lifetable: Lifetable functions with mutual conversions

Description

Lifetable related functions.

Usage

lifetable(mx, ns=NULL, class=5, mode=1) lifetable2(mx, ax=0.5, n=1) lifetable3(lx, ax=0.5, n=1) clifetable(qx) lxtodx(lx) dxtolx(dx) qxtodx(qx) dxtoqx(dx) qxtomx(qx, ax=0.5, n=1, mmax=NULL) mxtoqx(mx, ax=0.5, n=1) qxtolx(qx) lxtoqx(lx) uxtoqx(ux)

Arguments

Lifetable function mx, meaning the age (class)-specific death rates.

If given as a vector with the same length as mx, the duration for each age (class). Default is NULL: same duration with class is automatically used.

If given as a vector with the same length as mx or qx, the duration for each age (class). Default is 1, which means the length for all age-classes being 1 year.

class

Age-class of lifetable() function. Default is 5.

mode

How to set ax and correction method in conversion from mx to qx. 1 and 11: all ax is 0.5 except the open-ended class [where ax is reciprocal of mx], 2, 4, 12, 14: ax is 0.1 for age 0, 0.4 for age 1-4, 0.5 for the other ages except the open-ended class [where ax is reciprocal of mx], 3, 5, 13, 15: ax is 0.3 for age 0, 0.4 for age 1-4, 0.5 for the other ages except the open-ended class [where ax is reciprocal of mx], 6 and 16: Males value given in Preston SH (2001), pp.48 Table 3.3, 7 and 17: Females value given in Preston SH (2001), pp.48 Table 3.3. If less than 10, simply calculating qx as n*mx/(1+n*(1-ax)*mx) (Note: In the formula of Preston SH (2001) pp.47, the function is given as n*mx/(1+(n-ax)*mx). The difference is due to the formulation of ax. In this function, ax is given for single age, same as Newell C (1988), pp.71) except for the open-ended class where qx=1, otherwise calculating qx by Greville's method. Default is 1.

Lifetable function ax, fraction of last year lived. Default is 0.5 (scalar) for all classes. It can be given as scalar or vector. Note: This argument can only be specified in lifetable2() or lifetable3(), not in lifetable().

Lifetable function qx, which means the probability of dying between age x and x+1 (for lifetable(), x+class).

mmax

To calculate mx from qx, mx at the maximum open-ended age-class cannot be calculated from qx. In such situation, mmax gives a value for it. Default is NULL.

Lifetable function lx, which means number of people left alive at age x from 100,000 newborns.

Lifetable function dx, which means number of people dying between age x and x+1 (for lifetable(), x+class) from 100,000 newborns. Differentials of lx.

The force of mortality.

Value

ages: Lifetable's exact age x, which is the beginning of each interval.
n: Duration of each interval. If ns is not given, the value of the class is repeatedly used.
mx: Lifetable function mx, meaning the age (class)-specific death rates.
qx: Lifetable function qx, which means the probability of dying between age x and x+1 (for lifetable(), x+class).
ax: Lifetable function ax, which means the average number of person-years lived in the interval by those dying in the interval. In lifetable(), it's automatically specified by mode.
lx: Lifetable function lx, which means number of people left alive at age x from 100,000 newborns.
dx: Lifetable function dx, which means number of people dying between age x and x+1 (for lifetable(), x+class) from 100,000 newborns. Differentials of lx.
Lx: Lifetable function Lx, which means person-years lived between age x and x+class.
Tx: Lifetable function Tx, which means person-years lived above age x.
ex: Lifetable function ex, which means expectation of life at age x.

References

Preston SH, Heuveline P, Guillot M (2001) Demography: Measuring and Modeling Population Processes. Blackwell Publishing, Oxford. Newell C (1988) Methods and Models in Demography. The Guilford Press, New York.

Examples

Run this code

 lifetable(c(0.0087, 0.00015, 0.00019, 0.00098, 0.0013, 0.0011, 0.0014, 0.0019, 
             0.0029, 0.0048, 0.0071, 0.011, 0.019, 0.028, 0.041, 0.072, 0.11, 
             0.19), class=5, mode=11)
 lifetable2(c(0.008314, 0.000408, 0.000181, 0.000187, 0.000282, 0.000307, 0.000364, 
              0.000566, 0.000884, 0.001445, 0.002485, 0.004210, 0.007219, 0.012054, 
              0.018259, 0.029920, 0.049689, 0.085545, 0.177987), 
              ax = c(0.1, 0.4, rep(0.5, 16), NA), n = c(1, 4, rep(5, 16), NA) )
 lifetable3(lx=c(1.0, 0.8499, 0.8070, 0.7876, 0.7762, 0.7691, 0.7502, 0.7362,
                 0.7130, 0.6826, 0.6525, 0.6223, 0.5898, 0.5535, 0.5106, 0.4585,
                 0.3965, 0.3210, 0.2380, 0.1516, 0.0768, 0.0276, 0.0059, 0.0006, 0),
                 n=c(rep(1, 5), rep(5, 20)), ax=c(0.3, rep(0.5, 24))) # Newell, Table 13.1
 clifetable(Jlife$qx2000F)