axPreston approximation of a(x) using a few rules of thumb outlined by Preston et al (2001)
Description
a(x) estimated assuming death rate constant in each interval. Most a values are estimated using ax = n + (1/Mx)  n/(1exp(n*Mx))
, except for a0, which uses a few rules of thumb derived from Coale and Demeny (1983) and displayed in table 3.3 in Preston (2001). In the case of single ages, I found that ages a1a10 were all estimated very close to .5, whereas the older ages a50+ were all estimated very close to what other methods produce. In order to adjust a(x) values
Usage
1 
Arguments
Mx 
a numeric vector of the agespecific central death rates, calculated as D(x)/N(x) (deaths/exposure). 
n 
a numeric vector of age interval widths. 
axsmooth 
logical. default = 
sex 

Details
In the case of single ages, I found that ages a1a10 were all estimated very close to .5, whereas the older ages a50+ were all estimated very close to what other methods produce. In order to adjust a(x) values to reflect dropping mortality at young ages, I wrote the following rule of thumb, which scales based on the level of mortality at age 0 and age 8. Basically the drop in mortality from age 0 to 8 ought to produce successively larger a(x) values, approaching .5. The increments in a(x) at each age from 1 until 8 are thus applied according to some fixed proportions, contained in the variable 'jumps'. This is the last code chunk in the function, which is displayed below under 'examples'. For more info, look at the code.
Value
a numeric vector of a(x) values.
Author(s)
Tim Riffe
References
Coale Anseley and Paul Demeny, with B Vaughan (1983). Regional Model Life Tables and Stable Populations. New York Academic Press.
Preston, S. et al (2001) Demography: measuring and modeling population processes. Blackwell Publishing. Malden
See Also
See Also as axEstimate
, a wrapper function for this and three other a(x) estimation procedures (axMidpoint
, axKeyfitz
and axSchoen
).