BG/BB Posterior Mean Transaction Rate
Computes the mean value of the marginal posterior value of P, the Bernoulli transaction process parameter.
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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.
number of repeat transactions a customer made in the calibration period, or a vector of calibration period transaction frequencies.
recency - the last transaction opportunity in which a customer made a transaction, or a vector of recencies.
number of transaction opportunities in the calibration period, or a vector of calibration period transaction opportunities.
recency-frequency matrix. It must contain columns for frequency ("x"), recency ("t.x"), and the number of transaction opportunities in the calibration period ("n.cal"). Note that recency must be the time between the start of the calibration period and the customer's last transaction, not the time between the customer's last transaction and the end of the calibration period.
E(P | alpha, beta, gamma, delta, x, t.x, n). This is
calculated by setting l=1 and m=0 in
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.
The posterior mean transaction rate.
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. http://www.brucehardie.com/papers/020/
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data(donationsSummary) rf.matrix <- donationsSummary$rf.matrix # donationsSummary$rf.matrix already has appropriate column names # starting-point parameters startingparams <- c(1, 1, 0.5, 3) # estimated parameters est.params <- bgbb.EstimateParameters(rf.matrix, startingparams) # return the posterior mean transaction rate vector bgbb.rf.matrix.PosteriorMeanTransactionRate(est.params, rf.matrix)
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