CalcDiscrDemo {paramDemo}

Calculating Demographic Rates on Discrete Age Intervals from Parametric Age-Specific Mortality

Description

CalcDiscrDemo is used to calculate survival and fertility functions (i.e., lx, px, and qx) on discrete age intervals from an object of class “paramDemo” created with function CalcDemo.

Usage

CalcDiscrDemo(demo, dx = 1)

Arguments

demo

Object of class “paramDemo” created with function CalcDemo

dx

Numeric value for the age increments. Default is dx = 1

Details

CalcDiscrDemo takes the continuous survival functions from an object of class “paramDemo” and calculates the basic survival probabilities and, if available, fertility rates on discrete age intervals.

Let x \geq 0 and \omega \in \mathbb{N} be the next integer of the age when the survival function S(x) reaches the minimum. Given the age increments, \Delta x, specified with argument dx, the function creates a partition of [0, \omega] such that [x_i, x_i + \Delta x) \subset [0, \omega] for i = 1, \dots, n. At each age interval it calculates the discrete survival, lx, as

l_{x_i} = S(x_i).

The age- or stage-specific survival probability, px, is calculated as

p_{x_i} = \frac{S(x_i + \Delta x)}{S(x_i)},

while the age- or stage-specific mortality probability, qx, is q_{x_i} = 1 - p_{x_i}.

If fertility was also calculated with function CalcDemo, then the function includes the discrete age- or stage-specific fertility, bx, as

b_{x_i} = b\left(x_i + \frac{\Delta x}{2}\right) \Delta x,

where b(x) is the continuous fertility function.

Value

CalcDiscrDemo returns an object of class “discrDemo” that consist of a matrix with the following columns:

age

Partition of the full age subset into discrete intervals

lx

Survival or cumulative survival

px

The age- or stage-specific survival probability

qx

The age- or stage-specific mortality probability

bx

If available, the age- or stage-specific fertility

Author(s)

Fernando Colchero [e-mail]

See Also

CalcDemo to create an object of class “paramDemo”.

Examples

# Create paramDemo object from Gompertz mortality and
# quadratic fertility:
dem <- CalcDemo(theta = c(b0 = -5, b1 = 0.1), 
                 beta = c(b0 = 0.5, b1 = 0.01, b2 = 10),
                 summarStats = TRUE, agesAR = c(5, 10))

# Create discrete demographic object:
demDisc <- CalcDiscrDemo(dem, dx = 1)