From 56fa00cf0e2c6cad7fcbbfacb726fe8a8d4c2c79 Mon Sep 17 00:00:00 2001 From: Jerry Kuch Date: Tue, 30 Jul 2024 14:59:50 -0700 Subject: [PATCH] Clarify Student's t-distribution Text Add some bridging text to connect the table summarizing Student's t-distribution to the definition of the gamma function, which otherwise hovers in limbo, as a sentence fragment, a couple of pages away from where TeX actually floated the table to. --- chapterProbability.tex | 6 ++++-- machine-learning-cheat-sheet.pdf | Bin 1959957 -> 2354773 bytes 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/chapterProbability.tex b/chapterProbability.tex index ced8a40..ac19d4a 100644 --- a/chapterProbability.tex +++ b/chapterProbability.tex @@ -290,7 +290,8 @@ \subsection{Gaussian (normal) distribution} \subsection{Student's t-distribution} \begin{table} -\caption{Summary of Student's t-distribution.} + \caption{Summary of Student's t-distribution.} + \label{tab:student-t-dist} \centering \begin{tabular}{cccccc} \hline\noalign{\smallskip} @@ -300,6 +301,7 @@ \subsection{Student's t-distribution} \noalign{\smallskip}\hline \end{tabular} \end{table} +Student's $t$-distribution is summarized in Table \ref{tab:student-t-dist} where $\Gamma(x)$ is the gamma function: \begin{equation} \Gamma(x) \triangleq \int_0^\infty t^{x-1}e^{-t}\mathrm{d}t @@ -323,7 +325,7 @@ \subsection{Student's t-distribution} \subfloat[]{\includegraphics[scale=.70]{robustness-a.png}} \\ \subfloat[]{\includegraphics[scale=.70]{robustness-b.png}} \caption{Illustration of the effect of outliers on fitting Gaussian, Student and Laplace distributions. (a) No outliers (the Gaussian and Student curves are on top of each other). (b) With outliers. We see that the Gaussian is more affected by outliers than the Student and Laplace distributions.} -\label{fig:robustness} +\label{fig:robustness} \end{figure} If $\nu=1$, this distribution is known as the \textbf{Cauchy} or \textbf{Lorentz} distribution. 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