## 4 Results Obtained with the Modified Nelder-Mead Method
Figures 8 and 9 illustrate the accuracy of parameter extraction by comparing the measurement and simulation results for two phosphor-converted white power LEDs--one with the best fit (Figure 8) and one with the worst fit (Figure 9). The parameter extraction for these LEDs was performed for the full sets of forward currents applied during measurements. However, for visibility, only the measurement values are plotted that have a junction temperature equal to the target. This allows us to display the isothermal lines and better present model errors. The extraction process, however, utilizes all measured values, which is a significant advantage of the new extraction methodology enabled by the new method. The difference of the results obtained by the model compared with the measurements in Figures 8 and 9 shows only slight differences; however, the first has a maximum relative error of 1.5% and the second has a 4.7% radiant flux, but these differences appear in the low-current area. This confirms the hypothesis that the model adequately describes both the low- and high-current regions. There is only one original goal left that must be investigated: The new parameter extraction method should also effectively address sample-to-sample variations when the goal is to provide a single model parameter set representative of a given LED type or binning class. Because the extraction process is unknown for the specific LED samples, it can incorporate characteristics from all samples into the extended vertex used in the modified Nelder-Mead algorithm-based parameter extraction process. Figure 10 shows the extraction for one bin  
Note that the parameter sets obtained from the aggregate data of a larger number of LED samples of the same type differ from the parameter sets obtained by averaging individual samples. This highlights another advantage of our new approach: a significant reduction in required computational resources, particularly when extracting model parameter sets representative of an LED-type or binning class. Figure 10: Measurement results for aggregated 5 white (*) and the simulation with parameters estimated by the novel Nelder-Mead method (solid line); electrical (**left**), radiant flux (**middle**), and luminous flux (**right**) characteristics. Figure 9: Measurement results for a phosphor-converted power LED chip (No. 8.) (*) and the simulation with parameters estimated by the novel Nelder–Mead method (solid line); electrical (**left**), radiant flux (**middle**), and luminous flux (**right**) characteristics. It is conspicuous but not surprising that the parameter sets obtained for multiple LED samples from the same type (and same binning class) provide a fit with more or less the same accuracy, as one LED can replace another, i.e., the model-to-measurement error is in the same range as the measurement-to-measurement error. This holds both for the prior brute-force method-based and for the new modified Nelder-Mead algorithm-based parameter extraction methods. Not only are the accuracies of the simulations similar for the LED samples of the same type, but the actual parameter values are also close to one another, e.g., the different \(I_{0}\) values are within \(\pm 10\%\) in a logarithmic scale. In the case of a larger population of phosphor-converted white LEDs of the same type (and presumed binning class), much larger sample-to-sample variations in parameter values were observed. This finding aligns with the previous results of the Delphi4 LED project, which suggest that this population is a mix of two LED types exhibiting similar light output properties at the applied binning forward current and junction temperature [23]. The new parameter extractor was coded in Python 3.9. Extracting parameters for an LED sample measured at 33 operating points takes 10-18 s on a standard desktop computer (i5-12400, 3.2 GHz, 32 GB RAM) using a single core.