BG/NBD: Probability of Being Alive

Calculates the probability of a customer being alive at the end of the calibration period, based on a customer's past transaction behavior and the BG/NBD model parameters.

bgnbd_nocov_PAlive

P(alive) for the BG/NBD model without covariates

bgnbd_staticcov_PAlive

P(alive) for the BG/NBD model with static covariates

bgnbd_nocov_PAlive(r, alpha, a, b, vX, vT_x, vT_cal)

bgnbd_staticcov_PAlive(
  r,
  alpha,
  a,
  b,
  vX,
  vT_x,
  vT_cal,
  vCovParams_trans,
  vCovParams_life,
  mCov_trans,
  mCov_life
)

Arguments

r

shape parameter of the Gamma distribution of the purchase process

alpha

scale parameter of the Gamma distribution of the purchase process

a

shape parameter of the Beta distribution of the lifetime process

b

shape parameter of the Beta distribution of the lifetime process

vX

Frequency vector of length n counting the numbers of purchases.

vT_x

Recency vector of length n.

vT_cal

Vector of length n indicating the total number of periods of observation.

vCovParams_trans

Vector of estimated parameters for the transaction covariates.

vCovParams_life

Vector of estimated parameters for the lifetime covariates.

mCov_trans

Matrix containing the covariates data affecting the transaction process. One column for each covariate.

mCov_life

Matrix containing the covariates data affecting the lifetime process. One column for each covariate.

Value

Returns a vector with the PAlive for each customer.

Details

mCov_trans is a matrix containing the covariates data of the time-invariant covariates that affect the transaction process. Each column represents a different covariate. For every column a gamma parameter needs to added to vCovParams_trans at the respective position.

mCov_life is a matrix containing the covariates data of the time-invariant covariates that affect the lifetime process. Each column represents a different covariate. For every column a gamma parameter needs to added to vCovParams_life at the respective position.

References

Fader PS, Hardie BGS, Lee KL (2005). ““Counting Your Customers” the Easy Way: An Alternative to the Pareto/NBD Model” Marketing Science, 24(2), 275-284.

Fader PS, Hardie BGS (2013). “Overcoming the BG/NBD Model's #NUM! Error Problem” URL http://brucehardie.com/notes/027/bgnbd_num_error.pdf.

Fader PS, Hardie BGS (2007). “Incorporating time-invariant covariates into the Pareto/NBD and BG/NBD models.” URL http://www.brucehardie.com/notes/019/time_invariant_covariates.pdf.

Fader PS, Hardie BGS, Lee KL (2007). “Creating a Fit Histogram for the BG/NBD Model” URL https://www.brucehardie.com/notes/014/bgnbd_fit_histogram.pdf