\documentclass[crop,tikz]{standalone}
\usepackage{amsmath}
\usetikzlibrary{arrows.meta, positioning}
\begin{document}
\begin{tikzpicture}[
  dist/.style = {draw, rectangle, align=center, rounded corners},
  limit/.style = {dashed},
  >={Stealth[round,sep]}
  ]
  \node [align=left] at (3, -17.5) {
    Solid lines represent transformations and special cases\\
    Dashed lines represent limits\\
    \footnotesize Adapted from Casella + Berger (1990)
  };
  \node[dist] (Geometric) at (0,0) {
    \textbf{Geometric}\\
    $(p)$
  };
  \node[dist] (DiscreteUniform) at (6,0) {
    \textbf{Discrete Uniform}
  };
  \node[dist] (NegativeBinomial) at (2,-2) {
    \textbf{Negative binomial}\\
    $(n, p)$
  };
  \node[dist] (Poisson) at (2,-4) {
    \textbf{Poisson}\\
    $(\lambda)$
  };
  \node[dist] (BetaBinomial) at (6,-2) {
    \textbf{Beta-binomial}\\
    $(n,\alpha,\beta)$
  };
  \node[dist] (Binomial) at (6,-4) {
    \textbf{Binomial}\\
    $(n,p)$
  };
  \node[dist] (Hypergeometric) at (10,-2) {
    \textbf{Hypergeometric}\\
    $(M, N, K)$
  };
  \node[dist] (Bernoulli) at (10,-5) {
    \textbf{Bernoulli}\\
    $(p)$
  };
  \node[dist] (Normal) at (4, -6) {
    \textbf{Normal}\\
    $(\mu, \sigma^{2})$
  };
  \node[dist] (Lognormal) at (0, -6.5) {\textbf{Lognormal}};
  \node[dist] (Beta) at (8, -7.5) {
    \textbf{Beta}\\
    $(\alpha, \beta)$
  };
  \node[dist] (Gamma) at (5.5, -9) {
    \textbf{Gamma}\\
    $(r, \lambda)$
  };
  \node[dist] (Uniform) at (9, -10) {\textbf{Uniform}};
  \node[dist] (ChiSquared) at (4, -11) {
    \textbf{Chi-Squared}\\
    $(v)$
  };
  \node[dist] (NormalU) at (1, -8.5) {
    \textbf{Normal}\\
    $(0,1)$
  };
  \node[dist] (Cauchy) at (0, -11) {\textbf{Cauchy}};
  \node[dist] (Exponential) at (7.5, -13) {
    \textbf{Exponential}\\
    $(\lambda)$
  };
  \node[dist] (Weibull) at (5, -16) {
    \textbf{Weibull}\\
    $(\gamma, \lambda)$
  };
  \node[dist] (Dexponential) at (10, -16) {\textbf{Double exponential}};
  \node[dist] (F) at (3.5, -13.5) {
    \textbf{F}\\
    $(v_{1}, v_{2})$
  };
  \node[dist] (T) at (1, -15) {
    \textbf{t}\\
    $(v)$
  };
  
  \draw[->] (Geometric) to [loop above] node {$\min X_{i}$} (Geometric);
  \draw[->] (NegativeBinomial) to [bend right] node[right] {$n = 1$} (Geometric);
  \draw[->] (Geometric) to [bend right] node[left] {$\Sigma X_{i}$} (NegativeBinomial);
  \draw[->] (BetaBinomial) to node[left] {$\alpha=\beta=1$} (DiscreteUniform);
  \draw[->, limit] (NegativeBinomial) to node[left, align=right] {
    $\lambda=n(1 - p)$\\
    $n \to \infty$
  } (Poisson);
  \draw[->] (Poisson) to [loop left] node {$\Sigma X_{i}$} (Poisson);
  \draw[->,limit] (Binomial) to node[above, align=center] {
    $\lambda=np$\\
    $n \to \infty$
  } (Poisson);
  \draw[->,limit] (BetaBinomial) to node[right, align=left] {
    $p=\frac{\alpha}{\alpha+\beta}$\\
    $\alpha+\beta \to \infty$
  } (Binomial);
  \draw[->,limit] (Hypergeometric) to [bend left=15] node[right=20pt, align=left] {
    $p = \frac{M}{N}$\\
    $n = K$\\
    $N \to \infty$
  } (Binomial);
  \draw[->] (Bernoulli) to node[above right] {$\Sigma X_{i}$} (Binomial);
  \draw[->] (Binomial) to [bend right=20] node[near end, below] {$n = 1$} (Bernoulli);
  \draw[->,limit] (Poisson) to node[left=10pt, align=right] {
    $\lambda=\sigma^{2}$\\
    $\lambda \to \infty$
  } (Normal);
  \draw[->,limit] (Binomial) to node[near end, right=12pt, align=left] {
    $\mu=np$\\
    $\sigma^{2}=np(1-p)$\\
    $n \to \infty$
  } (Normal);
  \draw[->] (Normal) to [bend right=10] node[above] {$e^{x}$} (Lognormal);
  \draw[->] (Lognormal) to [bend right=10] node[below] {$\log X$} (Normal);
  \draw[->] (Normal) to [loop below] node[below] {$\Sigma X_{i}$} (Normal);
  \draw[->] (Lognormal) to [loop above] node {$\Pi X_{i}$} (Lognormal);
  \draw[->, limit] (Beta) to node [near end, right=12pt] {$\alpha=\beta \to \infty$} (Normal);
  \draw[->] (Gamma) to node [below right] {$\frac{X_{1}}{X_{1} + X_{2}}$} (Beta);
  \draw[->, limit] (Gamma) to node [right=6pt, align=left] {
    $\mu=r\lambda$\\
    $\sigma^{2}=r\lambda^{2}$\\
    $r\to\infty$
  } (Normal);
  \draw[->] (Normal) to node [left] {$\frac{X-\mu}{\sigma}$} (NormalU);
  \draw[->] (NormalU) to [bend right=20] node [below=10pt] {$\mu + \sigma X$} (Normal);
  \draw[->] (NormalU) to node [left] {$\frac{X_{1}}{X_{2}}$} (Cauchy);
  \draw[->] (Cauchy) to [loop left] node [left] {$\frac{1}{X}$} (Cauchy);
  \draw[->] (Cauchy) to [out=100, in=150, looseness=8] node [above] {$\Sigma X_{i}$} (Cauchy);
  \draw[->] (NormalU) to node [near start, above right] {$\Sigma X_{i}^{2}$} (ChiSquared);
  \draw[->] (ChiSquared) to [loop left, looseness=2] node [above left] {$\Sigma X_{i}$} (ChiSquared);
  \draw[->] (Gamma) to node [above left, align=right] {
    $r = \frac{v}{2}$\\
    $\lambda=2$
  } (ChiSquared);
  \draw[->] (Beta) to [bend left] node [right] {$\alpha=\beta=1$} (Uniform);
  \draw[->] (Uniform) to [bend left=10] node [right] {$-\lambda \log X$} (Exponential);
  \draw[->] (Exponential) to [bend left=10] node [near end, left] {$e^{-x\lambda}$} (Uniform);
  \draw[->] (Exponential) to [bend right] node [near end, right] {$\Sigma X_{i}$} (Gamma);
  \draw[->] (Gamma) to node [left] {$r=1$} (Exponential);
  \draw[<->] (ChiSquared) to node [below=8pt, align=center] {
    $\lambda=2$\\
    $v=2$
  } (Exponential);
  \draw[->] (ChiSquared) to [bend right] node [left] {$\frac{X_{1}/ v_{1}}{X_{2}/ v_{2}}$} (F);
  \draw[->,limit] (F) to node [right, align=left] {
    $v_{1}X$\\
    $v_{2} \to\infty$
  } (ChiSquared);
  \draw[->] (Exponential) to [out=190, in=210, looseness=5] node [left] {$\min X_{i}$} (Exponential);
  \draw[->] (Exponential) to node [left] {$X^{\frac{1}{\gamma}}$} (Weibull);
  \draw[->] (Weibull) to [bend right=20] node [right] {$\gamma=1$} (Exponential);
  \draw[->] (Dexponential) to node [left] {$\lvert X\rvert$} (Exponential);
  \draw[->] (Exponential) to [bend left=20] node [right] {$X_{1}-X_{2}$} (Dexponential);
  \draw[->,limit] (T) to [bend right=5] node [near start, right] {$v\to\infty$} (NormalU);
  \draw[->] (T) to node [left] {$v=1$} (Cauchy);
  \draw[->] (T) to node [above] {$X^{2}$} (F);
\end{tikzpicture}
\end{document}
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