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Maximum Likelihood Estimates

Quantum XL finds the optimal parameter estimates by maximizing the Log-Likelihood of the appropriate distribution. For some distributions, such as the Normal or the 1-Parameter Exponential, the optimal parameters can be calculated using closed form equations. However, for most distributions an iterative algorithm which maximizes the Log-Likelihood is used. Typically, this algorithm is Newton's method; however, in some cases alternative methods must be used. For example, for the 3-parameter Weibull when Beta is approximately 1, the Log-Likelihood is unstable.

Meeker, W. Q. and Escobar L. A., "Statistical Methods for Reliability Data", 1998, New York, Wiley