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 scale parameter of the Gamma distribution of the purchase process shape parameter of the Beta distribution of the lifetime process shape parameter of the Beta distribution of the lifetime process Frequency vector of length n counting the numbers of purchases. Recency vector of length n. Vector of length n indicating the total number of periods of observation. Vector of estimated parameters for the transaction covariates. Vector of estimated parameters for the lifetime covariates. Matrix containing the covariates data affecting the transaction process. One column for each covariate. 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.