Fig 6. (a): Representative simulated pdf by the Weibull model using the standard shape and scale parameters of populations maintained at 25°C (optimum temperature of development). b) Monovariate examination of the profile likelihood of the shape parameter (0<β<12) for fixed scale parameter (α = 0.7) (the MLEs maximize logL (f, x_i, a) over all possible β over the independent aging variable x_i) (c) Bivariate examination of the profile likelihood for both shape and scale parameters and parametric family of distributions specified by its pdf f (x, α, |b), the simulation results of the Newton-Raphson algorithm are: Local minimum: 60.92, score gradient vector: $\mathrm{h}(a,\beta )=\left[\begin{array}{l}2065.761-42.1044\\ -42.1049.6543\end{array}\right]$ and Hessian matrix: $\text{H}(a,\beta )=\left[\begin{array}{l}0.000531310.0023172\hfill \\ 0.002317170.1136870\hfill \end{array}\right]$.