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  /Title (t2-distribuciones-de-probabilidad.pdf)
  /Creator (Cheatography)
  /Author (julenx)
  /Subject (T2. Distribuciones de probabilidad Cheat Sheet)
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{T2. Distribuciones de probabilidad Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{julenx} via \textcolor{DarkBackground}{\uline{cheatography.com/168626/cs/35631/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}julenx \\
  \uline{cheatography.com/julenx} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 29th November, 2022.\\
   Updated 22nd November, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
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\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Probabilidades discretas}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución uniforme}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{dunif(k,a,b)\{\{nl\}\}punif(k,a,b)\{\{nl\}\}runif(n,a,b)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}variable que puede tomar n valores distintos con la misma probabilidad. \{\{nl\}\} Probabilidad de que x sea k en un intervalo de a a b \{\{nl\}\} runif: n muestras distintas} \tn 
% Row Count 6 (+ 5)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución binomial}}} \tn 
% Row Count 7 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{dbinom(x, size, prob) \{\{nl\}\} pbinom(q, size, prob) \{\{nl\}\}rbinom(n, size, prob)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}cuenta el número de éxitos en n pruebas independientes. x es el número de éxitos, size el número de pruebas y prob la probabilidad.} \tn 
% Row Count 12 (+ 5)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución geométrica}}} \tn 
% Row Count 13 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{dgeom(x, prob) \{\{nl\}\} pgeom(q, prob) \{\{nl\}\}rgeom(n, prob)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}probabilidad de que tenga que realizarse un número k de repeticiones antes de obtener un éxito por primera vez} \tn 
% Row Count 18 (+ 5)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución hipergeométrica}}} \tn 
% Row Count 19 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{dhyper(x, m, n, k) \{\{nl\}\} phyper(q, m, n, k)\{\{nl\}\} rhyper(nn, m, n, k)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Tenemos una cesta con {\bf{m}} pelotas blancas y {\bf{n}} pelotas negras. Si sacamos {\bf{k}} pelotas, probabilidad de que {\bf{x o q}} pelotas sean blancas.} \tn 
% Row Count 25 (+ 6)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución de Poisson}}} \tn 
% Row Count 26 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{dpois(x, lambda) \{\{nl\}\} ppois(q, lambda) \{\{nl\}\} rpois(n, lambda)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}es una forma límite de la distribución binomial que surge cuando se observa un evento raro después de un número grande de repeticiones. \{\{nl\}\} {\bf{Lambda}} es la media esperada, y {\bf{x o q}} es el resultado que queremos cosultar.} \tn 
% Row Count 33 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Distribuciones de probabilidad continuas}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución normal}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{dnorm(x, mean = 0, sd = 1) \{\{nl\}\}  pnorm(q, mean = 0, sd = 1) \{\{nl\}\}  rnorm(n, mean = 0, sd = 1)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Media es 0 y sd 1 por defecto} \tn 
% Row Count 4 (+ 3)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución log normal}}} \tn 
% Row Count 5 (+ 1)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{dlnorm(x, meanlog = 0, sdlog = 1) \{\{nl\}\} plnorm(q, meanlog = 0, sdlog = 1 \{\{nl\}\} rlnorm(n, meanlog = 0, sdlog = 1)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}si una variable x sigue una distribución lognormal entonces la variable ln(x) se distribuye normalmente. Es útil para cuando los valores de x se encuentra muy separados. \{\{nl\}\} A meanlog también se le llama parámetro de escala y a sdlog forma} \tn 
% Row Count 14 (+ 9)
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución beta}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}adecuada para variables aleatorias continuas que toman valores en el intervalo (0,1)} \tn 
% Row Count 17 (+ 3)
% Row 5
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\mymulticolumn{1}{x{5.377cm}}{dbeta(x, shape1, shape2) \{\{nl\}\} pbeta(q, shape1, shape2) \{\{nl\}\}  rbeta(n, shape1, shape2)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}x o q es la proporción que queremos calcular} \tn 
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución gamma}}} \tn 
% Row Count 21 (+ 1)
% Row 7
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\mymulticolumn{1}{x{5.377cm}}{dgamma(x, shape, rate = 1) \{\{nl\}\} pgamma(q, shape, rate = 1 \{\{nl\}\} rgamma(n, shape, rate = 1)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Mide el tiempo transcurrido hasta obtener n ocurrencias de un evento generado por un proceso de Poisson de media lambda} \tn 
% Row Count 26 (+ 5)
% Row 8
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Distribución exponencial}}} \tn 
% Row Count 27 (+ 1)
% Row 9
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\mymulticolumn{1}{x{5.377cm}}{dexp(x, rate = 1) \{\{nl\}\} pexp(q, rate = 1 \{\{nl\}\}  rexp(n, rate = 1)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Es un caso particular de la distribución gamma. describe procesos en los que interesa saber el tiempo hasta que ocurre determinado evento-} \tn 
% Row Count 32 (+ 5)
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\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Todas las que empiezan por p tienen lower.tail = TRUE}  \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Distribución que mejor se ajusta a unos datos}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{descdist(data = datos\$price)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Análisis exploratorio de la base de datos} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\seqsplit{distribucion=fitdist(datos\$price}, distr = "lnorm")} \tn 
% Row Count 3 (+ 1)
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\mymulticolumn{1}{x{5.377cm}}{summary(distribucion)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Ajuste a una distribución lognormal} \tn 
% Row Count 5 (+ 2)
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\mymulticolumn{1}{x{5.377cm}}{x=rlnorm(x, meanlog, sdlog)} \tn 
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% Row 4
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\mymulticolumn{1}{x{5.377cm}}{hist(x,freq=FALSE,col="lightsalmon",main="Histograma",sub="Datos simulados de una N(meanlog, sdlog)")} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}simular una muestra procedente de dicha distribución} \tn 
% Row Count 11 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Comparación de modelos/ajustes con AIC y BIC}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{AIC (Criterio de información de Akaike)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}AIC = −2log(likelihood) + 2 × no parametros} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{BIC (Bayesian information criterion)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}BIC = −2log(likelihood) + log(no observaciones) × no parametros} \tn 
% Row Count 5 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{AIC y BIC}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{require(fitdistrplus)} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{dist\_lnorm \textless{}- fitdist(datos\$price, distr = "lnorm")} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{dist\_weibull \textless{}- fitdist(datos\$price, distr = "weibull")} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{comparacion \textless{}- gofstat(f = list(dist\_lnorm, dist\_weibull))} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Además de los estadísticos AIC y BIC, la función gofstat() devuelve 3 estadísticos de bondad de ajuste, (Kolmogorov-Smirnov, Cramer-von Mises y Anderson-Darling). Estos estadísticos, también conocidos como goodness-of-fit, contrastan la similitud entre la distribución empírica obtenida y la distribución teórica con los parámetros estimados. Ninguno de estos 3 últimos tiene en consideración el número de parámetros, por lo que no deben emplearse para comparar distribuciones con distintos grados de libertad.} \tn 
% Row Count 18 (+ 11)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{gr = denscomp( \{\{nl\}\} list(dist\_lnorm, dist\_weibull), legendtext = c("lognormal", "Weibull"), xlab = "precio", fitcol = c("red", "blue"), \{\{nl\}\} fitlty = 1, xlegend = "topright", plotstyle = "ggplot", addlegend = FALSE)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Veamos gráficamente cuál de las dos distribuciones se ajustan mejor a nuestros datos} \tn 
% Row Count 25 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

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