bgbb.DERT {BTYD}

BG/BB Discounted Expected Residual Transactions

Description

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

Usage

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

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.

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.

Details

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.

Value

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

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. Web. See equation 14.

Examples

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)