GPT-4
Implement a period life table in Haskell.
GPT-4
A period life table is a statistical tool used to analyze the mortality rates and life expectancies of a population at different ages. In this example, we'll create a simple period life table in Haskell.
First, let's define the main data types and functions we'll be using:
module LifeTable (LifeTable, Age, DeathRate, LifeExpectancy, makeLifeTable, mortality, lifeExpectancy) where
type Age = Int
type DeathRate = Double
type LifeExpectancy = Double
type LifeTableEntry = (Age, DeathRate, LifeExpectancy)
type LifeTable = [LifeTableEntry]
Here, we're defining the LifeTable as a list of LifeTableEntry tuples, each containing an Age, a DeathRate, and a LifeExpectancy. We'll also create a makeLifeTable function to construct a life table from a list of age-specific death rates.
makeLifeTable :: [(Age, DeathRate)] -> LifeTable
makeLifeTable deathRates = zipWith3 (,,) ages deathRates lifeExpectancies
where
ages = map fst deathRates
lifeExpectancies = computeLifeExpectancies deathRates
To compute the life expectancies, we'll create a helper function called computeLifeExpectancies:
computeLifeExpectancies :: [(Age, DeathRate)] -> [LifeExpectancy]
computeLifeExpectancies deathRates = reverse $ snd $ foldr step (1, []) deathRates
where
step (age, deathRate) (prevLx, lifeExpectancies) =
let lx = prevLx / (1 - deathRate)
in (lx, lx : lifeExpectancies)
Lastly, we'll create two utility functions to query the life table for the mortality rate and life expectancy at a given age:
mortality :: LifeTable -> Age -> Maybe DeathRate
mortality lifeTable age = lookup age lifeTable >>= (\(_, dr, _) -> Just dr)
lifeExpectancy :: LifeTable -> Age -> Maybe LifeExpectancy
lifeExpectancy lifeTable age = lookup age lifeTable >>= (\(_, _, le) -> Just le)
Now, let's put everything together:
module LifeTable
( LifeTable
, Age
, DeathRate
, LifeExpectancy
, makeLifeTable
, mortality
, lifeExpectancy
) where
type Age = Int
type DeathRate = Double
type LifeExpectancy = Double
type LifeTableEntry = (Age, DeathRate, LifeExpectancy)
type LifeTable = [LifeTableEntry]
makeLifeTable :: [(Age, DeathRate)] -> LifeTable
makeLifeTable deathRates = zipWith3 (,,) ages deathRates lifeExpectancies
where
ages = map fst deathRates
lifeExpectancies = computeLifeExpectancies deathRates
computeLifeExpectancies :: [(Age, DeathRate)] -> [LifeExpectancy]
computeLifeExpectancies deathRates = reverse $ snd $ foldr step (1, []) deathRates
where
step (age, deathRate) (prevLx, lifeExpectancies) =
let lx = prevLx / (1 - deathRate)
in (lx, lx : lifeExpectancies)
mortality :: LifeTable -> Age -> Maybe DeathRate
mortality lifeTable age = lookup age lifeTable >>= (\(_, dr, _) -> Just dr)
lifeExpectancy :: LifeTable -> Age -> Maybe LifeExpectancy
lifeExpectancy lifeTable age = lookup age lifeTable >>= (\(_, _, le) -> Just le)
With this implementation, you can create a life table by providing a list of age-specific death rates and query it for mortality rates and life expectancies at different ages.
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