{
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   "cell_type": "code",
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   "id": "cb048d16-7e90-4a89-82d1-c87466caaea0",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area weight for q0.05: 0.1500\n",
      "Area weight for q0.25: 0.2250\n",
      "Area weight for q0.5: 0.2500\n",
      "Area weight for q0.75: 0.2250\n",
      "Area weight for q0.95: 0.1500\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# Function to calculate area weight between two quantiles\n",
    "def calculate_area_weight(lower_quantile, upper_quantile):\n",
    "    lower_bound = norm.ppf(lower_quantile)  # Lower bound of the range\n",
    "    upper_bound = norm.ppf(upper_quantile)  # Upper bound of the range\n",
    "    \n",
    "    area_weight = norm.cdf(upper_bound) - norm.cdf(lower_bound)\n",
    "    \n",
    "    return area_weight\n",
    "\n",
    "# Define the quantiles and ranges\n",
    "quantiles_ranges = {\n",
    "    'q0.05': (0, 0.15),\n",
    "    'q0.25': (0.15, 0.375),\n",
    "    'q0.5': (0.375, 0.625),\n",
    "    'q0.75': (0.625, 0.85),\n",
    "    'q0.95': (0.85, 1)\n",
    "}\n",
    "\n",
    "# Calculate area weights for each range\n",
    "area_weights = {}\n",
    "for quantile, (lower, upper) in quantiles_ranges.items():\n",
    "    area_weights[quantile] = calculate_area_weight(lower, upper)\n",
    "\n",
    "# Output the results\n",
    "for quantile, weight in area_weights.items():\n",
    "    print(f\"Area weight for {quantile}: {weight:.4f}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bb737bd4-bfb5-4ab9-8045-ab2f447b973a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.25+0.225+0.225+0.15+0.15\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e42fbcaa-abd9-4733-9b0b-9304affd8277",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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