Calculates the discounted expected residual transactions.
pnbd_nocov_DERT
Discounted expected residual transactions for the Pareto/NBD model without covariates
pnbd_staticcov_DERT
Discounted expected residual transactions for the Pareto/NBD model with static covariates
pnbd_nocov_DERT( r, alpha_0, s, beta_0, continuous_discount_factor, vX, vT_x, vT_cal ) pnbd_staticcov_DERT( r, alpha_0, s, beta_0, continuous_discount_factor, vX, vT_x, vT_cal, mCov_life, mCov_trans, vCovParams_life, vCovParams_trans )
r | shape parameter of the Gamma distribution of the purchase process. The smaller r, the stronger the heterogeneity of the purchase process |
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alpha_0 | scale parameter of the Gamma distribution of the purchase process |
s | shape parameter of the Gamma distribution for the lifetime process. The smaller s, the stronger the heterogeneity of customer lifetimes |
beta_0 | scale parameter for the Gamma distribution for the lifetime process. |
continuous_discount_factor | continuous discount factor to use |
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. |
mCov_life | Matrix containing the covariates data affecting the lifetime process. One column for each covariate. |
mCov_trans | Matrix containing the covariates data affecting the transaction process. One column for each covariate. |
vCovParams_life | Vector of estimated parameters for the lifetime covariates. |
vCovParams_trans | Vector of estimated parameters for the transaction covariates. |
Returns a vector with the DERT for each customer.
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.
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.