FunctionSurvivalEstimation

Library "FunctionSurvivalEstimation"
The Survival Estimation function, also known as Kaplan-Meier estimation or product-limit method, is a statistical technique used to estimate the survival probability of an individual over time. It's commonly used in medical research and epidemiology to analyze the survival rates of patients with different treatments, diseases, or risk factors.

What does it do?
The Survival Estimation function takes into account censored observations (i.e., individuals who are still alive at a certain point) and calculates the probability that an individual will survive beyond a specific time period. It's particularly useful when dealing with right-censoring, where some subjects are lost to follow-up or have not experienced the event of interest by the end of the study.

Interpretation
The Survival Estimation function provides a plot of the estimated survival probability over time, which can be used to:
1. Compare survival rates between different groups (e.g., treatment arms)
2. Identify patterns in the data that may indicate differences in mortality or disease progression
3. Make predictions about future outcomes based on historical data
4. In a trading context it may be used to ascertain the survival ratios of trading under specific conditions.

Reference:
global-developments.org/p/beyond-gdp-one-table-of-neoclassical
"Beyond GDP" ~ aeaweb.org/articles?id=10.1257/aer.20110236
en.wikipedia.org/wiki/Kaplan–Meier_estimator
kdnuggets.com/2020/07/complete-guide-survival-analysis-python-part1.html

survival_probability(alive_at_age, initial_alive)
  Kaplan-Meier Survival Estimator.
  Parameters:
    alive_at_age (int): The number of subjects still alive at a age.
    initial_alive (int): The Total number of initial subjects.
  Returns: The probability that a subject lives longer than a certain age.

utility(c, l)
  Captures the utility value from consumption and leisure.
  Parameters:
    c (float): Consumption.
    l (float): Leisure.
  Returns: Utility value from consumption and leisure.

welfare_utility(age, b, u, s)
  Calculate the welfare utility value based age, basic needs and social interaction.
  Parameters:
    age (int): Age of the subject.
    b (float): Value representing basic needs (food, shelter..).
    u (float): Value representing overall well-being and happiness.
    s (float): Value representing social interaction and connection with others.
  Returns: Welfare utility value.

expected_lifetime_welfare(beta, consumption, leisure, alive_data, expectation)
  Calculates the expected lifetime welfare of an individual based on their consumption, leisure, and survival probability over time.
  Parameters:
    beta (float): Discount factor.
    consumption (array<float>): List of consumption values at each step of the subjects life.
    leisure (array<float>): List of leisure values at each step of the subjects life.
    alive_data (array<int>): List of subjects alive at each age, the first element is the total or initial number of subjects.
    expectation (float): Optional, `defaut=1.0`. Expectation or weight given to this calculation.
  Returns: Expected lifetime welfare value.