Tikzpicture with Cumulative Distribution Function

graphstikz-pgf

I'm trying to recreate this picture in the tikz environment.

But with the Cumulative Distribution function that I found and altered.

What I have so far

\begin{tikzpicture}[scale=2]
% define normal distribution function 'normaltwo'
\def\normaltwo{\x,{2/exp(((\x-4)^2)/2)}}
% input y parameter
\def\y{5}
% this line calculates f(y)
\def\fy{2/exp(((\y-4)^2)/2)}

% Shade orange area underneath curve.
\fill [fill=orange!60] (2.6,0) -- plot[domain=0:3.5] (\normaltwo) -- ({\y-1.45},0) -- cycle;

% Draw and label normal distribution function
\draw[color=blue,domain=1:7] plot (\normaltwo) node[right] {};

% Add dashed line dropping down from normal.
\draw[-] (2,.05)--(2,-.05) node[below] {\footnotesize ${\mu}-{2}{\sigma}$};
\draw[-] (3,.05)--(3,-.05) node[below] {\footnotesize ${{\mu}-{\sigma}}$};
\draw[-] (3.55,.005)--(3.55,-.05) node[below] {\footnotesize ${x}$};
\draw[-] (4,.05)--(4,-.05) node[below] {\footnotesize ${\mu}$};
\draw[-] (5,.05)--(5,-.05) node[below] {\footnotesize ${\mu}+{\sigma}$};
\draw[-] (6,.05)--(6,-.05) node[below] {\footnotesize ${\mu}+{2}{\sigma}$};
% Optional: Add axis labels
\draw (-.2,2.5) ;
\draw (3,-.5) ;
% Optional: Add axes
\draw[->] (0,0) -- (7.2,0) node[right] {${x}$};
\draw[->] (0,0) -- (0,2.5) node[above] {${y}$};


\draw[-,dashed] (7,-1)--(-.08,-1) node[left] {\footnotesize ${1}$};
\draw[-] (7,-3)--(-.08,-3) node[left] {\footnotesize ${0}$};
\draw[-] (-.08,-3)--(7,-3) node[right] {\footnotesize ${z}$-scale};
\draw[-] (0,-3)--(0,-.9) node[above] {\footnotesize ${\Phi}\gobble{\Phi..}({z}\gobble{\Phi..})$};
\draw[-] (0,-2)--(-.05,-2);

%\draw[-] (1,-2.95)--(1,-3.05) node[below] {\footnotesize $-{3}$};
\draw[-] (2,-2.95)--(2,-3.05) node[below] {\footnotesize ${-2}$};
\draw[-] (3,-2.95)--(3,-3.05) node[below] {\footnotesize ${-1}$};
\draw[-] (4,-2.95)--(4,-3.05) node[below] {\footnotesize ${0}$};
\draw[-] (5,-2.95)--(5,-3.05) node[below] {\footnotesize ${1}$};
\draw[-] (6,-2.95)--(6,-3.05) node[below] {\footnotesize ${2}$};
%\draw[-] (7,-2.95)--(7,-3.05) node[below] {\footnotesize ${3}$};

\draw[-,dashed] (2,-.3)--(2,-3);
\draw[-,dashed] (3,-.3)--(3,-3);
\draw[-,dashed] (4,-.3)--(4,-3);
\draw[-,dashed] (5,-.3)--(5,-3);
\draw[-,dashed] (6,-.3)--(6,-3);

\end{tikzpicture}

Now I just need to draw the function through it. I found some function but they wouldn't line up with my top graph. I tried embedding atan(x-4)/2.6+.53 into the graph but than didn't even work. Help plz

Best Answer

Probably your main problem is that you think that the atan function gives the result in radians. But:

Use:

\draw[color=blue,domain=1:7] plot (\x,{rad(atan(\x-4))/2.6+0.53});

and adjust the curve position. Notice the extra braces needed to hide the internal parenthesis to the parser.

Anyway, this kind of diagram would be much easier with pgfplots.

Related Solutions

[Tex/LaTex] Declaration of cumulative distribution function

There are three issues in your code:

Missing semicolon at the end of the definition of myfun. All functions defined using declare function have to end with a semicolon.
Typo in the function name (it's normcdf, not normdcf).
Incorrect call of the normcdf function. It takes three parameters: The x value, the mean, and the standard deviation of the normal distribution.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}[
declare function={ normcdf(\x,\m,\s)          = 1/(1 + exp(-0.07056*((\x-\m)/\s)^3 - 1.5976*(\x-\m)/\s));
                   d2(\x,\y,\KK,\RR,\SIG)     = (ln(\x/\KK)+(\RR-(pow(\SIG,2)/2)*\y))/(\SIG*(sqrt(\y)));
                   myfun(\x,\y,\KK,\RR,\SIG)  = exp(-\RR*\y)*normcdf(d2(\x,\y,\KK,\RR,\SIG),0,1);
                 },
]
\begin{axis}[y domain=0.01:0.3,domain=95:105,view={210}{20}]
\addplot3[surf] {myfun(x,y,100,0,0.09)};
\end{axis}
\end{tikzpicture}


\end{document}

[Tex/LaTex] Poisson distribution with tikzpicture

Remember that you want to evaluate the funcition in eleven places (0,1,…,10), not ten. Anyway, I would use samples at = {0,...,10} to place the evaluating points at wish.

\documentclass{article}
\usepackage{pgfplots}
\pgfmathdeclarefunction{poiss}{1}{%
  \pgfmathparse{(#1^x)*exp(-#1)/(x!)}%
}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
  mark=none,domain=0:10,samples at = {0,...,10},
  axis x line*=bottom,
  axis y line*=left,
  enlargelimits=upper}]
  \addplot {poiss(1)};
  \addplot {poiss(2)};
  \addplot {poiss(3)};
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}

As pointed out in the comment on the question and in another question, since this is a discrete distribution, it should really not be plotted as a line plot, but rather with the ycomb option instead:

\documentclass{article}
\usepackage{pgfplots}
\pgfmathdeclarefunction{poiss}{1}{%
  \pgfmathparse{(#1^x)*exp(-#1)/(x!)}%
}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
  samples at = {0,...,15},
  axis x line*=bottom,
  axis y line*=left,
  enlargelimits=upper}]
  \addplot +[ycomb] {poiss(1)};
  \addplot +[ycomb] {poiss(4)};
  \addplot +[ycomb] {poiss(7)};
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Declaration of cumulative distribution function

[Tex/LaTex] Poisson distribution with tikzpicture

Related Question