The sum of two independent exponential distributions \begin{aligned}{Z=\omega_{1}X_{1}+\omega_{2}X_{2}}\end{aligned} is as follows. \begin{aligned}f_{Z}(z)=&\int _{0}^{z}\omega_{1}\omega_{2}f_{X_{1}}(x_{1})f_{X_{2}}(z-x_{1})\,dx_{1}\\=\omega_{1}\omega_{2}&\lambda _{1}\lambda _{2}\exp[-\lambda _{2}z]\int _{0}^{z}\exp[(\lambda _{2}-\lambda _{1})x_{1}]\,dx_{1}\\=&{\frac {\omega_{1}\omega_{2}\lambda _{1}\lambda _{2}}{\lambda _{2}-\lambda _{1}}}\left(\exp[-\lambda _{1}z]-\exp[-\lambda _{2}z]\right)\end{aligned}
But the following example doesn't follow the above equation. \begin{aligned}\omega_1=exp(-0.114989504)\end{aligned} \begin{aligned}\omega_2=exp(-7.5448246293224)\end{aligned} \begin{aligned}\lambda_1=1/(4.3258*10^{-08})\end{aligned} \begin{aligned}\lambda_1=1/(1.8737*10^{-03})\end{aligned}
The result is compared with conv(fX1,fX2)*(x_interval) in Matlab.
Can you tell me what the problem is?