pnbd.Expectation {BTYD}

Pareto/NBD Expectation

Description

Returns the number of repeat transactions that a randomly chosen customer (for whom we have no prior information) is expected to make in a given time period.

Usage

pnbd.Expectation(params, t)

Arguments

params

Pareto/NBD parameters - a vector with r, alpha, s, and beta, in that order. r and alpha are unobserved parameters for the NBD transaction process. s and beta are unobserved parameters for the Pareto (exponential gamma) dropout process.

t

The length of time for which we are calculating the expected number of repeat transactions.

Details

E(X(t) | r, alpha, s, beta)

Value

Number of repeat transactions a customer is expected to make in a time period of length t.

References

Fader, Peter S., and Bruce G.S. Hardie. "A Note on Deriving the Pareto/NBD Model and Related Expressions." November. 2005. Web. http://www.brucehardie.com/notes/008/

See Also

pnbd.ConditionalExpectedTransactions

Examples

params <- c(0.55, 10.56, 0.61, 11.64)

# Number of repeat transactions a customer is expected to make in 2 time intervals.
pnbd.Expectation(params = params, 
                 t = 2)

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