Supported Distributions

The SDK supports over 50 continuous and discrete probability distributions.

Parameter Estimation Methods

There are a number of well-known methods that can be used to estimate distribution parameters based on available sample data. For every supported distribution, the SDK implements one of the following parameter estimation methods:

• method of moments (MOM);
• maximum likelihood estimates (MLE);
• least squares estimates (LSE);
• method of L-moments.

Since the detailed description of these methods goes beyond the scope of this manual, we will just note that, where possible, the SDK uses the least computationally intensive methods. Thus, it employs the method of moments for those distributions whose moment estimates are available for all possible parameter values, and do not involve the use of iterative numerical methods.

For many distributions, the SDK uses the MLE method involving the maximization of the log-likelihood function. For some distributions, such as the 2-parameter Exponential and the 2-parameter Weibull, a closed form solution of this problem exists. For other distributions, the SDK implements the numerical method for multi-dimensional function minimization. Given the initial parameter estimates vector, this method tries to improve it on each subsequent iteration. The algorithm terminates when the stopping criteria is satisfied (the specified accuracy of the estimation is reached, or the number of iterations reaches the specified maximum).

The SPAApplication.FitOptions.MLMaxIterations and SPAApplication.FitOptions.MLAccuracy properties allow you to specify the maximum number of iterations and the accuracy of the estimation. In most cases, the default values should be used. However, if you need better accuracy, you may want to set it to a value of 1E-6 or less and increase the max. number of iterations. On the other hand, if your sample data contains many (tens of thousands) data points, you may want to decrease the max. number of iterations in order to speed up the analysis.

The advanced continuous distributions are fitted using the MLE, the modified LSE, and the L-moments methods.