I am looking for a library that does advanced math, statistics, statistical distribution, etc..
Currently I am looking for something that does binomial and poisson distribution.
MathDotNet should have the functions you are looking for, although it may be a bit of overkill depending on how much functionality you need. It offers:
For a complete list see this page.
.NET Framework languages C#, F# and VB.NET
ILNumerics.Net high performance, typesafe numerical array classes and functions for general math, FFT and linear algebra, aims .NET/mono, 32&64 bit, script-like syntax in C#, 2D & 3D plot controls, efficient memory management
IMSL Numerical Libraries for .NET is a set of mathematical, statistical, data mining, financial and charting classes written in C#.
Measurement Studio is an integrated suite UI controls and class libraries for use in developing test and measurement applications. The analysis class libraries provide various digital signal processing, signal filtering, signal generation, peak detection, and other general mathematical functionality.
NMath by CenterSpace Software: numerical component libraries for the .NET platform, including signal processing (FFT) classes, a linear algebra (LAPACK & BLAS) framework, and a statistics package.
suanshu.net by Numerical Method Inc.: is a large collection of numerical algorithms including linear algebra, (advanced) optimization, interpolation, Markov model, principal component analysis, time series analysis, hypothesis testing, regressions, statistics, ordinary and partial differential equation solvers, and suanshu. NLinear is a generic linear algebra toolkit in C# compatible with Silverlight.
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