In this manuscript, we present two novel algorithms for statistical circuit performance modeling.The first algorithm is a maximum entropy moment matching method (MAX-ENT) to model the overall distribution of the circuit performance considering process variations. A prior paper about this work was submitted by the same authors for publication in the ISQED-2013 proceedings, and cited in this manuscript with reference number [26]. This MAXENT algorithm is presented in Section III with more detailed derivation.In addition, we utilize the MAXENT approach, but apply it to a piecewise distribution model (PDM) framework, leading to a novel extension of the generic framework to model rare event failures in circuit modeling. We demonstrate why the prior work is not applicable to rare event circuit modeling and also provide a novel solution that showcases how the prior work can be abstracted for application to rare event circuit modeling. Furthermore, we provide several new experiments that demonstrate the advantage of using the current submissions framework over the prior papers framework. The PDM algorithm and experiment results are presented in Section IV and Section V respectively.Below is a brief summary of what is new to the manuscript and what was already proposed in the prior paper.Section I: Summary of basic statistical modeling algorithms and a brief overview of their strengths and weaknesses, including [26] Section II: A brief background on statistical modeling for circuits Section III: Detailed summary of the work proposed in [26], including derivations and experiment results (3 pages) Section IV: Completely new material (5 pages) that shows a new circuit modeling technique that extends the work in [26] by proposing new algorithms and models Section V: Completely new material (3 pages) that demonstrates the advantages of the current submissions algorithm over other algorithms including [26] The common denominator between [26] and the current submission is the fact that they utilize the same moment matching technique to obtain the probability distribution. However, although the underlying engine is the same, we estimate that at least 50% of the material is completely new because of the significant amount of new algorithms, models, and experimental results. 1 0278-0070 (c)Abstract-The impact of process variations continues to grow as transistor feature size shrinks. Such variations in transistor parameters lead to variations and unpredictability in circuit output and may ultimately cause them to violate specifications leading to circuit failure. In fact, timely failures in critical circuits may lead to catastrophic failures in the entire chip. As such, statistical modeling of circuit behavior is becoming increasingly important. However, existing statistical circuit simulation approaches fail to accurately and efficiently analyze the high sigma behavior of probabilistic circuit output. To this end, we propose PDM (Piecewise Distribution Model) -a piecewise distribution modeling approach via moment matching using ma...