BTYD: Implementing Buy 'Til You Die Models

Description Usage Arguments Details Value References Examples

Generalized probability mass function for the BG/NBD.

1	bgnbd.pmf.General(params, t.start, t.end, x)

`params`	BG/NBD parameters - a vector with r, alpha, a, and b, in that order. r and alpha are unobserved parameters for the NBD transaction process. a and b are unobserved parameters for the Beta geometric dropout process.
`t.start`	start of time period for which probability is being calculated. It can also be a vector of values.
`t.end`	end of time period for which probability is being calculated. It can also be a vector of values.
`x`	number of repeat transactions by a random customer in the period defined by (t.start, t.end]. It can also be a vector of values.

P(X(t.start, t.end)=x | r, alpha, a, b). Returns the probability that a customer makes x repeat transactions in the time interval (t.start, t.end].

It is impossible for a customer to make a negative number of repeat transactions. This function will return an error if it is given negative times or a negative number of repeat transactions. This function will also return an error if t.end is less than t.start.

t.start, t.end, and x 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 a vector of probabilities.

Probability of x transaction occuring between t.start and t.end conditional on model parameters. If t.start, t.end, and/or x has a length greater than one, a vector of probabilities will be returned.

Fader, Peter S.; Hardie, Bruce G.S.and Lee, Ka Lok. “Computing P(alive) Using the BG/NBD Model.” December. 2008. Web. http://www.brucehardie.com/notes/021/palive_for_BGNBD.pdf

params <- c(0.243, 4.414, 0.793, 2.426)
# probability that a customer will make 10 repeat transactions in the
# time interval (1,2]
bgnbd.pmf.General(params, t.start=1, t.end=2, x=10)
# probability that a customer will make no repeat transactions in the
# time interval (39,78]
bgnbd.pmf.General(params, t.start=39, t.end=78, x=0)