How to plot median Confidence interval and how to comape two model ? im trynig to find the diffrence bw 2 models under difrent error. Here error are diff distbution,

N= 10000; % Number of observation

jN = 20; % Number of JumpsF

jumpInd = randperm(N,jN);

jumpInd = sort(jumpInd,'ascend');

jumpHeights = random('logn',log(15),0.5,jN+1,1);

jumpInd = [0 jumpInd N];

f = zeros(N,1);

a =[0.1 0.2 0.1 1.05]; % Real Values

k = a(4);

ind=zeros(N,1);

interval_N = N/5; %requires N to be divisible by 5

S=10; % No of simulation

alpha = 0.05;

for i=1:5

ind(interval_N*(i-1)+1:interval_N*(i-1)+interval_N/2)=1;

ind=logical(ind);

c = zeros(S,4);

end

for j= 1:S

for i = 1:jN+1

f(jumpInd(i)+1:jumpInd(i+1)) = jumpHeights(i);

end

v1=a(1)+a(2)*f+a(3)*f.^2; % Model One

v2=k*(v1); % Model Two

v3 = zeros(size(v1));

v3(ind)= a(1) + a(2)*f(ind) + a(3)*f(ind).^2;

v3(~ind)=k*(a(1) + a(2)*f(~ind) + a(3)*f(~ind).^2);

%v3= v3 + 7*randn(size(v3));

v3= v3 + 3*random('t',4,size(v3)); % T distribution

%v3 = v3 + 5* random('ev',0,1,size(v3)); % extream values distribution

%v3 = v3 + 2*poissrnd(v3);

% Defines the residual function.

% Here we let a1 = c(1), a2 = c(2), a3 = c(3) and k = c(4)

F = @(c) ind.*(c(1) + c(2)*f + c(3)*f.^2 - v3) +(1-ind).*(c(4)*(c(1) + ...

c(2)*f + c(3)*f.^2) - v3);

% Here we set options for lsqnonlin

options = optimoptions(@lsqnonlin,'Algorithm','trust-region-reflective');

% Here we set the initial guess for the parameters

c0 = [0.1,0.2,0.1 1]; % Initail values

[c(j,:),resnorm,residual,output] = lsqnonlin(F,c0,[-1e6,-1e6,-1e6,-1e6],[1e10,1e10,1e10,2],options);

% To check the uncertanity in the estimated parameters

v3_fit = zeros(size(v1));

v3_fit(ind)= c(j,1) + c(j,2)*f(ind) + c(j,3)*f(ind).^2;

v3_fit(~ind)=c(j,4)*(c(j,1) + c(j,2)*f(~ind) + c(j,3)*f(~ind).^2);

end

mu= mean(c(:,4));

sigma = std(c(:,4));

Median = median(c(:,4));

ci95 = cint_median(c(:,4),alpha);

e = v3 -v3_fit;

table(mu,sigma,Median,ci95)

%%%%%%%%%%%%%%%%%%% function to determine the confidence interval of median%%%%%%%%%%%%%%%%

function [interval] = cint_median(M,alpha)

%creates a confidence interval for the median of a dataset using a sign

%test based on binomial distribution.

if nargin < 2

alpha = 0.05;

end

%sign test

n = length(M);

m = median(M);

%confidence intervall based on median

c = icdf('bino', alpha/2 , n , 0.5);

s = sort(M);

interval = [s(c) m s(end - c)];

end

%%%%%%%%% least square method for model1%%%%%

function coefficient = LSMcurvefit_v1(x,y)

A = [ones(size(x)) x x.^2];

coefficient=(A'*A)\(A'*y);

end,

%%%%%%%%%%%%%%%Least square method for model 2%%%%%

function coefficient = LSMcurvefit_v2(x,y,c)

z = c(1)+c(2)*x+c(3)*x.^2;

coefficient = sum(z.*y)/sum(z.^2);

end

Answer 1

[Balavignesh]

Hi Muhammad,

As per my understanding, you would like to plot median confidence interval of the models.

I would suggest you to calculate the 'median' of your data using 'median' function. You could calculate the confidence interval using the 'bootci' or 'prctile' function to calculate the confidence interval. You could use 'patch' or 'fill' function to plot the confidence interval as a shaded area around the median line.

Here is an example code that could help you understand this:

% This is an example datast. Use your own dataset
load carsmall;
weights = Weight

weights = 100×1

3504 3693 3436 3433 3449 4341 4354 4312 4425 3850

% Compute the median and confidence interval
medianValue = median(weights);
ci = bootci(1000, @median, weights);

% Plotting the Median Confidence Interval
figure;

plot(1, medianValue, 'ko', 'MarkerSize', 8, 'LineWidth', 2);
hold on;

patch([0.9, 1.1, 1.1, 0.9], [ci(1), ci(1), ci(2), ci(2)], 'b', 'FaceAlpha', 0.3);

% Add labels and customize the plot
xlabel('Car');
ylabel('Weight (lbs)');
title('Median Weight with Confidence Interval');

% Remove the extra tick mark
set(gca, 'XTick', 1);

% Remove the box around the plot
box off;
hold off;

Please refer to the following documentation links to have more information on:

• 'median' function: https://in.mathworks.com/help/matlab/ref/median.html
• 'bootci' function: https://in.mathworks.com/help/stats/bootci.html

Hope that helps!

Balavignesh.