Calculates the expected number of transactions in a given time period based on a customer's past transaction behavior and the Pareto/NBD model parameters.

• pnbd_nocov_CET Conditional Expected Transactions without covariates

• pnbd_staticcov_CET Conditional Expected Transactions with static covariates

pnbd_nocov_CET(r, alpha_0, s, beta_0, dPeriods, vX, vT_x, vT_cal)

pnbd_staticcov_CET(
r,
alpha_0,
s,
beta_0,
dPeriods,
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. The smaller r, the stronger the heterogeneity of the purchase process scale parameter of the Gamma distribution of the purchase process shape parameter of the Gamma distribution for the lifetime process. The smaller s, the stronger the heterogeneity of customer lifetimes scale parameter for the Gamma distribution for the lifetime process. number of periods to predict 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 containing the conditional expected transactions for the existing customers in the Pareto/NBD model.

## 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

Schmittlein DC, Morrison DG, Colombo R (1987). “Counting Your Customers: Who-Are They and What Will They Do Next?” Management Science, 33(1), 1–24.

Fader PS, Hardie BGS (2005). “A Note on Deriving the Pareto/NBD Model and Related Expressions.” URL http://www.brucehardie.com/notes/009/pareto_nbd_derivations_2005-11-05.pdf.

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