Computes the expected number of repeat transactions in the interval (0, vT_i] for a randomly selected customer, where 0 is defined as the point when the customer came alive.
ggomnbd_nocov_expectation(r, alpha_0, b, s, beta_0, vT_i)ggomnbd_staticcov_expectation(
r,
alpha_0,
b,
s,
beta_0,
vT_i,
vCovParams_trans,
vCovParams_life,
mCov_life,
mCov_trans
)
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 since the customer came alive
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.
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.
Bemmaor AC, Glady N (2012). “Modeling Purchasing Behavior with Sudden “Death”: A Flexible Customer Lifetime Model” Management Science, 58(5), 1012-1021.