From a quantum statistical viewpoint, four typical quantum states are Fock, Sub-Poissonian, Poissonian and SuperPoissonian states. Quantum interactions are focus among Fock and Poissonian states. Using quantum statistics, model and simulation, this paper proposes two models: matrix and variant transformations: 1. MT Matrix Transformation – eigenvalue states; 2. VT Variant Transformation – invariant states to analyze three random sequences: 1) random; 2) conditional random in a constant; 3) periodic pattern. Four procedures are proposed. Fast Fourier Transformation FFT is applied as one of MT schemes and two invariant scheme of VT schemes are applied, three random sequences are in M segments and each segment has a length m to generate a measuring sequence. Shifting operations are applied on each random sequence to create m+1 spectrum distributions. For FFT, a pair of eigenvalues are selected as the output. Two types of 1D and 2D variant maps are generated to illustrate multiple parameter selections to generate a series of results. Since sequences 1) and 3) are related simple, more cases are focus on sequences 2). Better than FFT, VT distinguishes various Fock, Sub-Poissonian, Poissonian states in random analysis to distinguish three random sequences as three levels of statistical ensembles: Micro-canonical, Canonical, and Grand-Canonical ensembles. Applying two transformations, quantum statistics, model and simulation of modern quantum theory and applications can be explored.