{"id":1970,"date":"2026-10-08T08:48:22","date_gmt":"2026-10-08T07:48:22","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-log-normal\/"},"modified":"2026-10-08T08:48:22","modified_gmt":"2026-10-08T07:48:22","slug":"calculadora-distribuicao-log-normal","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-log-normal\/","title":{"rendered":"Calculadora da distribui\u00e7\u00e3o log-normal"},"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 de uma vari\u00e1vel lognormal<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"1970\" data-favorite-title=\"Distribui\u00e7\u00e3o log-normal\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-log-normal\/\" data-favorite-excerpt=\"Informe a m\u00e9dia e o desvio-padr\u00e3o de ln(X) para calcular probabilidades log-normais: densidade e CDF em um ponto, ou a probabilidade em um intervalo, al\u00e9m da m\u00e9dia e da mediana de X.\" 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-log-normal\/\" method=\"POST\" class=\"calculator\" id=\"calculator-1970\" data-post=\"1970\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Vari\u00e1vel normal subjacente ln(X)<\/span><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">M\u00e9dia de ln(X)<\/label><div class=\"term\">\u03bc<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"mdia_de_lnx\" id=\"field-2\" aria-describedby=\"calc-info-2\" placeholder=\"e.g. 0\" step=\"any\" value=\"0\"\/><small id=\"calc-info-2\">M\u00e9dia \u03bc da distribui\u00e7\u00e3o normal de ln(X) \u2014 n\u00e3o a m\u00e9dia de X. A mediana de X \u00e9 igual a e^\u03bc.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Desvio padr\u00e3o de ln(X)<\/label><div class=\"term\">\u03c3<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"desvio_padro_de_lnx\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.5\" min=\"1.0E-6\" value=\"0.5\"\/><small id=\"calc-info-3\">Desvio padr\u00e3o \u03c3 de ln(X); valores maiores indicam uma cauda direita mais pesada de X.<\/small><\/div><div class=\"field is-single\" id=\"input-4\"><label for=\"field-4\">O que calcular<\/label><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"o_que_calcular\"><option value=\"point\" selected>Probabilidade em um valor \u00fanico x<\/option><option value=\"interval\">Probabilidade 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-5\" hidden><label for=\"field-5\">Valor de X<\/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_de_x\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 2\" min=\"1.0E-6\" value=\"2\"\/><small id=\"calc-info-5\">Um valor positivo da vari\u00e1vel lognormal.<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">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-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1.5\" min=\"1.0E-6\" value=\"1.5\"\/><small id=\"calc-info-6\">In\u00edcio do intervalo (positivo).<\/small><\/div><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-7\">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-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 3\" min=\"1.0E-6\" value=\"3\"\/><small id=\"calc-info-7\">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=\"1970\">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> Probabilidades e par\u00e2metros<\/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 valor)<\/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 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-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>M\u00e9dia de X<\/span><span class=\"result-term\">E(X)<\/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>Mediana de X<\/span><span class=\"result-term\">Med(X)<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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-6\"><span class=\"field-title\"><span>Como funciona e interpreta\u00e7\u00e3o<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/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=\"1970\" 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 log-normal<\/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{1}{x\\,\\sigma\\sqrt{2\\pi}}\\,\\exp\\!\\left(-\\frac{(\\ln x - \\mu)^2}{2\\sigma^2}\\right), \\quad x &gt; 0 \\\\\nF(x) = P(X \\le x) = \\Phi\\!\\left(\\frac{\\ln x - \\mu}{\\sigma}\\right) \\\\\nP(a \\le X \\le b) = \\Phi\\!\\left(\\frac{\\ln b - \\mu}{\\sigma}\\right) - \\Phi\\!\\left(\\frac{\\ln a - \\mu}{\\sigma}\\right) \\\\\nE(X) = e^{\\mu + \\sigma^2\/2}, \\quad \\mathrm{Med}(X) = e^{\\mu}\n\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(\\mu\\) \u2014 m\u00e9dia da distribui\u00e7\u00e3o normal de \\(\\ln(X)\\) (e n\u00e3o a m\u00e9dia da pr\u00f3pria \\(X\\))<\/li>\n<li>\\(\\sigma\\) \u2014 desvio-padr\u00e3o de \\(\\ln(X)\\), com \\(\\sigma &gt; 0\\)<\/li>\n<li>\\(x, a, b\\) \u2014 valores positivos da vari\u00e1vel log-normal \\(X\\)<\/li>\n<li>\\(\\Phi\\) \u2014 fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada da <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-normal\/\">distribui\u00e7\u00e3o normal<\/a> padr\u00e3o<\/li>\n<\/ul>\n<p>Uma vari\u00e1vel \\(X\\) \u00e9 log-normal quando o seu logaritmo natural \\(\\ln(X)\\) segue uma distribui\u00e7\u00e3o normal. Assim, qualquer probabilidade de \\(X\\) pode ser obtida exatamente transformando para a escala normal: subtraia \\(\\mu\\), divida por \\(\\sigma\\) e leia o resultado na CDF da normal padr\u00e3o.<\/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 log-normal \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> uma vari\u00e1vel log-normal com \\(\\mu = 0\\) e \\(\\sigma = 0.5\\) para \\(\\ln(X)\\). Quais s\u00e3o a densidade e a probabilidade acumulada em \\(x = 2\\)?<\/p>\n<p>\\[ z = \\frac{\\ln x - \\mu}{\\sigma} = \\frac{\\ln 2 - 0}{0.5} = \\frac{0.6931}{0.5} \\approx 1.3863 \\]<\/p>\n<p>\\[ F(2) = \\Phi(1.3863) \\approx 0.9172, \\qquad f(2) = \\frac{e^{-(1.3863)^2\/2}}{2 \\cdot 0.5 \\cdot \\sqrt{2\\pi}} = \\frac{0.3825}{2.5066} \\approx 0.1526 \\]<\/p>\n<p><strong>Resultado:<\/strong> \\(f(2) \\approx 0.1526\\), \\(P(X \\le 2) \\approx 0.9172\\) (ou seja, 91,72%), logo \\(P(X &gt; 2) \\approx 8.28\\%\\). Os par\u00e2metros da distribui\u00e7\u00e3o s\u00e3o \\(E(X) = e^{0 + 0.125} \\approx 1.1331\\) e \\(\\mathrm{Med}(X) = e^{0} = 1\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Digite a <strong>m\u00e9dia de ln(X)<\/strong> (\\(\\mu\\)) \u2014 a m\u00e9dia dos logaritmos, e n\u00e3o dos valores brutos.<\/li>\n<li>Digite o <strong>desvio-padr\u00e3o de ln(X)<\/strong> (\\(\\sigma\\)); ele precisa ser maior que 0.<\/li>\n<li>Em <strong>O que calcular<\/strong>, escolha entre <em>Probabilidade em um \u00fanico valor x<\/em> e <em>Probabilidade em um intervalo [a, b]<\/em>.<\/li>\n<li>Para um \u00fanico valor, preencha o <strong>valor de X<\/strong>; para um intervalo, preencha o <strong>limite inferior<\/strong> e o <strong>limite superior<\/strong>. Todos os valores de \\(X\\) devem ser positivos.<\/li>\n<li>Leia os resultados: a densidade \\(f(x)\\), a probabilidade acumulada \\(F(x)\\) ou a probabilidade do intervalo, junto com a m\u00e9dia e a mediana de \\(X\\). O bloco de interpreta\u00e7\u00e3o tamb\u00e9m mostra a probabilidade complementar e a moda.<\/li>\n<\/ol>\n<h2>O que \u00e9 a distribui\u00e7\u00e3o log-normal?<\/h2>\n<p>A distribui\u00e7\u00e3o log-normal descreve uma quantidade positiva que cresce de forma multiplicativa \u2014 o resultado acumulado de muitas varia\u00e7\u00f5es percentuais independentes. Como o fator subjacente \\(\\ln(X)\\) \u00e9 normal, a pr\u00f3pria \\(X\\) nunca pode ser zero ou negativa e tem uma cauda direita longa. Exemplos t\u00edpicos incluem pre\u00e7os de a\u00e7\u00f5es e retornos de ativos ao longo do tempo, rendas familiares, tamanho de cidades, volumes de chuva, tempos de espera em estudos de confiabilidade e tamanhos de part\u00edculas ou got\u00edculas na engenharia.<\/p>\n<p>Os dois par\u00e2metros \\(\\mu\\) e \\(\\sigma\\) controlam a forma na escala logar\u00edtmica: \\(\\mu\\) desloca toda a distribui\u00e7\u00e3o (a mediana de \\(X\\) \u00e9 exatamente \\(e^{\\mu}\\)), enquanto \\(\\sigma\\) define a dispers\u00e3o. Um \\(\\sigma\\) maior significa uma cauda direita mais pesada e uma distribui\u00e7\u00e3o mais assim\u00e9trica, de modo que poucas observa\u00e7\u00f5es muito grandes podem elevar a m\u00e9dia bem acima da mediana.<\/p>\n<p>Uma forma \u00fatil de interpretar o resultado \u00e9 a ordem m\u00e9dia &gt; mediana &gt; moda, que \u00e9 a marca registrada da assimetria \u00e0 direita. No exemplo acima, a mediana \u00e9 1 enquanto a m\u00e9dia \u00e9 de cerca de 1,1331 \u2014 a diferen\u00e7a \u00e9 causada inteiramente pela cauda no lado dos valores altos. Se os seus dados mostram esse padr\u00e3o (verifique com a <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-assimetria-e-curtose\/\">calculadora de assimetria e curtose<\/a>), um modelo log-normal costuma ser um candidato natural. Para relembrar rapidamente como probabilidades acumuladas se traduzem em chances de eventos, veja a <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-de-probabilidade\/\">calculadora de probabilidade<\/a>.<\/p>\n<h2>Premissas, limita\u00e7\u00f5es e dicas pr\u00e1ticas<\/h2>\n<ul>\n<li><strong>Os par\u00e2metros pertencem \u00e0 escala logar\u00edtmica.<\/strong> O erro mais comum \u00e9 digitar a m\u00e9dia ou o desvio-padr\u00e3o dos dados brutos \\(X\\). Se voc\u00ea s\u00f3 conhece \\(E(X)\\) e \\(\\mathrm{Med}(X)\\), inverta as rela\u00e7\u00f5es: \\(\\mu = \\ln(\\mathrm{Med})\\) e \\(\\sigma^2 = 2\\ln\\!\\left(E(X)\/\\mathrm{Med}(X)\\right)\\).<\/li>\n<li><strong>X precisa ser positiva.<\/strong> A distribui\u00e7\u00e3o log-normal atribui probabilidade zero a valores n\u00e3o positivos; a calculadora rejeita limites menores ou iguais a 0.<\/li>\n<li><strong>As probabilidades s\u00e3o exatas, n\u00e3o simuladas.<\/strong> Elas v\u00eam da CDF normal aplicada a \\((\\ln x - \\mu)\/\\sigma\\), portanto t\u00eam a mesma precis\u00e3o dos par\u00e2metros que voc\u00ea informar.<\/li>\n<li><strong>Valores de cauda podem enganar.<\/strong> Com \\(\\sigma\\) grande, a m\u00e9dia fica bem l\u00e1 na cauda; a mediana costuma ser o melhor resumo de um valor \"t\u00edpico\".<\/li>\n<li><strong>Modelos relacionados.<\/strong> Se voc\u00ea est\u00e1 modelando contagens, tempos de espera entre eventos raros ou tempos de vida com risco constante, considere as calculadoras das distribui\u00e7\u00f5es <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-de-poisson\/\">Poisson<\/a> ou <a href=\"https:\/\/wpcalc.com\/pt\/estatistica\/calculadora-distribuicao-exponencial\/\">exponencial<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Informe a m\u00e9dia e o desvio-padr\u00e3o de ln(X) para calcular probabilidades log-normais: densidade e CDF em um ponto, ou a probabilidade em um intervalo, al\u00e9m da m\u00e9dia e da mediana de X.<\/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-1970","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\/1970","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=1970"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/1970\/revisions"}],"predecessor-version":[{"id":2219,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/1970\/revisions\/2219"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=1970"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=1970"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=1970"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}