BTYDplus (version 0.5.0)

ggnbd.ConditionalExpectedTransactions: Gamma/Gompertz/NBD Conditional Expected Transactions

Description

Uses Gamma/Gompertz/NBD model parameters and a customer's past transaction behavior to return the number of transactions they are expected to make in a given time period.

Usage

ggnbd.ConditionalExpectedTransactions(params, T.star, x, t.x, T.cal)

Arguments

params

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

T.star

length of time for which we are calculating the expected number of transactions.

x

number of repeat transactions in the calibration period T.cal, or a vector of calibration period frequencies.

t.x

recency, i.e. length between first and last transaction during calibration period.

T.cal

length of calibration period, or a vector of calibration period lengths.

Value

Number of transactions a customer is expected to make in a time period of length t, conditional on their past behavior. If any of the input parameters has a length greater than 1, this will be a vector of expected number of transactions.

See Also

ggnbd.EstimateParameters

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
# }