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CLVTools (version 0.5.0)

pnbd_CET: Pareto/NBD: Conditional Expected Transactions

Description

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

Usage

pnbd_nocov_CET(vEstimated_params, dPrediction_period, vX, vT_x, vT_cal)
pnbd_staticcov_CET(
  vEstimated_params,
  dPrediction_period,
  vX,
  vT_x,
  vT_cal,
  vCovParams_trans,
  vCovParams_life,
  mCov_trans,
  mCov_life
)

Arguments

vEstimated_params

Vector with the Pareto/NBD model parameters at original scale.

dPrediction_period

time prediction time frame

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.

vCovParams_trans

Vector of estimated parameters for the transaction covariates.

vCovParams_life

Vector of estimated parameters for the dropout covariates.

mCov_trans

Matrix containing the covariates data affecting the transaction process. One column for each covariate.

mCov_life

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

vEstimated_params vector with the estimated parameters in original scale for the Pareto/NBD model, namely (r, alpha, s, beta). r and alpha: unobserved parameters that describe the NBD transaction process. s and beta: unobserved parameters that describe the pareto (exponential gamma) dropout process.

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, Peter S., and Bruce G.S. Hardie (2005). "A Note on Deriving the Pareto/NBD Model and Related Expressions.", Web. http://www.brucehardie.com/notes/008/.