# How can I fit this equation into my empirical cumulative density function (CDF) to find the unknowns?

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Farnood83 on 17 Sep 2021
Edited: Farnood83 on 17 Sep 2021
The following equation is the theoretical equation for the cumulative density function (cdf) for my problem:   p0 is the matrix for initial value and p1 is the matrix for final values of unknowns.
Farnood
KB= 1.38064852*(10^-23); %Boltzmann constant
Temp = 273+22.3; %Room Temperature in Kelvin
Beta = (KB*Temp)^(-1);
Vel = 81.38e-9; % Tip Velocity (m/sec)
X_nano = (10^-9).*X; % The Lateral Forces in Newton
Stat_DX_nano = (10^-9).*Stat_DELXX1_Trace; %The DeltaX stats in meter (average and standard deviation)
mean_K_eff1_array = mean(K_eff1_array); %Average of the stiffnesses
fun = @(p1,X_nano) 1-exp(-(p1(1,1)/(Vel*mean_K_eff1_array)).*X_nano(:,1)...
.*exp(-Beta.*(p1(1,2)-Stat_DX_nano(1,1).*X_nano(:,1)))).*(1+...
(Beta^2).*(p1(1,1)/(Vel*mean_K_eff1_array)).*X_nano(:,1)...
.*exp(-Beta.*(p1(1,2)-Stat_DX_nano(1,1).*X_nano(:,1))).*...
(p1(1,3)+(X_nano(:,1).*Stat_DX_nano(1,2)).^2)).^(-1/2);
p01(1) = 7.5;
p01(2) = 3.0200381506371e-9;
p01(3) = 1.0066793835457e-9;
[p1,res] = lsqcurvefit(fun,p01,X_nano,Y);%,lb,ub);%,options)
f_o1 = p1(1,1);
U_o1 = p1(1,2);
Var_U_o = p1(1,3);
yfit1 = fun(p1,X_nano);