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"Ran 10000 simulations of a 200-year lifespan model.\n",
"\n",
"Average age of death: 120.22\n",
"Average number of career changes: 4.22\n",
"Average number of major illnesses: 1.61\n"
]
}
],
"source": [
"import numpy as np\n",
"import random\n",
"import statistics\n",
"\n",
"def mortality_probability(age, max_age=200):\n",
" \"\"\"\n",
" A toy function that returns the probability of death at a given age.\n",
" The function is designed so that average lifespan hovers near 200,\n",
" but you can adjust it as needed.\n",
" \"\"\"\n",
" # Example: A small base rate, increasing with age.\n",
" # At age 0 --> prob ~ 0.0, at age 200 --> prob ~ 0.02\n",
" # This will lead to many individuals reaching 200,\n",
" # but is just a toy model. Tweak as necessary.\n",
" return 0.0001 * age\n",
"\n",
"def simulate_one_life(max_age=200):\n",
" \"\"\"\n",
" Simulate a single life path, returning:\n",
" - age of death (or 200 if still alive)\n",
" - record of 'career changes'\n",
" - record of 'major illnesses'\n",
" \"\"\"\n",
" current_age = 0\n",
" is_alive = True\n",
"\n",
" career_change_years = []\n",
" illness_years = []\n",
"\n",
" while is_alive and current_age <= max_age:\n",
" # Roll for mortality this year\n",
" death_chance = mortality_probability(current_age, max_age)\n",
" if random.random() < death_chance:\n",
" # Person dies this year\n",
" return current_age, career_change_years, illness_years\n",
"\n",
" # If still alive, check for events:\n",
" # 1) Career change (example ages 25-150, 5% chance each year)\n",
" if 25 <= current_age <= 150:\n",
" if random.random() < 0.05:\n",
" career_change_years.append(current_age)\n",
"\n",
" # 2) Major illness (example ages 40-190, 2% chance each year)\n",
" if 40 <= current_age <= 190:\n",
" if random.random() < 0.02:\n",
" illness_years.append(current_age)\n",
"\n",
" current_age += 1\n",
"\n",
" # If we exited the loop without dying, it means we reached max_age\n",
" return max_age, career_change_years, illness_years\n",
"\n",
"\n",
"def run_simulation(num_simulations=10000, max_age=200):\n",
" \"\"\"\n",
" Run multiple simulations and return:\n",
" - distribution of death ages\n",
" - average age of death\n",
" - average number of career changes\n",
" - average number of major illnesses\n",
" \"\"\"\n",
" death_ages = []\n",
" career_change_counts = []\n",
" illness_counts = []\n",
"\n",
" for _ in range(num_simulations):\n",
" death_age, career_changes, illnesses = simulate_one_life(max_age)\n",
" death_ages.append(death_age)\n",
" career_change_counts.append(len(career_changes))\n",
" illness_counts.append(len(illnesses))\n",
"\n",
" avg_death_age = statistics.mean(death_ages)\n",
" avg_career_changes = statistics.mean(career_change_counts)\n",
" avg_illnesses = statistics.mean(illness_counts)\n",
"\n",
" results = {\n",
" \"avg_death_age\": avg_death_age,\n",
" \"avg_career_changes\": avg_career_changes,\n",
" \"avg_illnesses\": avg_illnesses,\n",
" \"death_age_distribution\": death_ages\n",
" }\n",
" return results\n",
"\n",
"# -----------------------\n",
"# Run the simulation\n",
"# -----------------------\n",
"if __name__ == \"__main__\":\n",
" np.random.seed(42) # For reproducibility (optional)\n",
" random.seed(42)\n",
"\n",
" N = 10_000\n",
" simulation_results = run_simulation(num_simulations=N, max_age=200)\n",
"\n",
" print(f\"Ran {N} simulations of a 200-year lifespan model.\\n\")\n",
" print(f\"Average age of death: {simulation_results['avg_death_age']:.2f}\")\n",
" print(f\"Average number of career changes: {simulation_results['avg_career_changes']:.2f}\")\n",
" print(f\"Average number of major illnesses: {simulation_results['avg_illnesses']:.2f}\")\n",
" # You could also plot or further analyze death_age_distribution if desired."
]
},
{
"cell_type": "code",
"source": [
"import numpy as np\n",
"import random\n",
"import statistics\n",
"import plotly.graph_objects as go\n",
"from collections import Counter\n",
"\n",
"# ----------------------\n",
"# Step 1: Define the simulation\n",
"# ----------------------\n",
"def mortality_probability(age, max_age=200):\n",
" return 0.0001 * age\n",
"\n",
"def simulate_one_life(max_age=200):\n",
" current_age = 0\n",
" career_change_years = []\n",
" illness_years = []\n",
"\n",
" while current_age <= max_age:\n",
" death_chance = mortality_probability(current_age, max_age)\n",
" if random.random() < death_chance:\n",
" return current_age, career_change_years, illness_years\n",
"\n",
" if 25 <= current_age <= 150:\n",
" if random.random() < 0.05:\n",
" career_change_years.append(current_age)\n",
" if 40 <= current_age <= 190:\n",
" if random.random() < 0.02:\n",
" illness_years.append(current_age)\n",
"\n",
" current_age += 1\n",
" return max_age, career_change_years, illness_years\n",
"\n",
"def run_simulation(num_simulations=10000, max_age=200):\n",
" death_ages = []\n",
" career_change_counts = []\n",
" illness_counts = []\n",
"\n",
" for _ in range(num_simulations):\n",
" d_age, c_changes, i_ills = simulate_one_life(max_age)\n",
" death_ages.append(d_age)\n",
" career_change_counts.append(len(c_changes))\n",
" illness_counts.append(len(i_ills))\n",
"\n",
" results = {\n",
" \"death_ages\": death_ages,\n",
" \"career_change_counts\": career_change_counts,\n",
" \"illness_counts\": illness_counts\n",
" }\n",
" return results\n",
"\n",
"# ----------------------\n",
"# Step 2: Binning functions\n",
"# ----------------------\n",
"def bin_career_changes(count):\n",
" if count == 0:\n",
" return \"Career=0\"\n",
" elif count == 1:\n",
" return \"Career=1\"\n",
" elif count == 2:\n",
" return \"Career=2\"\n",
" else:\n",
" return \"Career=3+\"\n",
"\n",
"def bin_illnesses(count):\n",
" if count == 0:\n",
" return \"Ill=0\"\n",
" elif count == 1:\n",
" return \"Ill=1\"\n",
" elif count == 2:\n",
" return \"Ill=2\"\n",
" else:\n",
" return \"Ill=3+\"\n",
"\n",
"def bin_death_age(age):\n",
" if age <= 50:\n",
" return \"Age=0-50\"\n",
" elif age <= 100:\n",
" return \"Age=51-100\"\n",
" elif age <= 150:\n",
" return \"Age=101-150\"\n",
" else:\n",
" return \"Age=151-200\"\n",
"\n",
"# ----------------------\n",
"# Step 3: Build flow counters\n",
"# ----------------------\n",
"def build_flow_counts(results):\n",
" career_counts = results[\"career_change_counts\"]\n",
" illness_counts = results[\"illness_counts\"]\n",
" death_ages = results[\"death_ages\"]\n",
"\n",
" from collections import Counter\n",
" combos = []\n",
"\n",
" # Build the list of (career_bin, ill_bin, age_bin)\n",
" for c_count, i_count, d_age in zip(career_counts, illness_counts, death_ages):\n",
" c_bin = bin_career_changes(c_count)\n",
" i_bin = bin_illnesses(i_count)\n",
" a_bin = bin_death_age(d_age)\n",
" combos.append((c_bin, i_bin, a_bin))\n",
"\n",
" combo_counter = Counter(combos)\n",
"\n",
" flow1_counter = Counter() # (career_bin -> ill_bin)\n",
" flow2_counter = Counter() # (ill_bin -> age_bin)\n",
"\n",
" for (c_bin, i_bin, a_bin), count in combo_counter.items():\n",
" flow1_counter[(c_bin, i_bin)] += count\n",
" flow2_counter[(i_bin, a_bin)] += count\n",
"\n",
" return flow1_counter, flow2_counter\n",
"\n",
"# ----------------------\n",
"# Step 4: Convert counters -> Sankey format\n",
"# ----------------------\n",
"def build_sankey_data(flow1_counter, flow2_counter):\n",
" career_bins = [\"Career=0\", \"Career=1\", \"Career=2\", \"Career=3+\"]\n",
" illness_bins = [\"Ill=0\", \"Ill=1\", \"Ill=2\", \"Ill=3+\"]\n",
" age_bins = [\"Age=0-50\", \"Age=51-100\", \"Age=101-150\", \"Age=151-200\"]\n",
"\n",
" all_nodes = career_bins + illness_bins + age_bins\n",
" label_to_index = {label: i for i, label in enumerate(all_nodes)}\n",
"\n",
" source_list = []\n",
" target_list = []\n",
" value_list = []\n",
"\n",
" # (career -> illness)\n",
" for (c_bin, i_bin), val in flow1_counter.items():\n",
" source_list.append(label_to_index[c_bin])\n",
" target_list.append(label_to_index[i_bin])\n",
" value_list.append(val)\n",
"\n",
" # (illness -> age)\n",
" for (i_bin, a_bin), val in flow2_counter.items():\n",
" source_list.append(label_to_index[i_bin])\n",
" target_list.append(label_to_index[a_bin])\n",
" value_list.append(val)\n",
"\n",
" return all_nodes, source_list, target_list, value_list\n",
"\n",
"# ----------------------\n",
"# Step 5: Plot with Plotly\n",
"# ----------------------\n",
"def plot_sankey(all_nodes, source_list, target_list, value_list, title=\"Life Simulation Sankey\"):\n",
" fig = go.Figure(data=[go.Sankey(\n",
" node=dict(\n",
" pad=15,\n",
" thickness=20,\n",
" line=dict(color=\"black\", width=0.5),\n",
" label=all_nodes\n",
" ),\n",
" link=dict(\n",
" source=source_list,\n",
" target=target_list,\n",
" value=value_list\n",
" )\n",
" )])\n",
" fig.update_layout(title_text=title, font_size=12)\n",
" fig.show()\n",
"\n",
"# ----------------------\n",
"# Main execution\n",
"# ----------------------\n",
"if __name__ == \"__main__\":\n",
" # For reproducibility (optional)\n",
" np.random.seed(42)\n",
" random.seed(42)\n",
"\n",
" # 1) Run the simulation\n",
" results = run_simulation(num_simulations=10000, max_age=200)\n",
"\n",
" # 2) Build the flow counters (career->illness, illness->death_age)\n",
" flow1_counter, flow2_counter = build_flow_counts(results)\n",
"\n",
" # 3) Convert to Sankey data\n",
" all_nodes, source_list, target_list, value_list = build_sankey_data(flow1_counter, flow2_counter)\n",
"\n",
" # 4) Plot Sankey\n",
" plot_sankey(all_nodes, source_list, target_list, value_list,\n",
" title=\"Monte Carlo Life Simulation (200-year span) - Sankey Diagram\")"
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