TUD_MATH_BA/Erasmus/Applied statistics/TeX_files/Weibulls_Distribution.tex

\subsection{\person{Weibulls} Distribution - Graphs}

\begin{center}
    \begin{tabular}{p{5cm}|p{5cm}|p{5cm}}
        $shape = 0.5$ & $shape = 1$ & $shape = 2$ \\
        \hline
        \multicolumn{3}{c}{\cellcolor{gray!50}\textbf{Weibull PDF} ($scale = 1$)} \\
        \hline
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {0.5*x^(-0.5)*exp(-x^0.5)};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    restrict y to domain=0:1,
		    ]
		    \addplot+[mark=none] {1/exp(x)};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {2*x^(1)*exp(-x^2)};
		    \end{axis}
        \end{tikzpicture} \\
        \hline
        \multicolumn{3}{c}{\cellcolor{gray!50}\textbf{Weibull CDF} ($scale = 1$)} \\
        \hline
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {1-exp(-x^0.5)};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    restrict y to domain=0:1,
		    ]
		    \addplot+[mark=none] {1-1/exp(x)};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {1-exp(-x^2)};
		    \end{axis}
        \end{tikzpicture} \\
        \hline
        \multicolumn{3}{c}{\cellcolor{gray!50}\textbf{Hazard function} $\left(h = \frac{\text{PDF}}{1-\text{CDF}}\right)$} \\
        \hline
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {(0.5*x^(-0.5)*exp(-x^0.5))/(1-(1-exp(-x^0.5)))};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    restrict y to domain=0:1,
		    ]
		    \addplot+[mark=none] {(1/exp(x))/(1-(1-1/exp(x)))};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {(2*x^(1)*exp(-x^2))/(1-(1-exp(-x^2)))};
		    \end{axis}
        \end{tikzpicture} \\
        \hline
        \multicolumn{3}{c}{\cellcolor{gray!50}\textbf{Survival function} ($R = 1-\text{CDF}$)} \\
        \hline
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {1-(1-exp(-x^0.5))};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    restrict y to domain=0:1,
		    ]
		    \addplot+[mark=none] {1-(1-1/exp(x))};
		    \end{axis}
        \end{tikzpicture} &
        \begin{tikzpicture}[scale=0.6]
            \begin{axis}[
		    xmin=0, xmax=2, xlabel=$x$,
		    ymin=0, ymax=1, ylabel=$y$,
		    samples=400,
		    axis y line=middle,
		    axis x line=middle,
		    ]
		    \addplot+[mark=none] {1-(1-exp(-x^2))};
		    \end{axis}
        \end{tikzpicture} \\
    \end{tabular}
\end{center}