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The Solver Platform SDK includes complete facilities for creating models in C++, C#, VB.NET, Visual Basic,
Java, and MATLAB with uncertain variables and
functions, running Monte Carlo simulations, and collecting
statistics from the Monte Carlo samples. You could pay $1,200
or more for other software libraries that provide only probability
distribution modeling and Monte Carlo simulation -- but in the
Solver Platform SDK, all this power is included at no extra cost.
The Solver Platform SDK includes four different,
high quality random number generators, covering the full spectrum of
tradeoffs between long periods and statistical independence of the
samples:
 | Park-Miller “Minimal” Generator with
Bayes-Durham shuffle and safeguards. This generator has a period
of 231-2, and very good statistical independence of
samples. |
| Combined Multiple Recursive Generator
(CMRG) of L’Ecuyer. This generator has a period of 2191,
and excellent statistical independence of samples within its
period. |
| Well Equidistributed Long-period Linear
(WELL1024) generator of Panneton, L’Ecuyer and Matsumoto. This
very new generator combines a long period of 21024
with very good statistical independence. |
| Mersenne Twister generator of
Matsumoto and Nishimura. This generator has the longest period
of 219937-1, but the samples are not as
“equidistributed” as for the WELL1024 and CMRG generators.
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Monte
Carlo samples are generated from a wide range of probability
distributions, using any of three methods:
| Standard Monte Carlo |
| Latin Hypercube |
| Sobol Numbers |
Sobol numbers are an innovation in the
Solver Platform SDK that's not found in other software for Monte
Carlo simulation. They are widely used by application developers in
quantitative finance. For low to moderate dimensional
problems, Sobol numbers offer the "best of both worlds" --
the speed of Standard Monte Carlo with the "coverage" of
Latin Hypercube sampling.
The Solver Platform SDK provides a complete
set of analytic probability distributions. And you can specify
shifting and truncation to
customize your probability distributions.
| Bernoulli |
Integer Uniform |
Pareto |
| Beta |
Inverse Gaussian |
Pareto2 |
| BetaGeneral |
Laplace |
Pearson5 |
| BetaSubjective |
Logarithmic |
Pearson6 |
| Binomial |
Logistic |
Pert |
| Cauchy |
Log-Logistic |
Poisson |
| Chi Squared |
Lognormal |
Rayleigh |
| Erf |
Lognorm2 |
Student |
| Erlang |
MaxExtreme |
Triangular |
| Exponential |
MinExtreme |
TriGeneral |
| Gamma |
Myerson |
Uniform |
| Geometric |
Neg. Binomial |
Weibull |
| Hypergeometic |
Normal |
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You can easily create an instance of a
Distribution object, with the properties of any of these probability
distributions. By simply accessing properties of this object,
you can obtain the probability density (PDF) or cumulative density (CDF)
function, or analytic values for the moments of the distribution,
based on its type and parameters.
The Solver Platform SDK makes it easy to fit an
analytic distribution and its parameters to sample data. You
can specify the distribution type and ask the SDK to find the
best-fitting parameters, or you can just supply the sample data,
specify continuous or discrete, and let the SDK automatically choose
the best-fitting distribution type and the best parameters. This is
illustrated in the Example Source Code.
The SDK can fit 22 different distributions (from the list of 38
above), including both continuous and discrete distributions.
The Solver Platform SDK makes it easy to create
correlated input distributions, by creating a DoubleMatrix object
that specifies rank correlations between two or more
distributions. You simply assign this correlation matrix to
the appropriate property of the Model object. This is
illustrated in the Example Source Code.
To consistently specify correlations among multiple
distributions, a rank correlation matrix must be positive
semidefinite (PSD). Users often have "desired
correlations" among the key distributions, but insufficient information
to fill out the matrix. The Solver Platform SDK includes
methods to test a DoubleMatrix for positive semidefiniteness (IsPSD)
and to transform a non-PSD matrix into a "nearest" matrix
that is positive semidefinite (MakePSD). Unlike other
software, the SDK can find a PSD matrix that leaves your "desired
correlations" among key distributions nearly unchanged.
In the Solver Platform SDK, you can obtain any of
the statistics listed below for both uncertain variables and
uncertain functions, by simply accessing the appropriate property or method of
a Statistics object embedded in each Variable and Function object.
You can obtain confidence intervals (CI) for the mean or standard deviation, or the number of Monte Carlo trials
required to
obtain a result within your specified confidence interval.
| Number of Values |
Standard Deviation |
Target |
| Number of Errors |
Variance |
Mean CI |
| Minimum |
Skewness |
Std Dev CI |
| Maximum |
Kurtosis |
Trials for CI |
| Mean |
Mode |
Percentiles |
100 percentile values (0 to 99) are computed for
each variable and function. In addition, you can obtain the observed
correlation in the Monte Carlo sample between any two uncertain
functions, or between an uncertain function and an uncertain
variable, by accessing a property of the Function object.
The Solver Platform SDK goes beyond computation of
"standard moments" to compute several risk measures popular
in quantitative finance applications. Again you can
obtain these values by simply accessing the appropriate property or method of a
Statistics object embedded in each Variable and Function object.
| Mean Absolute Deviation |
| Semivariance or Lower Partial Moment |
| Semideviation (square root or pth
root) |
| Value at Risk |
| Conditional Value at Risk |
Back to Solver
Platform SDK Product Overview
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