Chisquared Distribution Plot (xfig example) - Revision history

Obst: Obst moved page Example: Chisquared Plot to Chisquared Distribution Plot (xfig example) without leaving a redirect

2018-04-17T08:53:12Z

Obst moved page Example: Chisquared Plot to Chisquared Distribution Plot (xfig example) without leaving a redirect

Obst at 13:55, 16 April 2018

2018-04-16T13:55:30Z

Gokus at 12:43, 13 April 2018

2018-04-13T12:43:57Z

Gokus at 12:25, 13 April 2018

2018-04-13T12:25:50Z

Gokus: Created page with " Category:SLxfig {{:isis:slxfig:chisqr.png?nolink&600|}} The Chi²-distribution and its according cumulative distribution function for a large number of degrees of freed..."

2018-04-13T12:23:26Z

Created page with " Category:SLxfig {{:isis:slxfig:chisqr.png?nolink&600|}} The Chi²-distribution and its according cumulative distribution function for a large number of degrees of freed..."

New page

[[Category:SLxfig]]
{{:isis:slxfig:chisqr.png?nolink&600|}}

The Chi²-distribution and its according cumulative distribution function for a large number of degrees of freedom for illustrative purposes. Confidence levels are indicated in the CDF. Feel free to use it in your thesis, there are some customization options in the header.

<pre octave>
#!/usr/bin/env isis-script

require("isisscripts");

%---------options-----------------------------
variable CHISQRMIN = 0.0003,
CHISQRMAX = 150,
KVALUES = [1,2,4,8,15,30,60,100],
COLOR = ["blue","crimson"],
LOG = 1,
dx=0.001;

%---------we-need-the-gamma-function------------------
% defined for integer and half-integer values
define gamma_function(n){
variable gamma = 0;

if(n mod 1 == 0){
gamma = factorial(n-1);
}else if(n mod 1 == 0.5){
n -= 0.5;
gamma = sqrt(PI)*factorial(2*n)/(4^n*factorial(n));
}

return gamma;
}

%-------initializing-panels-----------------------
variable panel = Struct_Type[2];

panel[0] = xfig_plot_new(12, 9);
panel[0].world( CHISQRMIN+LOG*0.1, 0.999*CHISQRMAX, 0, 0.5; xlog=LOG);
panel[0].ylabel("$f_k (\chi^2)$"R);

panel[1] = xfig_plot_new(12, 6);
panel[1].world( CHISQRMIN+LOG*0.1, 0.999*CHISQRMAX, 0, 1.1; xlog=LOG);
panel[1].ylabel("$F_k (\chi^2)$"R);

variable chisqr = [CHISQRMIN:CHISQRMAX:dx];
variable prob_density = Double_Type[length(chisqr)];
variable cumulative_distr = Double_Type[length(chisqr)];

%-------calculate-and-plot-distribution-for-k-values------------------------------
% (k larger than 100 not possible as factorial breaks down)
variable i, k, labely = 0.9, labelx = 0.8, ystep = 0.06, sigma_flag;

foreach k (KVALUES){
variable kcolor = xfig_mix_colors(COLOR[0], COLOR[1], log(k-1)/5 );
sigma_flag = 0;

% calculating probability densities and integrating them in the same loop
for(i=0; i<length(chisqr)-1; i++){
prob_density[i] = ( chisqr[i]^(k/2.-1.)*E^(-chisqr[i]/2.) )/( 2.^(k/2.)*gamma_function(k/2.) );
cumulative_distr[i] = cumulative_distr[i-1]+prob_density[i]*dx;

% plot a line at edge of confidence level
if(cumulative_distr[i] >=0.9 && sigma_flag == 0){
panel[0].plot([chisqr[i],chisqr[i]], [0,prob_density[i]]; line=2, color = kcolor, depth=100-k);
panel[1].plot([chisqr[i],chisqr[i]], [0.9,1.1]; line=2, color = kcolor, depth=100-k);
sigma_flag = 1;
}
}

% plot and label the probability density for k
panel[0].plot(chisqr, prob_density; line=0, color = kcolor, depth=100-k);
panel[0].xylabel(labelx, labely , "k$\,=\,$"R + string(k), -0.5, 0; world0, color = kcolor);
labely -= ystep;

% plot according cumulative distribution function
panel[1].plot(chisqr, cumulative_distr; line=0, color = kcolor, depth=100-k);
}

% dashed line in second panel
panel[1].plot([0.1,200], [1,1]; line=1, color = "gray", depth=100);
panel[1].plot([0.1,200], [0.9,0.9]; line=1, color = "gray", depth=100);
panel[1].xylabel(0.05, 0.77, "90\%-level"R, -0.5, 0; world0, color = "gray");

%-------render-all---------------------------------------
variable multi = xfig_multiplot(panel; xlabel=`$\chi^2$`, cols=1);
multi.render("chisqr.pdf");

quit;
</pre>

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 [[Category:SLxfig]]
-[[File:chisq.png]]
+[[File:Chisqr.png|500px]]
 The Chi²-distribution and its according cumulative distribution function for a large number of degrees of freedom for illustrative purposes. Confidence levels are indicated in the CDF. Feel free to use it in your thesis, there are some customization options in the header.

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 [[Category:SLxfig]]
-[[File:chisq.png|560px|]]
+[[File:chisq.png]]
 The Chi²-distribution and its according cumulative distribution function for a large number of degrees of freedom for illustrative purposes. Confidence levels are indicated in the CDF. Feel free to use it in your thesis, there are some customization options in the header.

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