BTYD (version 2.4)

bgbb.ConditionalExpectedTransactions: BG/BB Conditional Expected Transactions

Description

Calculates the number of expected transactions in the holdout period, conditional on a customer's behavior in the calibration period.

Usage

bgbb.ConditionalExpectedTransactions(params, n.cal, n.star, x, t.x)

Arguments

params

BG/BB parameters - a vector with alpha, beta, gamma, and delta, in that order. Alpha and beta are unobserved parameters for the beta-Bernoulli transaction process. Gamma and delta are unobserved parameters for the beta-geometric dropout process.

n.cal

number of transaction opportunities in the calibration period, or a vector of calibration period transaction opportunities.

n.star

number of transaction opportunities in the holdout period, or a vector of holdout period transaction opportunities.

x

number of repeat transactions the customer made in the calibration period, or a vector of calibration period transaction frequencies.

t.x

recency - the last transaction opportunity in which this customer made a transaction, or a vector of recencies.

Value

The number of transactions a customer is expected to make in the n.star transaction opportunities following the calibration period, conditional on their behavior during the calibration period.

Details

E(X(n, n+n*) | alpha, beta, gamma, delta, x, t.x, n). This function requires the holdout period to immediately follow the calibration period.

n.cal, n.star, x, and t.x may be vectors. The standard rules for vector operations apply - if they are not of the same length, shorter vectors will be recycled (start over at the first element) until they are as long as the longest vector. It is advisable to keep vectors to the same length and to use single values for parameters that are to be the same for all calculations. If one of these parameters has a length greater than one, the output will be a vector of probabilities.

References

Fader, Peter S., Bruce G.S. Hardie, and Jen Shang. “Customer-Base Analysis in a Discrete-Time Noncontractual Setting.” Marketing Science 29(6), pp. 1086-1108. 2010. INFORMS. http://www.brucehardie.com/papers/020/

Examples

params <- c(1.20, 0.75, 0.66, 2.78)
# the number of transactions a customer is expected
# to make in the 10 transaction opportunities
# following the calibration period, which consisted
# of 6 transaction opportunities (during which they
# made 3 transactions, the last of which occurred
# in the 4th opportunity)
bgbb.ConditionalExpectedTransactions(params, n.cal=6, n.star=10, x=3, t.x=4)

# We can also use vectors as input:
bgbb.ConditionalExpectedTransactions(params, n.cal=6, n.star=1:10, x=3, t.x=4)
bgbb.ConditionalExpectedTransactions(params, n.cal=6, n.star=10, x=1:4, t.x=4)