(*^
::[ Information =
"This is a Mathematica Notebook file. It contains ASCII text, and can be
transferred by email, ftp, or other text-file transfer utility. It should
be read or edited using a copy of Mathematica or MathReader. If you
received this as email, use your mail application or copy/paste to save
everything from the line containing (*^ down to the line containing ^*)
into a plain text file. On some systems you may have to give the file a
name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
The line below identifies what version of Mathematica created this file,
but it can be opened using any other version as well.";
FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2";
MacintoshStandardFontEncoding;
fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times";
fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times";
fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times";
fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times";
fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times";
fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times";
fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier";
fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier";
fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier";
fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier";
fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva";
fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = leftheader, inactive, L2, 12, "Times";
fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times";
fontset = leftfooter, inactive, L2, 12, "Times";
fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
paletteColors = 128; automaticGrouping; currentKernel;
]
:[font = input; preserveAspect]
ClearAll;
$DefaultFont = {"Times-Roman",10};
Needs["Statistics`DataManipulation`"];
Needs["Graphics`Graphics`"];
npoints = 5;
cumprob = {1,23,75,142,256,513,690,731,733}/733;
sizes = Table[3k,{k,1,9}];
datapoints = Map[Thread,Transpose[{sizes,cumprob}]];
scale = cumprob[[npoints]];
cumscaled = cumprob/scale;
datapointscond = Map[Thread,Transpose[{sizes,cumscaled}]];
n = 5;
F[a_,x_]:= 1 - E^(-(a x)^n);
f[a_,x_]:= n a (a x)^(n-1) E^(-(a x)^n);
err[a_] = N[Apply[Plus,Table[(F[a,sizes[[k]]]-cumprob[[k]])^2,{k,1,9}]]];
Plot[err[a],{a,0.05,0.07}]
leasterr = FindMinimum[err[a],{a,0.06,0.05,0.07}];
aopt = a/.leasterr[[2]];
corrleft = 1/F[aopt,15];
corrright = 1/(1-F[aopt,15]);
left = Plot[f[aopt,x],{x,0,15}];
right = Plot[f[aopt,x],{x,15,27},PlotStyle->Dashing[{0.01,0.01}]];
modleft = Plot[corrleft f[aopt,x],{x,0,15},PlotStyle->Thickness[0.0075]];
modright = Plot[corrright f[aopt,x],{x,15,27},PlotStyle->{{Dashing[{0.01,0.01}],Thickness[0.005]}}];
mini = {left, modleft};
big = {right, modright};
plot1 = Show[mini, PlotRange->{{0,15},{0,0.3}},
PlotLabel->"(a) p.d.f. of mini-minnow distribution (upper curve)",
Axes->True,AxesLabel->{" x","y"},
AxesOrigin->{-0.5,-0.02}];
plot2 = Show[big, PlotRange->{{15,27},{0,0.2}},
PlotLabel->"(b) p.d.f. of big-minnow distribution (upper curve)",
Axes->True,AxesLabel->{" x","y"},
AxesOrigin->{14.5,-0.01}];
Show[GraphicsArray[{{plot1},{plot2}}],PlotLabel->"Figure 10.2"]
^*)