse em problemas de confiabilidade e filas. A m\u00e9dia \\(k\\theta\\) \u00e9 o valor esperado, a vari\u00e2ncia \\(k\\theta^2\\) mede a dispers\u00e3o e a moda \\((k-1)\\theta\\) \u00e9 o valor isolado mais prov\u00e1vel. Como a distribui\u00e7\u00e3o \u00e9 assim\u00e9trica \u00e0 direita, a moda fica abaixo da m\u00e9dia.<\/p>\n<h2>Parametriza\u00e7\u00e3o, premissas e dicas pr\u00e1ticas<\/h2>\n<ul>\n<li><strong>Escala vs. taxa:<\/strong> esta calculadora usa a escala \\(\\theta\\). Muitos livros e programas usam em vez disso a taxa \\(\\beta = 1\/\\theta\\). Se a sua fonte informa uma taxa, digite \\(\\theta = 1\/\\beta\\) no campo do par\u00e2metro de escala. Com \\(k\\) fixo, um \\(\\theta\\) maior estica a distribui\u00e7\u00e3o (valores maiores), e uma taxa maior a encolhe.<\/li>\n<li><strong>Dom\u00ednio:<\/strong> a distribui\u00e7\u00e3o gama est\u00e1 definida apenas para \\(x \\ge 0\\). Valores negativos s\u00e3o rejeitados; informe zero ou valores positivos.<\/li>\n<li><strong>Moda para k pequeno:<\/strong> a moda \\((k-1)\\theta\\) s\u00f3 existe quando \\(k \\ge 1\\). Para \\(k &lt; 1\\), a densidade \u00e9 ilimitada em zero, e por isso a calculadora informa moda igual a 0.<\/li>\n<li><strong>Aproxima\u00e7\u00e3o normal:<\/strong> para \\(k\\) grande (aproximadamente \\(k &gt; 30\\)), a distribui\u00e7\u00e3o gama \u00e9 bem aproximada por uma distribui\u00e7\u00e3o normal com m\u00e9dia \\(k\\theta\\) e vari\u00e2ncia \\(k\\theta^2\\).<\/li>\n<li><strong>Escolha dos par\u00e2metros:<\/strong> se voc\u00ea conhece a m\u00e9dia \\(\\mu\\) e a vari\u00e2ncia \\(\\sigma^2\\) desejadas, estime \\(k = \\mu^2\/\\sigma^2\\) e \\(\\theta = \\sigma^2\/\\mu\\). Depois voc\u00ea pode refin\u00e1-los ajustando as probabilidades acumuladas que observa.<\/li>\n<li><strong>Modelos relacionados:<\/strong> a distribui\u00e7\u00e3o gama \u00e9 uma alternativa comum \u00e0 <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-weibull\/\">distribui\u00e7\u00e3o de Weibull<\/a> e \u00e0 <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-log-normal\/\">distribui\u00e7\u00e3o lognormal<\/a> para modelar dados positivos e assim\u00e9tricos \u00e0 direita, como tempos de vida e valores de sinistros \u2014 as tr\u00eas diferem principalmente no formato das caudas.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calcule a densidade, a probabilidade acumulada e da cauda, a probabilidade de intervalo, m\u00e9dia, vari\u00e2ncia e moda da distribui\u00e7\u00e3o gama. Informe o par\u00e2metro de forma k, a escala \u03b8 e um valor ou intervalo.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[12],"tags":[34],"class_list":["post-1973","post","type-post","status-publish","format-standard","hentry","category-estatistica","tag-distribuicoes"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/1973","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/comments?post=1973"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/1973\/revisions"}],"predecessor-version":[{"id":2593,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/1973\/revisions\/2593"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=1973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=1973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=1973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}