Matlab statistic toolbox is most extensive for quant analsys which includes Markov and probability, multivariate, regression, etc
As you know, understanding quant on the math involves lots of statistics. This is probably the most feature of Matlab. It also the most extensive toolkit I have come across for quant modelling and stragey building. This toolkit includes all things you would definitely need. Do any of those open source code base projects include this? Probably not.
There are various ways to do resampling if needed. This includes:
The Bootstrap
The Jackknife
Parallel Computing Support for Resampling Methods. You have various distribution plots which include:
Normal Probability Plots
Quantile-Quantile Plots
Cumulative Distribution Plots
There are various supported distribution methods which include:
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pdf — Probability density functions
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cdf — Cumulative distribution functions
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inv — Inverse cumulative distribution functions
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stat — Distribution statistics functions
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fit — Distribution fitting functions
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like — Negative log-likelihood functions
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rnd — Random number generators
There is some enhanced random generator methodologies which are supported:
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Generating Random Data
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Random Number Generation Functions
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Common Generation Methods
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Parallel Computing Support for Random Number Generation
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Representing Sampling Distributions Using Markov Chain Samplers
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Generating Quasi-Random Numbers
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Generating Data Using Flexible Families of Distributions
These most like blow away even Quantlib and Quantlib XL with its own ease. I must also add that the documentation that comes with Matlab is very stellar. It is worth the price indeed.
Linear regression models include:
Linear Regression Models
Multiple Linear Regression
Robust Regression
Stepwise Regression
Ridge Regression
Partial Least Squares
Polynomial Models
Response Surface Models
Generalized Linear Models
Multivariate Regression
Multi dimensional scaling include:
Classical Multidimensional Scaling
Nonclassical Multidimensional Scaling
Nonmetric Multidimensional Scaling
This would be an excellent introduction into your foray into the world of stats which will of course give you a very broad based understanding of how quant works. Do note that there is a ton more in this toolkit but had no time to mention all of it.
