R help - Apr 2012 - summing two probability density functions from Gompertz hazard model

Hi, r-help members.

I have a question about summing two density distributions.  I have two
samples from which I've estimated hazard parameters for a Gompertz mortality
model.  With those parameters, I can calculate the PDF (survival function
times hazard function) of ages-at-death in a birth cohort subject to the
hazard function at each age.  I'd like to combine these two density
functions and recalculate the resultant hazard parameters that describe the
combined group.  Is there any way to do so?  Unfortunately, the two
datasets, from which I estimated the initial parameters, are not in the same
format, so I can't just combine counts of individuals by age or age category
and calculate the parameters that way.   I've included my functions for the
two distributions below.  Any suggestions are welcome.  Thanks.

--Trey

group1<- function (t){
		x=c(0.05893007, 0.03339980)
		a3<-x[1]
		b3<-x[2]
		shift<-15
		
		S.t <- exp(a3/b3*(1-exp(b3*(t-shift))))
		h.t <- a3*exp(b3*(t-shift))
		return<-S.t*h.t}

plot(seq(15,80,1),group1(seq(15,80,1)),type='l',xlab='Age
years)',ylim=c(0,0.12))  # plot age-at-death distribution for group 1


group2<- function (t){
		x=c(0.05920472, 0.01128975)
		a3<-x[1]
		b3<-x[2]
		shift<-15
		
		S.t <- exp(a3/b3*(1-exp(b3*(t-shift))))
		h.t <- a3*exp(b3*(t-shift))
		return<-S.t*h.t}

plot(seq(15,80,1),group2(seq(15,80,1)),type='l',xlab='Age
(years)',ylim=c(0,0.12))   # plot age-at-death distribution for group 2

-----
Trey Batey---Anthropology Instructor
Division of Social Sciences
Mt. Hood Community College
Gresham, OR  97030
Alt. Email:  trey.batey[at]mhcc[dot]edu
--
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