lognormal_pdf.tex

\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\usepackage[scaled]{helvet}
\usepackage[T1]{fontenc}
\renewcommand\familydefault{\sfdefault}
\usepackage[eulergreek]{sansmath}
\pgfplotsset{
tick label style = {font=\sansmath\sffamily}}

\pgfkeys{/pgf/number format/fixed, /pgf/number format/precision=5, /pgf/number format/.cd, 1000 sep = {}}
\pgfplotsset{compat=newest}
\begin{document}
\pgfmathdeclarefunction{lognormal}{2}{\pgfmathparse{1/(x*#2*sqrt(2*pi))*exp(-((ln(x)-#1)^2)/(2*#2^2))}%
}

\begin{tikzpicture}
\begin{axis}[
    scaled ticks=false,
    axis lines=left,
    enlargelimits=upper,
    line width=0.5,
    ymin=0,
    xlabel = {$x$},
    ylabel = {$f(x)$}
]
\addplot + [smooth, mark=none, domain=0:30, samples=100, color=red, line width=1.5] {lognormal(1.9, 1.0724)};
\node at (20,0.06) {$\ln\mathcal{N}(1.9,1.0724^2)$};
\end{axis}
\end{tikzpicture}
\end{document}