Update stereology_analysis.ipynb

grain_size_tools/stereology_analysis.ipynb

@@ -363,9 +363,7 @@
    "id": "458148cc-b7c4-431b-8006-27a11d0a544a",
    "metadata": {},
    "source": [
-    "## Using the two-step method\n",
-    "\n",
-    "TODO"
+    "## Using the two-step method"
    ]
   },
   {
@@ -406,43 +404,80 @@
    "id": "473f283f",
    "metadata": {},
    "source": [
-    "### Estimate volume fractions from a lognormal distribution"
+    "### Estimate volume fractions from a lognormal distribution\n",
+    "\n",
+    "#### Generate a lognormal distribution using the calculated optimal values"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
    "id": "effea92e",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "volume fraction = 70.6 %\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "# import lognorm\n",
+    "# import lognorm from Scipy\n",
     "from scipy.stats import lognorm\n",
     "\n",
     "# set calculated variables\n",
     "geo_mean = 36.05\n",
     "sigma = np.log(1.63)\n",
     "\n",
     "# Calculate the lognormal distribution\n",
-    "dist = lognorm(s=sigma, scale=geo_mean)\n",
-    "\n",
-    "# Calculate the volume fraction between sizes 75 and 25\n",
-    "volume_fraction = dist.cdf(75) - dist.cdf(25)\n",
-    "\n",
-    "print(f'volume fraction = {volume_fraction * 100:.1f} %')"
+    "dist = lognorm(s=sigma, scale=geo_mean)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5dba15b3",
+   "metadata": {},
+   "source": [
+    "#### Examples of volume fractions representing a particular range of grain sizes using the cumulative distribution function (CDF) of the lognormal distribution"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 7,
+   "id": "c6f5648c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Volume fraction of grains below 50 microns: 74.8 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Calculate the CDF value at 50 microns in percentage\n",
+    "volume_fraction_below_50 = dist.cdf(50)\n",
+    "print(f\"Volume fraction of grains below 50 microns: {100 * volume_fraction_below_50:.1f} %\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "bdf1a171",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Volume fraction of grains between 15 and 35 microns: 0.44\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Calculate the volume fraction between 15 and 35 microns \n",
+    "volume_fraction_15_to_35 = dist.cdf(35) - dist.cdf(15)\n",
+    "print(f\"Volume fraction of grains between 15 and 35 microns: {volume_fraction_15_to_35:.2f}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
    "id": "38f0bf26",
    "metadata": {},
    "outputs": [