BTYDplus (version 0.6.0)

ggnbd.EstimateParameters: Parameter Estimation for Gamma/Gompertz/NBD model

Description

Estimates parameters for the Gamma/Gompertz/NBD model via Maximum Likelihood Estimation.

Usage

ggnbd.EstimateParameters(cal.cbs, par.start = c(1, 1, 0.5, 1, 1),
  min.param.value = 1e-05, max.param.value = 10000, trace = 0)

Arguments

cal.cbs

calibration period CBS. It must contain columns for frequency x, for recency t.x and total time observed T.cal. Optionally a column custs can be provided, which represents number of customers with a specific combination of frequency x, recency t.x and T.cal.

par.start

initial Gamma/Gompertz/NBD parameters - a vector with r, alpha, b, s and beta in that order.

min.param.value

the lower bound on parameters

max.param.value

the upper bound on parameters

trace

print logging step every trace iteration

Value

list of estimated parameters

References

Bemmaor, Albert C., and Nicolas Glady. "Modeling Purchasing Behavior with Sudden 'Death': A Flexible Customer Lifetime Model." Management Science 58.5 (2012): 1012-1021.

Examples

# NOT RUN {
set.seed(1)

# generate artificial GG/NBD data 
n      <- 5000 # no. of customers
T.cal  <- 32   # length of calibration period
T.star <- 32   # length of hold-out period
params <- c(r=0.85, alpha=4.45,        # purchase frequency lambda_i ~ Gamma(r, alpha)
            b=0.12, s=0.75, beta=9.55) # lifetime tau_i ~ Gompertz(b, eta_i); eta_i ~ Gamma(s, beta)

cbs <- ggnbd.GenerateData(n, T.cal, T.star, params)$cbs

# estimate parameters, and compare to true parameters
est <- ggnbd.EstimateParameters(cbs[, c("x", "t.x", "T.cal")], trace=10)
rbind(params, est=round(est, 2))
#           r alpha    b    s beta
# params 0.85  4.45 0.12 0.75 9.55
# est    0.86  4.45 0.13 0.57 8.19
# -> underlying parameters are successfully identified via Maximum Likelihood Estimation

# estimate future transactions in holdout-period
cbs$x.est <- ggnbd.ConditionalExpectedTransactions(est, cbs$T.star, cbs$x, cbs$t.x, cbs$T.cal)

# compare forecast accuracy to naive forecast
c("ggnbd"=sqrt(mean((cbs$x.star-cbs$x.est)^2)),
  "naive"=sqrt(mean((cbs$x.star-cbs$x)^2)))
#    ggnbd    naive 
# 2.871434 6.104031 
# -> Gamma/Gompertz/NBD forecast better than naive forecast

# estimate P(alive)
cbs$palive <- ggnbd.PAlive(est, cbs$x, cbs$t.x, cbs$T.cal)

# compare to true (usually unobserved) alive status
prop.table(table(cbs$palive>.5, cbs$alive))
#        FALSE   TRUE
# FALSE 0.6878 0.1264
# TRUE  0.0420 0.1438
# -> 83% of customers are correctly classified
# }