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MathGroup Archive 1999

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Re: [Q] Graphics with 2 Y-axis

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18450] Re: [mg18372] [Q] Graphics with 2 Y-axis
  • From: BobHanlon at aol.com
  • Date: Wed, 7 Jul 1999 00:11:34 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 6/30/99 8:55:51 PM, dtruong at irisa.fr writes:

>How can one make a graphic with 2 Y-axis, either to
>show 2 curves holding different value ranges or the same
>curve using 2 scales (typically, percents and real value)
>

Following is my response to an earlier question which should provide some 
insight into an approach:

Needs["Statistics`ContinuousDistributions`"];
mu = 2; sigma = 4;
dist = NormalDistribution[mu, sigma];
Plot[{PDF[dist, x], CDF[dist, x]}, 
			{x, mu-3sigma, mu+3sigma}];

(* plot removed *)

To put the plots on the same size scale, the PDF values will be scaled by

scale = CDF[dist, mu+3sigma]/PDF[dist, mu]//N

10.013

and the second y-axis will have its Ticks labeled accordingly.  
Simultaneously, the second x-axis will be labelled in standard deviations 
about the mean.

red = RGBColor[1, 0, 0]; blue = RGBColor[0, 0, 1];

pdfTicks =  Join[Table[{y, 
				StyleForm[y/scale, FontColor -> red]}, 
			{y, 0, 1.1, 
				step = N[scale*Round[.2*(f = 
					10^(2+MantissaExponent[scale][[2]]))/
			scale]/f]}], 
		Table[{y,""}, {y,step/2, 1.1,step}]];

cdfTicks =  Join[Table[{y, 
				StyleForm[y, FontColor ->blue]}, 
			{y, 0, 1, 0.2}], 
		Table[{y,""}, {y, 0.1, 1, 0.2}]];

sigmaTicks = Join[{{mu-3sigma,"\[Mu]-3\[Sigma]"}, 
		{mu-2sigma,"\[Mu]-2\[Sigma]"}, {mu-sigma,"\[Mu]-\[Sigma]"}, 
		{mu,"\[Mu]"}, {mu+sigma,"\[Mu]+\[Sigma]"},
		{mu+2sigma,"\[Mu]+2\[Sigma]"},{mu+3sigma,"\[Mu]+3\[Sigma]"}}, 
		Table[{mu+k*sigma, ""}, {k, -2.5, 2.5}]];

Plot[{scale*PDF[dist, x], CDF[dist, x]}, 
			{x, mu-3.1sigma, mu+3.1sigma}, ImageSize -> {420, 
260}, 
  PlotStyle -> {red,blue}, 
Axes -> False, Frame -> True, PlotLabel -> 
StyleForm["Normal Distribution\n", 
			FontWeight -> "Bold", FontSize -> 12], 
	FrameLabel -> 
		{"x", "PDF\n", None, "CDF"}, FrameTicks -> 
{Automatic, pdfTicks, sigmaTicks,cdfTicks}, 
Epilog -> {Text["\[Mu] = " <> ToString[mu], 
				{mu-2.75sigma, .9}, {-1, 0}], 
		Text["\[Sigma] = " <> ToString[sigma], 
				{mu-2.75sigma, .8}, {-1, 0}]}];


Bob Hanlon


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