Hi Kash022
1.
The attached function lognormal_pdf_123sigma_locations.m calculates the non symmetric locations of +-sigma1 +-sigma2 +-sigma3, along with the mean value and also returns the interpolated curve of the pdf to achieve 1 decimal accuracy, on the pdf, not the data.
mu0: mean
sm1: sigma 1 minus
sp1: sigma 1 plus
sm2: sigma 2 minus
sp2: sigma2 plus
sm3: sigma 3 minus
sp3: sigma 3 plus
call example, replace b with data:
b = betarnd(3,10,100,1); % replace betarand() with data
[mu0,sm1,sp1,sm2,sp2,sm3,sp3,y2,ny2]=lognormal_pdf_123sigma_locations(b)
2.
lognormal_pdf_123sigma_locations.m also returns a couple figures showing data, pdf approximation, and the location of the requested points:
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.
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3.
Copy of the function
function [mu0,sm1,sp1,sm2,sp2,sm3,sp3,y2,ny2]=lognormal_pdf_123sigma_locations(b)
% mu0: mean
% sm1: sigma 1 minus
% sp1: sigma 1 plus
% sm2: sigma 2 minus
% sp2: sigma2 plus
% sm3: sigma 3 minus
% sp3: sigma 3 plus
% author: John Bofarull Guix, jgb2012@sky.com
% b = betarnd(3,10,100,1); % simulated data, replace betarand() with real data
figure(1);
% h1=histfit(b,20,'lognormal') % test
h1=histfit(b,20,'lognormal')
b_histogram=h1(1);grid on;
b_pdf_lognormal_fit=h1(2)
y=b_pdf_lognormal_fit.YData;
sumy=sum(y);y=y/sumy;
ny=b_pdf_lognormal_fit.XData;
N=100;
y2=interp(y,N);y2=y2/sum(y2);
ny2=[1:1:numel(y)]*N;
pc_target=50; % mu: distribution mean value
n=2
pc=sum(y2([1:n])) *100
while pc<pc_target
n=n+1;pc=sum(y2([1:n])) *100;
end
mu=n;
figure(2);plot(y2);hold all
figure(2);plot(mu,y2(n),'bo');grid on
pc_target=34; [s1_min,s1_plus]=go_get_it(pc_target,mu,y2); % +- sigma
figure(2);plot(s1_min,y2(s1_min),'ro');
figure(2);plot(s1_plus,y2(s1_plus),'ro');
pc_target=47.5; [s2_min,s2_plus]=go_get_it(pc_target,mu,y2); % +-2*sigma
figure(2);plot(s2_min,y2(s2_min),'ro')
figure(2);plot(s2_plus,y2(s2_plus),'ro');
pc_target=49.7;[s3_min,s3_plus]=go_get_it(pc_target,mu,y2); % +-3*sigma
figure(2);plot(s3_min,y2(s3_min),'ro');
figure(2);plot(s3_plus,y2(s3_plus),'ro');
mu0=mu;
sm1=s1_min;
sp1=s1_plus;
sm2=s2_min;
sp2=s2_plus;
sm3=s3_min;
sp3=s3_plus;
function [sdown,sup]=go_get_it(pc_target,mu,y2)
% support function finds t1 t2 such sum(y([t1:mu]))=sum(y([mu:t2]))
n=1;pc=sum(y2([mu-n:mu])) *100; % search - s
while pc<pc_target
n=n+1;pc=sum(y2([mu-n:mu])) *100;
end
sdown=mu-n;
% figure(h);
% plot(h,sdown,y2(sdown),'ro');hold all;
n=1;pc=sum(y2([mu:mu+n])) *100; % search + s
while pc<pc_target
n=n+1;pc=sum(y2([mu:mu+n])) *100 ;
end
sup=n+mu;
% figure(2);
% plot(h,sup,y2(sup),'ro');
end
end
4.
checks
sum(y2([mu0:sp1]))
sum(y2([sm1:mu0]))
sum(y2([mu0:sp2]))
sum(y2([sm2:mu0]))
sum(y2([mu0:sp3]))
sum(y2([sm3:mu0]))
% upper tail
sum(y2([sp3:end]))
% lower tail
sum(y2([1:sm3]))
=
0.340091218398777
=
0.340121503890558
=
0.475010605933624
=
0.475120352505811
=
0.497000712621476
=
0.497028227492323
=
0.003110773668274
ans =
0.003254677216922
5.
lognormal pdf is normal pdf skewed righ, the sigma1,2,3 locations are no longer symmetric.
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Kash022
if you find this answer useful would you please be so kind to mark my answer as Accepted Answer?
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please click on the thumbs-up vote link,
thanks in advance
John BG
