how integrate is supposed to be used. Details can be found below.
Thanks for your thoughts and best regards,
Daniel
This is the output of the function calls:
bergernasr.clv.continuous(10)
112.1139 with absolute error < 6.2e-13
111.1077 with absolute error < 6.2e-13
[1] 243.2216
bergernasr.clv.continuous(59954)
112.1139 with absolute error < 6.2e-13
150.2340 with absolute error < 3e-07
[1] 282.3478
bergernasr.clv.continuous(59955)
112.1139 with absolute error < 6.2e-13
6.137708e-05 with absolute error < 0.00012
[1] 132.1139
These are the functions required to see this effect.
bergernasr.clv.continuous.f1 <- function(t, h, v, ret, d)
{
(h*t^2 + v) * (ret / ( 1 + d ))^t
}
bergernasr.clv.continuous.f2 <- function (t, g,h, v, ret, N, d)
{
(h*g^2 + v + N*(1-exp(-t+g))) * (ret / ( 1 + d ))^t
}
bergernasr.clv.continuous <- function(t)
{
g <- 5 # Wendepunkt
v <- 20 # Sockelbetrag
h <- 4 # Umsatzwachstum
N <- 80 # Wachstum ab Wendepunkt
r <- .9 # Retention rate
d <- .2 # Discount rate
i1 <- integrate(bergernasr.clv.continuous.f1, h=h,v=v,ret=r,d=d,
lower=0, upper=5)
i2 <- integrate(bergernasr.clv.continuous.f2, g=g, h=h,v=v,ret=r,N=N,
d=d, lower=g, upper=t)
print(i1)
print(i2)
return (
v
+ i1[[1]]
+ i2[[1]]
)
}
For better readability the function in Mathtype / Tex format:
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% feaafaart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbb
% a9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0-vr
% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadoeacaWGmb
% GaamOvaiabg2da9iaadAhacqGHRaWkdaWdXbqaamaabmaabaGaamiA
% aiaadshadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaWG2baacaGLOa
% GaayzkaaGaeyyXIC9aaeWaaeaadaWcaaqaaiaadkhaaeaacaaIXaGa
% ey4kaSIaamizaaaaaiaawIcacaGLPaaadaahaaWcbeqaaiaadshaaa
% GccaWGKbWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaey4kaSYaa8qC
% aeaadaqadaqaaiaadIgacaWGNbWaaWbaaSqabeaacaaIYaaaaOGaey
% 4kaSIaamODaiabgUcaRiaad6eacqGHflY1caGGOaGaaGymaiabgkHi
% TiaadwgadaahaaWcbeqaaiabgkHiTiaadshacqGHRaWkcaWGNbaaaO
% GaaiykaaGaayjkaiaawMcaaaWcbaGaam4zaaqaaiaad6gaa0Gaey4k
% IipakiabgwSixpaabmaabaWaaSaaaeaacaWGYbaabaGaaGymaiabgU
% caRiaadsgaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaWG0baaaOGa
% amizamaabmaabaGaamiDaaGaayjkaiaawMcaaaWcbaGaaGimaaqaai
% aadEgaa0Gaey4kIipaaaa!74B6!
\[
CLV = v + \int\limits_0^g {\left( {ht^2 + v} \right) \cdot \left(
{\frac{r}{{1 + d}}} \right)^t d\left( t \right) + \int\limits_g^n
{\left( {hg^2 + v + N \cdot (1 - e^{ - t + g} )} \right)} \cdot
\left( {\frac{r}{{1 + d}}} \right)^t d\left( t \right)}
\]
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