rehan asked . 2022-07-20

How can I fit a Gumbel Maximum distribution using both

How can I fit a Gumbel Maximum distribution using both Maximum Likelihood Estimates and Method of Moments Estimates?

AI, Data Science, and Statistics , Statistics and Machine Learning Toolbox , Probability Distribut

Expert Answer

Prashant Kumar answered . 2024-03-28 07:16:33

The usual Gumbel distribution models the *minimum *of a sample and it is captured in MATLAB by the "Extreme Value Distribution".

The maximum likelihood estimates in this distribution for a particular dataset are obtained by means of the "evfit" function.

However, if we would like to model the *maximum* instead, we need to resort to a different approach. Essentially, the Gumbel maximum distribution is the mirror image of the Gumbel minimum distribution and, therefore, we can still model it using the "Extreme Value Distribution". Transforming the dataset by taking negatives allows us to send maximums to minimums (and vice versa). As a consequence, fitting a "Extreme Value Distribution" will now model the maximum:

 

rng default;
xMaxima = max(randn(1000,500), [], 2);

pd = fitdist(-xMaxima,'ev')

The maximum likelihood estimates are given by "evfit":

paramEstsMaxima = evfit(-xMaxima)

Bear in mind that any subsequent computations are now based on the transformed dataset. For example, if we would like to calculate a maximum extreme value at p=0.99, we would need to obtain a minimum extreme value at p=0.01 in the counterpart dataset and transform it back to maximum by taking negatives:

value = - icdf(pd,0.01)

Yet if we would like to use method of moments estimates, we would need to resort to another approach. In this case, the starting point is the "Generalized Extreme Value" distribution.

If the shape parameter "k" of this distribution is set to 0, then this distribution is suitable for modelling the maximum as well. The method of moments estimates for Gumbel maximum are given by:

gamma = 0.5772;
sigmaHat = sqrt(6)*std(xMaxima)/pi;
muHat = mean(xMaxima) - gamma*sigmaHat;

where "gamma" is the Euler constant. Instantiating the "Generalized Extreme Value" distribution with the above parameters produces a Gumbel Maximum with method of moments estimates:

pd = makedist('GeneralizedExtremeValue','k',0,'sigma',sigmaHat,'mu',muHat);

In this case, the maximum extreme value at p=0.99 would be given by:

extremeValue = icdf(pd,0.99);

 


Not satisfied with the answer ?? ASK NOW

Frequently Asked Questions

MATLAB offers tools for real-time AI applications, including Simulink for modeling and simulation. It can be used for developing algorithms and control systems for autonomous vehicles, robots, and other real-time AI systems.

MATLAB Online™ provides access to MATLAB® from your web browser. With MATLAB Online, your files are stored on MATLAB Drive™ and are available wherever you go. MATLAB Drive Connector synchronizes your files between your computers and MATLAB Online, providing offline access and eliminating the need to manually upload or download files. You can also run your files from the convenience of your smartphone or tablet by connecting to MathWorks® Cloud through the MATLAB Mobile™ app.

Yes, MATLAB provides tools and frameworks for deep learning, including the Deep Learning Toolbox. You can use MATLAB for tasks like building and training neural networks, image classification, and natural language processing.

MATLAB and Python are both popular choices for AI development. MATLAB is known for its ease of use in mathematical computations and its extensive toolbox for AI and machine learning. Python, on the other hand, has a vast ecosystem of libraries like TensorFlow and PyTorch. The choice depends on your preferences and project requirements.

You can find support, discussion forums, and a community of MATLAB users on the MATLAB website, Matlansolutions forums, and other AI-related online communities. Remember that MATLAB's capabilities in AI and machine learning continue to evolve, so staying updated with the latest features and resources is essential for effective AI development using MATLAB.

Without any hesitation the answer to this question is NO. The service we offer is 100% legal, legitimate and won't make you a cheater. Read and discover exactly what an essay writing service is and how when used correctly, is a valuable teaching aid and no more akin to cheating than a tutor's 'model essay' or the many published essay guides available from your local book shop. You should use the work as a reference and should not hand over the exact copy of it.

Matlabsolutions.com provides guaranteed satisfaction with a commitment to complete the work within time. Combined with our meticulous work ethics and extensive domain experience, We are the ideal partner for all your homework/assignment needs. We pledge to provide 24*7 support to dissolve all your academic doubts. We are composed of 300+ esteemed Matlab and other experts who have been empanelled after extensive research and quality check.

Matlabsolutions.com provides undivided attention to each Matlab assignment order with a methodical approach to solution. Our network span is not restricted to US, UK and Australia rather extends to countries like Singapore, Canada and UAE. Our Matlab assignment help services include Image Processing Assignments, Electrical Engineering Assignments, Matlab homework help, Matlab Research Paper help, Matlab Simulink help. Get your work done at the best price in industry.