bgbb.Expectation {BTYD}

BG/BB Expectation

Description

Returns the number of transactions that a randomly chosen customer (for whom we have no prior information) is expected to make in the first n transaction opportunities.

Usage

bgbb.Expectation(params, n)

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

number of transaction opportunities; may also be a vector.

Details

E(X(n) | alpha, beta, gamma, delta)

Value

Mean of the BG/BB probability mass function.

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.

Examples

params <- c(1.20, 0.75, 0.66, 2.78)
# Expected number of transactions that a randomly chosen customer
# will make in the first 10 transaction opportunities.
bgbb.Expectation(params, n=10)

# We can also compare expected transactions over time:
bgbb.Expectation(params, n=1:10)