Simulating Life Paths
One-year death probabilities derived from previous sections can also be used to simulate life paths for a single individual or a particular cohort. Each individual or cohort will be alive at a specified initial age, and deaths are sampled according to the one-year death probabilities given at each age.
When simulating for an individual, the function keeps track of their dead or alive status at each age. When simulating for a cohort, the number of people still alive at each age is recorded.
Simulate Individual Life Path
sim_indiv_path(init_age, female = 1, death_probs = NULL, closure_age = 130, n_sim = 10000, seed = NULL)
Parameters:
init_age : numeric
integer denoting initial age of individual
female : numeric
numeric denoting the gender of individuals, 1 for female and 0 for male
death_probs : vector
vector of 1-year death probabilities. If not supplied, an M7 age-period-cohort model will be
fitted on mortality_AUS_data to produce forecasted
death probabilities for an individual
starting at init_age in 2022
closure_age : numeric
maximum age
n_sim : numeric
integer denoting number of path simulations
seed : numeric
integer to be used as the seed for simulation
Returns:
a matrix where each row is a different path of the individual's dead (-1) or alive (0) status
across the years
An example looks like:
Note that the first column of the matrix will always be 0 as everyone is alive at the initial age, and the last column will always be -1, signifying everyone will be dead at age 131 (if we assume 130 is the maximum age one can be).
Usage:
# Simulate life paths for females starting at age 60
sim_indiv_path(init_age = 60, female = 1)
# Suppose we want to use period 1-yr death probabilities instead
AUS_male_rates <- mortality_AUS_data$rate$male
ages <- mortality_AUS_data$age # 0:110
old_ages <- 91:130
AUS_male_qx <- rate2rate(AUS_male_rates, from = "central", to = "prob")
kannisto_q <- complete_old_age(AUS_male_qx, ages, old_ages, method = "kannisto",
type = "prob", fitted_ages = 80:90)
# Consider males aged 55 in the year 2018
qx_55_2018 <- kannisto_q[as.character(55:130), "2018"]
sim_indiv_path(init_age = 55, female = 0, death_probs = qx_55_2018)
Simulate Cohort Life Path
sim_cohort_path_realised(init_age, female = 1, death_probs = NULL, closure_age = 130, cohort = 1000, n_sim = 10000, seed = NULL)
Parameters:
init_age : numeric
integer denoting initial age of cohort
female : numeric
numeric denoting the gender of individuals, 1 for female and 0 for male
death_probs : vector
vector of 1-year death probabilities. If not supplied, an M7 age-period-cohort model will be
fitted on mortality_AUS_data to produce forecasted
death probabilities for a cohort
starting at init_age in 2022
closure_age : numeric
maximum age
cohort : numeric
integer denoting initial cohort size
n_sim : numeric
integer denoting number of path simulations
seed : numeric
integer to be used as the seed for simulation
Returns:
a matrix where each row represents the number of individuals still alive from the given cohort
at each age. Each row is a different path of the same cohort.
An example looks like:
Note that the first column of the matrix will always be the initial cohort size as everyone is alive at the initial age, and the last column will always be 0, signifying everyone will be dead at age 131 (if we assume 130 is the maximum age one can be).
Usage:
# Simulate life paths for cohort of 1000 females starting at age 60
sim_cohort_path_realised(init_age = 60, female = 1)
# Suppose we want to use period 1-yr death probabilities instead
AUS_male_rates <- mortality_AUS_data$rate$male
ages <- mortality_AUS_data$age # 0:110
old_ages <- 91:130
AUS_male_qx <- rate2rate(AUS_male_rates, from = "central", to = "prob")
kannisto_q <- complete_old_age(AUS_male_qx, ages, old_ages, method = "kannisto",
type = "prob", fitted_ages = 80:90)
# Consider 100 males aged 55 in the year 2018
qx_55_2018 <- kannisto_q[as.character(55:130), "2018"]
sim_cohort_path_realised(init_age = 55, female = 0,
death_probs = qx_55_2018, cohort = 100)
Simulate Expected Cohort Life Path
sim_cohort_path_expected(init_age, female = 1, death_probs = NULL, closure_age = 130, cohort = 1000)
Parameters:
init_age : numeric
integer denoting initial age of cohort
female : numeric
numeric denoting the gender of individuals, 1 for female and 0 for male
death_probs : vector
vector of 1-year death probabilities. If not supplied, an M7 age-period-cohort model will be
fitted on mortality_AUS_data to produce forecasted
death probabilities for a cohort
starting at init_age in 2022
closure_age : numeric
maximum age
cohort : numeric
integer denoting initial cohort size
Returns:
vector of expected number of individuals still alive from a given cohort at each age
An example looks like:
Note that the first entry of the matrix will always be the initial cohort size as everyone is alive at the initial age, and the last entry will always be 0, signifying everyone will be dead at age 131 (if we assume 130 is the maximum age one can be).
Usage:
# Simulate expected life path for cohort of 1000 females starting at age 60
sim_cohort_path_expected(init_age = 60, female = 1)
# Suppose we want to use period 1-yr death probabilities instead
AUS_male_rates <- mortality_AUS_data$rate$male
ages <- mortality_AUS_data$age # 0:110
old_ages <- 91:130
AUS_male_qx <- rate2rate(AUS_male_rates, from = "central", to = "prob")
kannisto_q <- complete_old_age(AUS_male_qx, ages, old_ages, method = "kannisto",
type = "prob", fitted_ages = 80:90)
# Consider 100 males aged 55 in the year 2018
qx_55_2018 <- kannisto_q[as.character(55:130), "2018"]
sim_cohort_path_expected(init_age = 55, female = 0,
death_probs = qx_55_2018, cohort = 100)