How to derive the mode of a Gamma Distribution

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SUMMARY

The discussion focuses on deriving the mode of a Gamma Distribution by taking the first derivative of its density function and setting it to zero. This method is confirmed to be effective for unimodal cases. However, the conversation highlights the complexity of multimodal distributions, suggesting that an analytic approach, particularly for mixed Gaussian distributions, is more appropriate. A referenced article provides further insights into this topic.

PREREQUISITES
  • Understanding of Gamma Distribution properties
  • Knowledge of calculus, specifically differentiation
  • Familiarity with unimodal and multimodal distributions
  • Basic concepts of Gaussian distributions
NEXT STEPS
  • Read the article on mixed Gaussian distributions for analytic mode finding
  • Explore advanced calculus techniques for analyzing multimodal distributions
  • Study the implications of mode derivation in statistical modeling
  • Investigate software tools for statistical analysis, such as R or Python's SciPy library
USEFUL FOR

Statisticians, data scientists, and researchers involved in statistical modeling and analysis of probability distributions.

Bachelier
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Do I take the derivative of the density fct and set it equal to 0, then solve for t?
 
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Bachelier said:
Do I take the derivative of the density fct and set it equal to 0, then solve for t?

Yes, for the first derivative in the unimodal case. However, the problem is more interesting for multimodal distributions. The following article discusses an analytic approach to finding the modes of mixed Gaussian distributions.

http://faculty.ucmerced.edu/mcarreira-perpinan/papers/pami00.pdf
 
Last edited:
thanks. great article
 

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