Making the assumption to be the same as results

Hi everyone! I dont know how to fit the parameter of b and n in my code to get the calculation of area equal 1. Could someone help me to modify it? I literally confuse how to fix this up. Thank you in advance before!

ro_init=0.2:0.1:100;
b=0.0517;                                                    % assume
n=1.0145;                                                    % assume
cdfVdp=(1-exp(-b*((2*ro_init).^n)));                       
pdfvdp=2*b*n*exp(-b*(2*ro_init).^n).*(2*ro_init).^(n-1);

area=trapz(ro_init,pdfvdp); %this results should be 1

[KSSV]

Do you have range of values for b and n?

[Kevin Isakayoga]

b is from 0 to 0.1 n is from 0.8 to 2

Answer 1

[KSSV]

ro_init=0.2:0.1:100;

r = 200 ; c = 200 ; % Try increasing these values 
B = linspace(0,0.1,r) ;
N = linspace(0.8,2,c) ;
[B,N] = meshgrid(B,N) ; 
A = zeros(r,c) ; 
for i = 1:r
  for j = 1:c
      b=B(i,j) ; % 0.0517;                                                    % assume
      n=N(i,j) ; % 1.0145;                                                    % assume
      % cdfVdp=(1-exp(-b*((2*ro_init).^n)));                       
      pdfvdp=2*b*n*exp(-b*(2*ro_init).^n).*(2*ro_init).^(n-1);

      area=trapz(ro_init,pdfvdp); %this results should be 1
      A(i,j) = area ;
   end
end
% GEt area equal to one 
idx = abs(A-1)<10^-3 ;
[B(idx) N(idx)]    % these are the values of b and n   

[Kevin Isakayoga]

Thank you! You are the best!

[Kevin Isakayoga]

By the way ,could you help me to explain why are my codes still not working if i change the value? and also what should i change?

clc;clear;
n=1000;                                                 %number of trial
rlower=0.002;
rupper=130;                                             % Assume the initial radius in micron meter
r_initial=rlower+(rupper-rlower).*rand(1,n);
r_initial=sort(r_initial);
%r_initial=0.2:0.1:100;
r = 500 ; c = 500 ; % Try increasing these values 
B = linspace(0.01,0.09,r) ;
N = linspace(0.9,1.4,c) ;
[B,N] = meshgrid(B,N) ; 
A = zeros(r,c) ; 
for i = 1:r
  for j = 1:c
      b=B(i,j) ; % 0.0517;                                                    % assume
      n=N(i,j) ; % 1.0145;                                                    % assume
      % cdfVdp=(1-exp(-b*((2*ro_init).^n)));                       
      pdfvdp=2*b*n*exp(-b*(2*r_initial).^n).*(2*r_initial).^(n-1);
      area=trapz(r_initial,pdfvdp); %this results should be 1
      A(i,j) = area ;
   end
end
% GEt area equal to one 
idx = abs(A-1)<10^-3 ;
[B(idx) N(idx)]    % these are the values of b and n  

the answer will be like this,

ans =
  0×2 empty double matrix

Looking forward to hearing from you. Thank you!

[KSSV]

Try decreasing the tolerance value.

idx = abs(A-1)<10^-2 ;