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

• ggomnbd_nocov_CET Conditional Expected Transactions without covariates

• ggomnbd_staticcov_CET Conditional Expected Transactions with static covariates

ggomnbd_nocov_CET(r, alpha_0, b, s, beta_0, dPeriods, vX, vT_x, vT_cal)

ggomnbd_staticcov_CET(
r,
alpha_0,
b,
s,
beta_0,
dPeriods,
vX,
vT_x,
vT_cal,
vCovParams_trans,
vCovParams_life,
mCov_life,
mCov_trans
)

## 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. scale parameter of the Gompertz distribution (constant across customers) 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 lifetime process. One column for each covariate. Matrix containing the covariates data affecting the transaction process. One column for each covariate.

## Value

Returns a vector containing the conditional expected transactions for the existing customers in the GGompertz/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

Bemmaor AC, Glady N (2012). “Modeling Purchasing Behavior with Sudden “Death”: A Flexible Customer Lifetime Model” Management Science, 58(5), 1012-1021.