BTYDplus (version 0.6.4)

nbd.EstimateParameters: Parameter Estimation for the NBD model

Description

Estimates parameters for the NBD model via Maximum Likelihood Estimation.

Usage

nbd.EstimateParameters(cal.cbs, par.start = c(1, 1),
  max.param.value = 10000)

Arguments

cal.cbs

calibration period CBS. It must contain columns for frequency 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 and T.cal.

par.start

initial NBD parameters - a vector with r and alpha in that order.

max.param.value

the upper bound on parameters

Value

list of estimated parameters

References

EHRENBERG, ASC. "The Pattern of Consumer Purchases." Quantitative techniques in marketing analysis: text and readings (1962): 355.

Examples

# NOT RUN {
set.seed(1)

# generate artificial NBD data 
n      <- 1000 # 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)

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

# estimate parameters, and compare to true parameters
est <- nbd.EstimateParameters(cbs[, c("x", "T.cal")])
rbind(params, est=round(est, 2))
#        r    alpha
# params 0.85 4.45
# est    0.84 4.56
# -> underlying parameters are successfully identified via Maximum Likelihood Estimation

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

# compare forecast accuracy to naive forecast
c("nbd"=sqrt(mean((cbs$x.star-cbs$x.est)^2)),
  "naive"=sqrt(mean((cbs$x.star-cbs$x)^2)))
#      nbd    naive 
# 3.446776 3.469582
# -> NBD forecast only marginally better than naive forecast
# }