BTYD (version 2.4)

spend.expected.value: Conditional expected transaction value

Description

Calculates the expected transaction value for a customer, conditional on the number of transaction and average transaction value during the calibration period.

Usage

spend.expected.value(params, m.x, x)

Arguments

params

a vector of gamma-gamma parameters: p, q, and gamma, in that order. p is the shape parameter for each transaction. The scale parameter for each transaction is distributed across customers according to a gamma distribution with parameters q (shape) and gamma (scale).

m.x

the customer's average observed transaction value in the calibration period. May also be a vector of average observed transaction values - see details.

x

the number of transactions the customer made in the calibration period. May also be a vector of frequencies - see details.

Value

The expected transaction value for a customer conditional on their transaction behavior during the calibration period. If m.x or x has a length greater than one, then a vector of expected transaction values will be returned.

Details

E(M | p, q, gamma, m.x, x).

m.x and x may be vectors. The standard rules for vector operations apply - if they are not of the same length, the shorter vector will be recycled (start over at the first element) until it is 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 Ka L. Lee. “RFM and CLV: Using Iso-Value Curves for Customer Base Analysis.” Journal of Marketing Research Vol.42, pp.415-430. November. 2005. http://www.brucehardie.com/papers.html

Examples

params <- c(6, 4, 16)
# calculate the expected transaction value of a customer
# who spent an average of $35 over 3 transactions.
spend.expected.value(params, m.x=35, x=3)

# m.x and x may be vectors:
spend.expected.value(params, m.x=30:40, x=3)
spend.expected.value(params, m.x=35, x=1:10)
spend.expected.value(params, m.x=30:40, x=1:11)