How to draw pdf curves for Beta distribution?

Question

I need to draw two pdf curves with known shape parameters for a beamer presentation. I really appreciate if I can get some advise on that.

Answer 1

As was already suggested by Bobyandbob in the comment below the question you can adopt my answer given here to get what you need.

To summarize what is given there:
If you have installed gnuplot you can use PGFPlots raw gnuplot function to define the functions needed for the beta function, then plotting a data file which is read by PGFPlots and used for the plot.

% used PGFPlots v1.14
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    % define a command which stores all commands that are needed for every
    % `raw gnuplot' call
    \newcommand*\GnuplotDefs{
        % set number of samples
        set samples 51;
        %
        % define beta distribution function
        % (copied from <http://gnuplot.sourceforge.net/demo/prob.5.gnu>)
        Binv(p,q)=exp(lgamma(p+q)-lgamma(p)-lgamma(q));
        beta(x,p,q)=p<=0||q<=0?1/0:x<0||x>1?0.0:Binv(p,q)*x**(p-1.0)*(1.0-x)**(q-1.0);
    }
\begin{document}
\begin{tikzpicture}
        % define macros which are needed for the axis limits as well as for
        % setting the domain of calculation
        \pgfmathsetmacro{\xmin}{0}
        \pgfmathsetmacro{\xmax}{1}
    \begin{axis}[
        xmin=\xmin,
        xmax=\xmax,
        no markers,
    ]
        \addplot gnuplot [raw gnuplot] {
            % first call all the "common" definitions
            \GnuplotDefs
            % and then create the data tables
            % in GnuPlot `x` key is identical to PGFPlots `domain` key
            %
            % "plot" beta function
            plot [x=\xmin:\xmax] beta(x,1,1);
        };
        \addplot gnuplot [raw gnuplot] {
            \GnuplotDefs
            plot [x=\xmin:\xmax] beta(x,7,5);
        };
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

A short code with pstricks and its module pst-func, which defines a \psBetaDist command (to be compiled with pdflatex with the --enable-write18 switch (MiKTeX) or -shell-escape (TeX Live, MacTeX):

\documentclass[x11names, border=1pt]{standalone}

\usepackage{pst-func, pst-plot}
\usepackage{auto-pst-pdf}

\begin{document}

\psset{xunit=8cm, yunit=2cm}
\begin{pspicture*}(-1,-1)(1.1,3.1)
\psaxes[linecolor=LightSteelBlue3, tickcolor=LightSteelBlue3, ticksize=3pt -3pt, ticks=all, tickstyle=bottom, Dx=0.1, Dy=0.5, labelFontSize=\scriptstyle]{-}(0,0)(1.005,3.005)
\psBetaDist[linecolor=DarkGoldenrod1, alpha=1, beta=1]{0.005}{0.995}
\psBetaDist[linecolor=OliveDrab4, alpha=7, beta=5]{0.005}{0.995}
\end{pspicture*}

\end{document}