In this study, a mathematical model is developed based on algebraic equations which is capable of generating artificially normal events of electrocardiogram (ECG) signals such as P-wave, QRS complex, and T-wave. This model can also be implemented for the simulation of abnormal phenomena of electrocardiographic signals such as STsegment episodes (i.e. depression, elevation, and sloped ascending or descending) and repolarization abnormalities such as T-Wave Alternans (TWA). Event parameters such as amplitude, duration, and incidence time in the conventional ECG leads can be a good reflective of heart electrical activity in specific directions. The presented model can also be used for the simulation of ECG signals on torso plane or limb leads. To meet this end, the amplitude of events in each of the 15-lead ECG waveforms of 80 normal subjects at MITBIH Database (www.physionet.org) are derived and recorded. Various statistical analyses such as amplitude mean value, variance and confidence intervals calculations, Anderson- Darling normality test, and Bayesian estimation of events amplitude are then conducted. Heart Rate Variability (HRV) model has also been incorporated to this model with HF/LF and VLF/LF waves power ratios. Eventually, in order to demonstrate the suitable flexibility of the presented model in simulation of ECG signals, fascicular ventricular tachycardia (left septal ventricular tachycardia), rate dependent conduction block (Aberration), and acute Qwave infarctions of inferior and anterior-lateral walls are finally simulated. The opensource simulation code of above abnormalities will be freely available.