bgbb.DERT: BG/BB Discounted Expected Residual Transactions
In BTYD: Implementing BTYD Models with the Log Sum Exp Patch

Description Usage Arguments Details Value References Examples

Computes the number of discounted expected residual transactions by a customer, conditional on their behavior in the calibration period.

1	bgbb.DERT(params, x, t.x, n.cal, d)

`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.
`x`	the number of repeat transactions made by the customer in the calibration period. Can also be vector of frequencies - see details.
`t.x`	recency - the transaction opportunity in which the customer made their last transaction. Can also be a vector of recencies - see details.
`n.cal`	number of transaction opportunities in the calibration period. Can also be a vector of calibration period transaction opportunities - see details.
`d`	discount rate.

DERT(d | alpha, beta, gamma, delta, x, t.x, n). This is the present value of the expected future transaction stream for a customer with x transactions and a recency of t.x in n.cal transaction opportunities, discounted by a rate d.

x, t.x, and n.cal 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 also be a vector.

The present value of the expected future transaction stream for a particular customer.

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. Web. See equation 14.

params <- c(1.20, 0.75, 0.66, 2.78)
# Compute DERT for a customer who made 3 transactions
# in the calibration period(consisting of 6 transaction
# opportunities), with the last transaction occurring
# during the 4th transaction opportunity, discounted at
# 10%.
bgbb.DERT(params, x=3, t.x=4, n.cal=6, d=0.1)

# We can also compare DERT for several customers:
bgbb.DERT(params, x=1:6, t.x=6, n.cal=6, d=0.1)