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\documentclass{article} 

\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}
\pgfplotsset{every axis legend/.append style={ at={(0.5,1.03)}, anchor=south}}
  \begin{loglogaxis}[
    enlargelimits = auto,
    %width = 0.5\textwidth,
    %height = 0.5\textheight,
    grid = both,
    log basis x = 10,
    log basis y = 10,
    xlabel = x,
    %ylabel = {Probability Density Function},
    title= {Probability Density Function},
    legend columns = -1,
    legend entries = {prior\makebox[1cm]{}, posterior},
    legend to name =Legende]
    \addplot[mark=none, blue] coordinates {
    (1.61E-08, 2.30E+06)
(2.36E-08, 3.05E+06)
(2.96E-08, 3.53E+06)
(3.50E-08, 3.89E+06)
(4.00E-08, 4.16E+06)
(4.46E-08, 4.36E+06)
(4.91E-08, 4.52E+06)
(5.35E-08, 4.65E+06)
(5.78E-08, 4.74E+06)
(6.20E-08, 4.81E+06)
(6.61E-08, 4.85E+06)
(7.02E-08, 4.88E+06)
(7.43E-08, 4.89E+06)
(7.84E-08, 4.89E+06)
(8.25E-08, 4.87E+06)
(8.66E-08, 4.84E+06)
(9.07E-08, 4.80E+06)
(9.49E-08, 4.75E+06)
(9.91E-08, 4.69E+06)
(1.03E-07, 4.62E+06)
(1.08E-07, 4.55E+06)
(1.12E-07, 4.46E+06)
(1.17E-07, 4.37E+06)
(1.21E-07, 4.27E+06)
(1.26E-07, 4.17E+06)
(1.31E-07, 4.06E+06)
(1.36E-07, 3.94E+06)
(1.41E-07, 3.82E+06)
(1.47E-07, 3.69E+06)
(1.52E-07, 3.56E+06)
(1.58E-07, 3.42E+06)
(1.64E-07, 3.28E+06)
(1.70E-07, 3.14E+06)
(1.76E-07, 2.99E+06)
(1.83E-07, 2.83E+06)
(1.91E-07, 2.67E+06)
(1.98E-07, 2.51E+06)
(2.07E-07, 2.34E+06)
(2.16E-07, 2.17E+06)
(2.25E-07, 1.99E+06)
(2.36E-07, 1.82E+06)
(2.47E-07, 1.63E+06)
(2.60E-07, 1.45E+06)
(2.75E-07, 1.25E+06)
(2.92E-07, 1.06E+06)
(3.13E-07, 8.58E+05)
(3.40E-07, 6.54E+05)
(3.77E-07, 4.44E+05)
(4.39E-07, 2.27E+05)
(5.76E-07, 4.81E+04)
};
    \addplot[mark=none, red] coordinates {
    (4.23E-08, 1.22E+06)
(5.56E-08, 1.77E+06)
(6.58E-08, 2.16E+06)
(7.44E-08, 2.47E+06)
(8.21E-08, 2.71E+06)
(8.92E-08, 2.91E+06)
(9.59E-08, 3.08E+06)
(1.02E-07, 3.21E+06)
(1.08E-07, 3.33E+06)
(1.14E-07, 3.42E+06)
(1.20E-07, 3.50E+06)
(1.26E-07, 3.56E+06)
(1.31E-07, 3.60E+06)
(1.37E-07, 3.63E+06)
(1.42E-07, 3.66E+06)
(1.48E-07, 3.66E+06)
(1.53E-07, 3.66E+06)
(1.59E-07, 3.66E+06)
(1.64E-07, 3.64E+06)
(1.70E-07, 3.61E+06)
(1.75E-07, 3.58E+06)
(1.81E-07, 3.54E+06)
(1.87E-07, 3.49E+06)
(1.92E-07, 3.43E+06)
(1.98E-07, 3.37E+06)
(2.04E-07, 3.30E+06)
(2.10E-07, 3.23E+06)
(2.17E-07, 3.15E+06)
(2.23E-07, 3.07E+06)
(2.30E-07, 2.98E+06)
(2.37E-07, 2.88E+06)
(2.44E-07, 2.78E+06)
(2.51E-07, 2.68E+06)
(2.59E-07, 2.57E+06)
(2.66E-07, 2.46E+06)
(2.75E-07, 2.34E+06)
(2.84E-07, 2.22E+06)
(2.93E-07, 2.09E+06)
(3.03E-07, 1.96E+06)
(3.13E-07, 1.82E+06)
(3.25E-07, 1.68E+06)
(3.37E-07, 1.54E+06)
(3.51E-07, 1.39E+06)
(3.66E-07, 1.23E+06)
(3.84E-07, 1.07E+06)
(4.04E-07, 9.07E+05)
(4.28E-07, 7.37E+05)
(4.59E-07, 5.62E+05)
(5.02E-07, 3.79E+05)
(5.76E-07, 1.88E+05)
};
  \end{loglogaxis}
\end{tikzpicture}
\end{document}

xmin=1e-8,xmax=1e-6,