Hello all,

I have three  generational sales data, and want to estimate their three parameters p, q, and m. 

I have followed Norton-Bass multigenerational model which is the non-linear equation system. here what I don't clearly understand is How I am going to estimate these three parameters? in three different cases? Should I use 

F(t)=(1−exp(−(p+q)t))/(1+(q/p)*exp(−(p+q)t)) individually and use 

X1(t)=m1F1(t)[1−F2(t−t2)]X1(t)=m1F1(t)[1−F2(t−t2)]

X2(t)=F2(t−t2)[m2+F1(t)m1][1−F3(t−t3)]X2(t)=F2(t−t2)[m2+F1(t)m1][1−F3(t−t3)]

X3(t)=F3(t−t3)[m3+F2(t−t2)[m2+Fl(t)m1]] for forecasting? or 

estimate three parameters using these three non-linear equations and then forecast?

my understanding is it should be used in both cases (to estimate parameter and for forecasting), but when I try this it produces lots of error in R, sometimes like  "singular gradient matrix at initial parameter estimates", sometimes "step factor 0.000488281 reduced below 'minFactor' of 0.000976562" I tried to debug by changing parameters but nothing improved at al....

any suggestion is highly appreciated!

I used "nlstools" package in R and is quite cumbersome to adjust parameters ! do you have any other suggestions! I saw some other package like BB but im not quite sure !