add relevant documentation for generating random values from ensemble…

… distribution

simulations.ipynb

@@ -24,6 +24,15 @@
     "from ensemble.distributions import distribution_dict\n",
     "from ensemble.ensemble_model import EnsembleFitter\n",
     "\n",
+    "# reference: https://github.com/scipy/scipy/blob/v1.14.0/scipy/stats/_distn_infrastructure.py#L994\n",
+    "# relevant lines: 1026, 1048, 1938, 1941\n",
+    "# summary:\n",
+    "#   create ensemble cdf with at least 2 distributions/corresponding weights with shared mean and variance\n",
+    "#   draw sample from Unif(0, 1)\n",
+    "#   give sample to vectorized ppf_single\n",
+    "#   optimize (using Brent's method) with objective function ensemble_cdf(x) - q, where q is your Unif(0, 1) sample\n",
+    "#   return quantiles which minimize the objective function (i.e. which values of x minimize ensemble_cdf(x) - q)\n",
+    "\n",
     "def ensemble_cdf(x, distributions, weights, mean, variance):\n",
     "  my_objs = []\n",
     "  for distribution in distributions:\n",