The graphing applet in TI Nspire is a great tool for visualizing Weibull distribution, by adjusting the variable sliders for shape and scale parameters. Cumulative distribution is easily obtained by the Integral function under analyze graph feature.
This mean nothing more than to prove that implementing the Nelder-Mead algorithm on the TI-84 is possible. In reality, the time it will take for a TI-84 Plus SE to arrive a solution for any practical non-linear problem renders this somewhat a last resort option. That is, in the absence of any modern computer or even a decent mobile phone 🙂
The program is implemented in the native TI-Basic, which is ported from the program for the same problem previously done on TI Nspire and Casio fx-9860GII. It took some efforts to port the program as the resources on the TI-84 is comparatively limited. For example,variable names are also restricted to single character, but thanks to list, things are easier.
With the availability of the new generation TI-Connect software, the Program Editor has returned and this tool greatly helped programming the Nelder-Mead on TI-84. Although unlike the more advanced Nspire Software which is able to run the program on PC instead of having to download the program to the TI-84 every time, editing TI-Basic in PC with a full keyboard and full screen is way more comfortable than to doing so on the calculator. The new TI-Connect CE PC software looks really nice.
Screens of the actual program running on a TI-84 Plus Pocket SE. The equation to solve is the Rosenbrock function of f(x,y) = (a-x)^2 + b(y-x^2)^2, using a=1 and b=100.
The TI-84 Plus Pocket SE took 12 minutes to complete, while its big brother TI Nspire took only 22 seconds.