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均匀分布的概率密度函数

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均匀分布的概率密度函数

有人能帮我在 Latex 中绘制均匀分布函数的 PDF 吗？我是这方面的新手，找不到任何有用的东西。谢谢！

答案1

如果有人有兴趣，这里是另一个带有符号坐标的解决方案。

\documentclass[10pt]{standalone}
\usepackage{mathtools}

\usepackage{tkz-euclide}

% arrow and line for 'tkzPointShowCoord'
\makeatletter
\tikzset{arrow coord style/.style={%
    densely dashed,
    \tkz@euc@linecolor,
    %>=stealth',
    %->,
    }}
    \tikzset{xcoord style/.style={%
    \tkz@euc@labelcolor,
    font=\normalsize,text height=1ex,
    inner sep = 0pt,
    outer sep = 0pt,
    fill=\tkz@fillcolor,
    below=6pt
    }} 
\tikzset{ycoord style/.style={%
    \tkz@euc@labelcolor,
    font=\normalsize,text height=1ex, 
    inner sep = 0pt,
    outer sep = 0pt, 
    fill=\tkz@fillcolor,
    left=6pt
    }}  
\makeatother

\begin{document}

\begin{tikzpicture}
\tkzInit[xmax=1,xstep=0.2,ymax=1,ystep=0.2]
\tkzDrawX[noticks,label={$x$}]
\tkzDrawY[noticks,label={$f_X(x)$}]
\tkzDefPoint(0.2,0.8){A}
\tkzDefPoint(0.8,0.8){B}
\tkzDefShiftPoint[A](-90:4){AB}
\tkzDefShiftPoint[B](-90:4){BB}
\tkzDefShiftPoint[AB](0:-0.6){ABL}
\tkzDefShiftPoint[BB](0:0.6){BBR}
\tkzPointShowCoord[xlabel=$a$,ylabel=$\frac{1}{b-a}$](A)
\tkzPointShowCoord[xlabel=$b$](B)
\tkzDrawSegments[color=cyan,thick](A,B AB,ABL BB,BBR)
\tkzDrawPoints[color=cyan,fill=cyan,size=6pt](A,B)
\tkzDrawPoints[color=cyan,fill=white,size=6pt](AB,BB)
\end{tikzpicture}

\end{document}

在此处输入图片描述

答案2

你可以使用 PGFPlots 来实现这一点。默认情况下，均匀分布的 PDF 不实现，但你可以使用以下方法轻松定义它：

declare function={unipdf(\x,\xl,\xu)= (\x>\xl)*(\x<\xu)*1/(\xu-\xl);}

你可以这样写unipdf(<variable>,<lower>,<upper>)：

\documentclass{article}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}[
    declare function={unipdf(\x,\xl,\xu)= (\x>\xl)*(\x<\xu)*1/(\xu-\xl);}
]
\begin{axis}[
    samples=100,
    const plot mark mid,
    ymin=0,ymax=1
]
\addplot [very thick, orange] {unipdf(x,0,2)};
\addplot [very thick, cyan] {unipdf(x,-3,1)};
\end{axis}
\end{tikzpicture}
\end{document}

为了获得具有开/闭区间标记的适当的不连续函数，您可以使用该scatter/@pre marker code功能来决定是否绘制标记：

\documentclass{article}
\usepackage{pgfplots}

\makeatletter
\long\def\ifnodedefined#1#2#3{%
    \@ifundefined{pgf@sh@ns@#1}{#3}{#2}%
}

\pgfplotsset{
    discontinuous/.style={
    scatter,
    scatter/@pre marker code/.code={
        \ifnodedefined{marker}{
            \pgfpointdiff{\pgfpointanchor{marker}{center}}%
             {\pgfpoint{0}{0}}%
             \ifdim\pgf@y>0pt
                \tikzset{options/.style={mark=*}}
                \draw [densely dashed] (marker-|0,0) -- (0,0);
                \draw plot [mark=*,mark options={fill=white}] coordinates {(marker-|0,0)};
             \else
                \ifdim\pgf@y<0pt
                    \tikzset{options/.style={mark=*,fill=white}}
                    \draw [densely dashed] (marker-|0,0) -- (0,0);
                    \draw plot [mark=*] coordinates {(marker-|0,0)};
                \else
                    \tikzset{options/.style={mark=none}}
                \fi
             \fi
        }{
            \tikzset{options/.style={mark=none}}        
        }
        \coordinate (marker) at (0,0);
        \begin{scope}[options]
    },
    scatter/@post marker code/.code={\end{scope}}
    }
}

\makeatother

\begin{document}
\begin{tikzpicture}[
    declare function={unipdf(\x,\xl,\xu)= (\x>=\xl)*(\x<\xu)*1/(\xu-\xl);}
]

\begin{axis}[
    samples=11,
    jump mark left,
    ymin=0,ymax=1,
    xmin=-5, xmax=5,
    every axis plot/.style={very thick},
    discontinuous
]
\addplot [orange] {unipdf(x,0,2)};
\end{axis}

\end{tikzpicture}
\end{document}

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