how to estimate parameters of nonlinear complex equations having summation terms

how to use MLE for mathematical model having cdf/mean value function

m(t) = x(1-exp(yt)) +at^b +zt and intensity function as

I(t)= xyexp(-yt) + abt^(b-1) +z

for estimating parameters x,y,z,a and b what i need to do...do i need to write a script or do i need to solve the attached equations using fsolve and how..can you suggest any tutorial or course which help me in analysing the above model.

thanks

shalini

Answer 1

[Shubham Rawat]

Hi Shalini,

You may use the following documentation of fsolve for solving the non linear equations:

Solve system of nonlinear equations - MATLAB fsolve (mathworks.com)

For further information about non linear equations in MATLAB. You may use this documentation:

Systems of Nonlinear Equations - MATLAB & Simulink (mathworks.com)

Hope this Helps!

[shalini sharma]

thanks...i am trying to use fsolve for simpler models having 2 or three parameters before evaluating it for 5 parameters but i am having problem while evaluating the value of unknown parameters a,b and c as function equation consist of summative term where ti is fault data stored in array and tn is nth term of the cummulative addition of array.

f1 = n/b -Sk + summation((2*c*ti)/c+exp(b*tn),i=1 ton) -a((n*exp(-b*tn)*(1-c))/(1+c*exp(-b*tn))^2

i asked many math scholars but none was able to help me to find the sum of if underlined term so that i can include it in equation in reduced form.

i tried using symsum but it gives error

f =n/b-Sk+symsum((2*c*A(i))/(c+exp(b*A(i)))-a*(n*exp(-b*Sn)*(1-c))/(1+c*exp(-b*Sn))^2

if i use code

for i=1:n

Sk = Sk + A(i);

g1=(2*c*A(i))/(c+exp(b*A(i)));

g2=2/(c+exp(b*A(i)));

end

f = n/b-Sk+g1-a*(n*exp(-b*Sn)*(1-c))/(1+c*exp(-b*Sn))^2;

will it give correct result, as i dont know how fsolve work,does it use newton ralpson method and iterativly solve the unknown parameters from initial guess.

can you plese suggest the best way to find unknown parameter values of nonlinear equations resulting from MLE.