ukol 5

ukol.ipynb

@@ -32,6 +32,7 @@
     "import pandas as pd\n",
     "#np.set_printoptions(precision=3)\n",
     "#from sympy import *\n",
+    "from scipy import stats \n",
     "from scipy.stats import norm, uniform, expon\n",
     "#from scipy.optimize import minimize"
    ]
@@ -46,7 +47,8 @@
     "K = 28\n",
     "L = 8\n",
     "M = (((K + L) * 47) % 11) + 1\n",
-    "print(M)"
+    "print(\"M =\",M)\n",
+    "print(\"dataset ex0221\")"
    ]
   },
   {
@@ -207,10 +209,18 @@
     "Zaneste příslušné hustoty s odhadnutými parametry do grafů histogramu. Diskutujte, které z rozdělení odpovídá pozorovaným datům nejlépe."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "542a742d-2c96-4d06-bf05-49823752ed6d",
+   "metadata": {},
+   "source": [
+    "Odhady získáme pomocí momentové metody"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "98f1d4c1-f86b-4a39-aae1-bafbb951c3ca",
+   "id": "b1995dc6-a79c-4859-a720-5dca78d63e44",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -230,10 +240,10 @@
     "    sp4.hist(data, bins=10, density=True, alpha=0.5)\n",
     "    sp5.hist(data, bins=10, density=True, alpha=0.5)\n",
     "    \n",
-    "    mu, std = norm.fit(data)  # Get mean and standard deviation\n",
-    "    xmin, xmax = sp1.get_xlim()  # Get x-axis limits from the histogram\n",
+    "    mu, std = norm.fit(data)\n",
+    "    xmin, xmax = sp1.get_xlim()\n",
     "    x = np.linspace(xmin, xmax, 100)\n",
-    "    p_norm = norm.pdf(x, mu, std)  # Generate the PDF for the normal distribution\n",
+    "    p_norm = norm.pdf(x, mu, std)\n",
     "    sp2.plot(x, p_norm, 'red')\n",
     "    sp2.fill_between(x, p_norm, alpha=0.2, color='red')\n",
     "    sp2.set_title(f'Normal fit ($\\mu={mu:.2f}, \\sigma={std:.2f}$)')\n",
@@ -342,6 +352,70 @@
     "(1b) Pro každou skupinu zvlášť spočítejte oboustranný 95% konfidenční interval pro střední hodnotu."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "dec7a5cc-4c6b-4213-b3b8-8b58813f73cb",
+   "metadata": {},
+   "source": [
+    "Dle Studentova rozdělení:\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "\\left( \\overset{\\_}{X_{n}} - t_{\\frac{\\alpha}{2},n-1}\\frac{s}{\\sqrt{n}}, \\overset{\\_}{X_{n}} + t_{\\frac{\\alpha}{2},n-1}\\frac{s}{\\sqrt{n}} \\right)\n",
+    "\\end{align}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "69ad2d59-bdc0-4cc7-b51c-7453f2126157",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def conf_interval(data, name):\n",
+    "    conf = stats.t.interval(confidence = 0.95, df = len(data) - 1, loc = np.mean(data), scale = stats.sem(data))\n",
+    "    print(f\"Oboustranný konfidenční interval 95% střední hodnoty skupiny \\\"{name}\\\":\", conf)\n",
+    "    return conf"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "16ee6a87-8b6a-472c-9689-9d3877d31084",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_conf_interval(title, list, interval):\n",
+    "    fig, ax = plt.subplots(figsize = (6, 4))\n",
+    "    ax.hist(list, bins = 10, color = \"blue\", alpha=0.5)\n",
+    "    ax.set_title(f\"Oboustranný 95% interval skupiny \\\"{title}\\\"\")\n",
+    "    ax.axvline(x = interval[0], color = \"red\")\n",
+    "    ax.axvline(x = interval[1], color = \"red\")\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b5fd12a4-8517-4c5e-9f18-eaf627c56afa",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "conf_survived = conf_interval(survived, \"survived\")\n",
+    "conf_perished = conf_interval(perished, \"perished\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f17915e9-aef8-430d-8096-c13f078e25eb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plot_conf_interval(\"survived\", survived, conf_survived)\n",
+    "plot_conf_interval(\"perished\", perished, conf_perished)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "1c7cf77b",