In this study, a cosmic ray muon sampling capability using a phenomenological model that captures the main characteristics of the experimentally measured spectrum coupled with a set of statistical algorithms is developed. The "muon generator" produces muons with zenith angles in the range 0-90 o and energies in the range 1-100 GeV and is suitable for Monte Carlo simulations with emphasis on muon tomographic and monitoring applications. The muon energy distribution is described by the Smith & Duller (1959) phenomenological model. Statistical algorithms are then employed for generating random samples. The inverse transform provides a means to generate samples from the muon angular distribution, whereas the Acceptance-Rejection and Metropolis-Hastings algorithms are employed to provide the energy component. The predictions for muon energies 1 to 60 GeV and zenith angles 0-90 o are validated with a series of actual spectrum measurements and with estimates from the software library CRY. The results confirm the validity of the phenomenological model and the applicability of the statistical algorithms to generate polyenergetic-polydirectional muons. The response of the algorithms and the impact of critical parameters on computation time and computed results were investigated. Final output from the proposed "muon generator" is a look-up table that contains the sampled muon angles and energies and can be easily integrated into Monte Carlo particle simulation codes such as Geant4 and MCNP.