lifetable

Life Tables - Loads and calculates life tables

class actuarialmath.lifetable.LifeTable(udd: bool = True, verbose: bool = False, **kwargs)[source]

Bases: Reserves

Calculate life table, and iteratively fill in missing values

Parameters:

udd – assume UDD or constant force of mortality for fractional ages
verbose – whether to echo update steps

Notes

4 types of columns can be loaded and calculated in the life table:

‘q’ : probability (x) dies in one year
‘l’ : number of lives aged x
‘d’ : number of deaths of age x
‘p’ : probability (x) survives at least one year

set_table(radix: int = 100000, minage: int = -1, maxage: int = -1, fill: bool = True, l: Dict[int, float] | None = None, d: Dict[int, float] | None = None, p: Dict[int, float] | None = None, q: Dict[int, float] | None = None) → LifeTable[source]

Update life table

Parameters:

l – lives at start of year x, or
d – deaths in year x, or
p – probabilities that (x) survives one year, or
q – probabilities that (x) dies in one year
fill – whether to automatically fill table cells (default is True)
minage – minimum age in table
maxage – maximum age in table
radix – initial number of lives

Examples:

>>> life = LifeTable(udd=True).set_table(l={90: 1000, 93: 825},
>>>                                      d={97: 72},
>>>                                      p={96: .2},
>>>                                      q={95: .4, 97: 1})

fill_table(radix: int) → LifeTable[source]

Iteratively fill in missing table cells (does not check consistency)

Parameters:: radix – initial number of lives

mu_x(x: int, s: int = 0, t: int = 0) → float[source]

Compute mu_x from p_x in life table

Parameters:

x – age of selection
s – years after selection
t – death within next t years

l_x(x: int, s: int = 0) → float[source]

Lookup l_x from life table

Parameters:

x – age of selection
s – years after selection

d_x(x: int, s: int = 0, t: int = 1) → float[source]

Compute deaths as lives at x_t divided by lives at x

Parameters:

x – age of selection
s – years after selection
t – death within next t years

p_x(x: int, s: int = 0, t: int = 1) → float[source]

t_p_x = lives beginning year x+t divided lives beginning year x

Parameters:

x – age of selection
s – years after selection
t – death within next t years

q_x(x: int, s: int = 0, t: int = 1, u: int = 0) → float[source]

Deferred mortality: u|t_q_x = (l[x+u] - l[x+u+t]) / l[x]

Parameters:

x – age of selection
s – years after selection
u – survive u years, then…
t – death within next t years

e_x(x: int, s: int = 0, n: int = -999, curtate: bool = True, moment: int = 1) → float[source]

Expected curtate lifetime from sum of lives in table

Parameters:

x – age of selection
s – years after selection
n – future lifetime limited at n years
curtate – whether curtate (True) or complete (False) expectations
moment – whether to compute first (1) or second (2) moment

E_x(x: int, s: int = 0, t: int = 1, moment: int = 1) → float[source]

Pure Endowment from life table and interest rate

Parameters:

x – age of selection
s – years after selection
t – survives t years
moment – return first (1) or second (2) moment or variance (-2)

__getitem__(col: str) → Dict[int, float][source]

Returns a column of the life table

Parameters:: col – name of life table column to return

frame() → DataFrame[source]: Return life table columns and values in a DataFrame