In [1]:
# Life Expectancy Modeling in Python
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
# Parameters for life expectancy
mean_life_expectancy = 80 # Mean life expectancy in years
std_dev_life_expectancy = 8 # Standard deviation for life expectancy in years
# Define age x
x = 70 # Example: current age
# Simulate life expectancy distribution for a general population
def simulate_life_expectancy(mean, std_dev, size=10000):
"""
Simulates a life expectancy distribution.
"""
return np.random.normal(mean, std_dev, size=size)
# Filter life expectancies for individuals of age x
def remaining_life_expectancy_distribution(age, life_expectancies):
"""
Adjust life expectancy distribution for someone of current age.
"""
return life_expectancies[life_expectancies > age] - age
# Simulate general life expectancy
general_life_expectancies = simulate_life_expectancy(mean_life_expectancy, std_dev_life_expectancy)
# Compute remaining life expectancy distribution for a person of age x
remaining_life_expectancies = remaining_life_expectancy_distribution(x, general_life_expectancies)
# Plot distributions
sns.set(style="whitegrid")
plt.figure(figsize=(12, 6))
# General life expectancy distribution
sns.histplot(general_life_expectancies, bins=50, kde=True, label="General Life Expectancy", color="blue", stat="density")
# Remaining life expectancy distribution
sns.histplot(remaining_life_expectancies + x, bins=50, kde=True, label=f"Total Life Expectancy for Age {x}", color="green", stat="density")
# Add mean lines
plt.axvline(mean_life_expectancy, color='blue', linestyle='dashed', linewidth=2, label="Mean General Life Expectancy")
plt.axvline(np.mean(remaining_life_expectancies) + x, color='green', linestyle='dashed', linewidth=2, label=f"Mean Total Life Expectancy for Age {x}")
plt.title(f"Life Expectancy Distributions (Age {x})")
plt.xlabel("Years")
plt.ylabel("Density")
plt.legend()
plt.show()
# Display some statistics
print(f"General Life Expectancy Mean: {np.mean(general_life_expectancies):.2f} years")
print(f"Total Life Expectancy Mean for Age {x}: {np.mean(remaining_life_expectancies) + x:.2f} years")
General Life Expectancy Mean: 80.04 years Total Life Expectancy Mean for Age 70: 81.72 years
In [2]:
number_of_peeps = 100
# Simulate population with current age and expected life expectancy
def simulate_population_with_current_age_and_le(size, mean, std_dev):
"""
Simulate a population with random current ages and corresponding life expectancies.
"""
life_expectancies = simulate_life_expectancy(mean, std_dev, size=size)
current_ages = np.random.uniform(0, life_expectancies, size=size) # Random age within life expectancy
remaining_life = life_expectancies - current_ages
return list(zip(current_ages, remaining_life))
# Simulate 100 individuals
population_data = simulate_population_with_current_age_and_le(number_of_peeps, mean_life_expectancy, std_dev_life_expectancy)
# Display simulated data
print("\nSimulated Population (Current Age and Remaining Life Expectancy):")
for i, (age, remaining) in enumerate(population_data):
print(f"Individual {i + 1}: Current Age = {age:.2f} years, Remaining Life Expectancy = {remaining:.2f} years")
# Plot current age and remaining life expectancy
ages, remaining_life = zip(*population_data)
plt.figure(figsize=(12, 6))
bars = plt.bar(range(len(ages)), remaining_life, color=["green" if r > 50 else "orange" if r > 10 else "red" for r in remaining_life])
# Add lines at 10 and 50 years
plt.axhline(10, color='red', linestyle='dashed', linewidth=1, label="10 Years Remaining")
plt.axhline(50, color='orange', linestyle='dashed', linewidth=1, label="50 Years Remaining")
plt.title("Remaining Life Expectancy")
plt.xlabel("Individual")
plt.ylabel("Remaining Life Expectancy (years)")
plt.legend()
plt.show()
Simulated Population (Current Age and Remaining Life Expectancy): Individual 1: Current Age = 5.78 years, Remaining Life Expectancy = 74.88 years Individual 2: Current Age = 8.37 years, Remaining Life Expectancy = 73.20 years Individual 3: Current Age = 15.24 years, Remaining Life Expectancy = 61.56 years Individual 4: Current Age = 66.02 years, Remaining Life Expectancy = 22.07 years Individual 5: Current Age = 29.35 years, Remaining Life Expectancy = 69.70 years Individual 6: Current Age = 17.38 years, Remaining Life Expectancy = 66.27 years Individual 7: Current Age = 1.92 years, Remaining Life Expectancy = 72.07 years Individual 8: Current Age = 54.13 years, Remaining Life Expectancy = 22.64 years Individual 9: Current Age = 50.62 years, Remaining Life Expectancy = 30.55 years Individual 10: Current Age = 26.79 years, Remaining Life Expectancy = 58.26 years Individual 11: Current Age = 56.97 years, Remaining Life Expectancy = 14.82 years Individual 12: Current Age = 80.61 years, Remaining Life Expectancy = 7.07 years Individual 13: Current Age = 87.61 years, Remaining Life Expectancy = 0.40 years Individual 14: Current Age = 69.45 years, Remaining Life Expectancy = 10.47 years Individual 15: Current Age = 0.16 years, Remaining Life Expectancy = 73.37 years Individual 16: Current Age = 41.13 years, Remaining Life Expectancy = 47.37 years Individual 17: Current Age = 73.88 years, Remaining Life Expectancy = 14.40 years Individual 18: Current Age = 80.87 years, Remaining Life Expectancy = 3.09 years Individual 19: Current Age = 6.97 years, Remaining Life Expectancy = 80.53 years Individual 20: Current Age = 21.92 years, Remaining Life Expectancy = 72.44 years Individual 21: Current Age = 40.99 years, Remaining Life Expectancy = 27.62 years Individual 22: Current Age = 42.73 years, Remaining Life Expectancy = 37.72 years Individual 23: Current Age = 24.61 years, Remaining Life Expectancy = 43.93 years Individual 24: Current Age = 30.41 years, Remaining Life Expectancy = 57.89 years Individual 25: Current Age = 85.52 years, Remaining Life Expectancy = 4.94 years Individual 26: Current Age = 68.92 years, Remaining Life Expectancy = 9.75 years Individual 27: Current Age = 47.24 years, Remaining Life Expectancy = 36.36 years Individual 28: Current Age = 19.51 years, Remaining Life Expectancy = 59.73 years Individual 29: Current Age = 11.37 years, Remaining Life Expectancy = 88.02 years Individual 30: Current Age = 47.06 years, Remaining Life Expectancy = 32.08 years Individual 31: Current Age = 54.77 years, Remaining Life Expectancy = 30.44 years Individual 32: Current Age = 59.25 years, Remaining Life Expectancy = 10.42 years Individual 33: Current Age = 66.87 years, Remaining Life Expectancy = 5.11 years Individual 34: Current Age = 65.62 years, Remaining Life Expectancy = 21.78 years Individual 35: Current Age = 58.03 years, Remaining Life Expectancy = 33.03 years Individual 36: Current Age = 10.28 years, Remaining Life Expectancy = 64.40 years Individual 37: Current Age = 51.81 years, Remaining Life Expectancy = 22.58 years Individual 38: Current Age = 37.17 years, Remaining Life Expectancy = 52.47 years Individual 39: Current Age = 37.86 years, Remaining Life Expectancy = 56.57 years Individual 40: Current Age = 56.50 years, Remaining Life Expectancy = 22.68 years Individual 41: Current Age = 34.50 years, Remaining Life Expectancy = 43.86 years Individual 42: Current Age = 1.00 years, Remaining Life Expectancy = 79.22 years Individual 43: Current Age = 1.63 years, Remaining Life Expectancy = 83.44 years Individual 44: Current Age = 36.81 years, Remaining Life Expectancy = 57.68 years Individual 45: Current Age = 47.09 years, Remaining Life Expectancy = 35.37 years Individual 46: Current Age = 22.56 years, Remaining Life Expectancy = 40.71 years Individual 47: Current Age = 1.45 years, Remaining Life Expectancy = 62.13 years Individual 48: Current Age = 59.18 years, Remaining Life Expectancy = 26.38 years Individual 49: Current Age = 14.84 years, Remaining Life Expectancy = 65.78 years Individual 50: Current Age = 84.37 years, Remaining Life Expectancy = 3.11 years Individual 51: Current Age = 40.51 years, Remaining Life Expectancy = 28.08 years Individual 52: Current Age = 8.25 years, Remaining Life Expectancy = 64.65 years Individual 53: Current Age = 63.60 years, Remaining Life Expectancy = 16.93 years Individual 54: Current Age = 65.38 years, Remaining Life Expectancy = 12.39 years Individual 55: Current Age = 19.27 years, Remaining Life Expectancy = 68.68 years Individual 56: Current Age = 41.41 years, Remaining Life Expectancy = 53.60 years Individual 57: Current Age = 28.84 years, Remaining Life Expectancy = 46.00 years Individual 58: Current Age = 12.23 years, Remaining Life Expectancy = 52.55 years Individual 59: Current Age = 16.44 years, Remaining Life Expectancy = 71.74 years Individual 60: Current Age = 34.24 years, Remaining Life Expectancy = 42.85 years Individual 61: Current Age = 57.94 years, Remaining Life Expectancy = 31.48 years Individual 62: Current Age = 43.67 years, Remaining Life Expectancy = 27.89 years Individual 63: Current Age = 5.51 years, Remaining Life Expectancy = 65.29 years Individual 64: Current Age = 17.41 years, Remaining Life Expectancy = 57.80 years Individual 65: Current Age = 46.85 years, Remaining Life Expectancy = 9.60 years Individual 66: Current Age = 20.11 years, Remaining Life Expectancy = 54.77 years Individual 67: Current Age = 50.21 years, Remaining Life Expectancy = 22.81 years Individual 68: Current Age = 74.92 years, Remaining Life Expectancy = 5.72 years Individual 69: Current Age = 31.35 years, Remaining Life Expectancy = 45.30 years Individual 70: Current Age = 17.58 years, Remaining Life Expectancy = 53.28 years Individual 71: Current Age = 27.37 years, Remaining Life Expectancy = 44.33 years Individual 72: Current Age = 61.31 years, Remaining Life Expectancy = 29.93 years Individual 73: Current Age = 76.17 years, Remaining Life Expectancy = 1.85 years Individual 74: Current Age = 90.87 years, Remaining Life Expectancy = 3.85 years Individual 75: Current Age = 11.45 years, Remaining Life Expectancy = 73.68 years Individual 76: Current Age = 86.45 years, Remaining Life Expectancy = 2.18 years Individual 77: Current Age = 43.75 years, Remaining Life Expectancy = 40.33 years Individual 78: Current Age = 31.27 years, Remaining Life Expectancy = 67.55 years Individual 79: Current Age = 75.75 years, Remaining Life Expectancy = 2.06 years Individual 80: Current Age = 53.70 years, Remaining Life Expectancy = 42.04 years Individual 81: Current Age = 38.30 years, Remaining Life Expectancy = 34.51 years Individual 82: Current Age = 4.58 years, Remaining Life Expectancy = 79.08 years Individual 83: Current Age = 70.03 years, Remaining Life Expectancy = 11.47 years Individual 84: Current Age = 35.70 years, Remaining Life Expectancy = 43.44 years Individual 85: Current Age = 41.63 years, Remaining Life Expectancy = 37.25 years Individual 86: Current Age = 7.12 years, Remaining Life Expectancy = 57.38 years Individual 87: Current Age = 2.97 years, Remaining Life Expectancy = 62.16 years Individual 88: Current Age = 49.23 years, Remaining Life Expectancy = 22.44 years Individual 89: Current Age = 20.19 years, Remaining Life Expectancy = 66.78 years Individual 90: Current Age = 51.86 years, Remaining Life Expectancy = 51.39 years Individual 91: Current Age = 47.09 years, Remaining Life Expectancy = 30.06 years Individual 92: Current Age = 32.54 years, Remaining Life Expectancy = 51.04 years Individual 93: Current Age = 23.85 years, Remaining Life Expectancy = 71.64 years Individual 94: Current Age = 41.83 years, Remaining Life Expectancy = 35.14 years Individual 95: Current Age = 52.38 years, Remaining Life Expectancy = 16.08 years Individual 96: Current Age = 50.13 years, Remaining Life Expectancy = 27.50 years Individual 97: Current Age = 53.76 years, Remaining Life Expectancy = 27.19 years Individual 98: Current Age = 9.32 years, Remaining Life Expectancy = 70.35 years Individual 99: Current Age = 70.33 years, Remaining Life Expectancy = 13.06 years Individual 100: Current Age = 58.29 years, Remaining Life Expectancy = 27.46 years
In [3]:
def costs(x=10, factor=5, output=True, pop=population_data):
max_x_counter = [min(remaining, x) for _, remaining in pop]
max_y_counter = [min(remaining, x*factor) for _, remaining in pop]
average_max_x = np.mean(max_x_counter)
average_max_y = np.mean(max_y_counter)
total_cost_x = factor*average_max_x
total_cost_y = average_max_y
if output:
print("#############")
print(f"avg cost of 1x {factor*x}: {total_cost_y:.2f} years")
print(f"avg cost of {factor}x {x}: {total_cost_x:.2f} years")
print(f"cost of split = {(100*total_cost_x/total_cost_y)-100:.2f}%")
return total_cost_x, total_cost_y
In [4]:
x= 10
factor = 5
xcost, ycost = costs(x, factor)
############# avg cost of 1x 50: 34.42 years avg cost of 5x 10: 46.44 years cost of split = 34.91%
In [8]:
bigpop = simulate_population_with_current_age_and_le(100000, mean_life_expectancy, std_dev_life_expectancy)
xvals = []
yvals = []
for i in range(1, 11):
xcost, ycost = costs(x=i, factor=5, output=True, pop=bigpop)
xvals.append(5*i)
yvals.append((100*xcost/ycost)-100)
plt.plot(xvals, yvals)
# Adding labels
plt.xlabel('Total Lifetime')
plt.ylabel('Cost of Splitting in %')
plt.title('Splitting of Lifetime penalty for 5 people')
# Display the plot
plt.show()
############# avg cost of 1x 5: 4.84 years avg cost of 5x 1: 4.97 years cost of split = 2.62% ############# avg cost of 1x 10: 9.37 years avg cost of 5x 2: 9.87 years cost of split = 5.40% ############# avg cost of 1x 15: 13.58 years avg cost of 5x 3: 14.71 years cost of split = 8.37% ############# avg cost of 1x 20: 17.47 years avg cost of 5x 4: 19.49 years cost of split = 11.55% ############# avg cost of 1x 25: 21.06 years avg cost of 5x 5: 24.21 years cost of split = 14.94% ############# avg cost of 1x 30: 24.33 years avg cost of 5x 6: 28.86 years cost of split = 18.60% ############# avg cost of 1x 35: 27.29 years avg cost of 5x 7: 33.45 years cost of split = 22.58% ############# avg cost of 1x 40: 29.92 years avg cost of 5x 8: 37.97 years cost of split = 26.90% ############# avg cost of 1x 45: 32.24 years avg cost of 5x 9: 42.43 years cost of split = 31.61% ############# avg cost of 1x 50: 34.24 years avg cost of 5x 10: 46.83 years cost of split = 36.77%
