Some authors have commented that maximum likelihood method has a robustness problem in estimating parameters. Among other things , does Gaussian hypothesis required to use this method ?
No ! It is widely used to fit non Gaussian models (eg Poisson, binomial, etc).
Thanks for your answer. In which case, maximum likelihood should not be recommended ?
Dear Prof.
Maximum Likelihood Estimation method can be used to estimate the parameters with a sample as long as the form any of the probability mass function (discrete) or the any probability density function (continuous).
Gaussian hypothesis does not required to use the maximum likelihood method. However we have the effective estimates only for Gaussian probability density function.
There is no general rule for deciding when to apply the Maximum Likelihood Estimation (MLE). The MLE results in suitable expressions for some distributions (Gaussian, Log-Normal and Pareto Distributions) and not so suitable for others (K distribution). Alternatively, the Method of Moments (MoM) provides a viable option when the MLE does not work well. Moreover, some artificial intelligence methods have been applied to estimate distribution parameters. You can read more about it in:
Improved Shape Parameter Estimation in K Clutter with Neural Networks and Deep Learning. International Journal of Interactive Multimedia and Artificial Intelligence 01/2016; 3(7-7):96-103. DOI:10.9781/ijimai.2016.3714
2015, “A Neural Network Approach to Weibull Distributed Sea Clutter Parameter’s Estimation”. Revista Iberoamericana de Inteligencia Artificial, Vol. 18, No. 56, pp. 3-13, España, ISSN: 1988-3064.
Good Luck!
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