(Basic Statistics for Citizen Data Scientist)
Gumbel Distribution
The Gumbel distribution is used to model the largest value from a relatively large set of independent elements from distributions whose tails decay relatively fast, such as a normal or exponential distribution. As a result, it can be used to analyze annual maximum daily rainfall volumes. In this way, it can be used to predict extreme events such as floods, earthquakes or hurricanes.
For this reason, the Gumbel distribution is also called the extreme value type I distribution and is used to find a maximum extreme value. Setting x to –x will find the minimum extreme value.
The pdf of the Gumbel distribution with location parameter μ and scale parameter β is
where β > 0. The cdf is
The inverse of the Gumbel distribution is
The standard Gumbel distribution is the case where μ = 0 and β = 1.
The Gumbel distribution is sometimes called the double exponential distribution, although this term is often used for the Laplace distribution.
If x has a Weibull distribution, then -ln(x) has a Gumbel distribution.
Key statistical properties of the Gumbel distribution are:
Figure 1 – Statistical properties of the Gumbel distribution
Here, γ is the Euler-Mascheroni constant whose value is –ψ0(1), the negative of the digamma function at 1 (see MLE Fitting Gamma Distribution) with a value approximately equal to .577215665.
Figure 2 shows a graph of the Gumbel distribution for different values of μ and β.
Figure 2 – Chart of the Gumbel distribution
Real Statistics Functions: The Real Statistics Resource Pack provides the following functions for the Gumbel distribution.
GUMBEL_DIST(x, μ, β, cum) = the pdf of the Gumbel distribution f(x) when cum = FALSE and the corresponding cumulative distribution function F(x) when cum = TRUE.
GUMBEL_INV(p, μ, β) = the inverse of the Gumbel distribution at p
How to get CLASS Distribution in Data for Classification | Jupyter Notebook | Python Data Science
Statistics for Beginners in Excel – Gumbel Distribution
Disclaimer: The information and code presented within this recipe/tutorial is only for educational and coaching purposes for beginners and developers. Anyone can practice and apply the recipe/tutorial presented here, but the reader is taking full responsibility for his/her actions. The author (content curator) of this recipe (code / program) has made every effort to ensure the accuracy of the information was correct at time of publication. The author (content curator) does not assume and hereby disclaims any liability to any party for any loss, damage, or disruption caused by errors or omissions, whether such errors or omissions result from accident, negligence, or any other cause. The information presented here could also be found in public knowledge domains.
Learn by Coding: v-Tutorials on Applied Machine Learning and Data Science for Beginners
Latest end-to-end Learn by Coding Projects (Jupyter Notebooks) in Python and R:
All Notebooks in One Bundle: Data Science Recipes and Examples in Python & R.
End-to-End Python Machine Learning Recipes & Examples.
End-to-End R Machine Learning Recipes & Examples.
Applied Statistics with R for Beginners and Business Professionals
Data Science and Machine Learning Projects in Python: Tabular Data Analytics
Data Science and Machine Learning Projects in R: Tabular Data Analytics
Python Machine Learning & Data Science Recipes: Learn by Coding
R Machine Learning & Data Science Recipes: Learn by Coding
Comparing Different Machine Learning Algorithms in Python for Classification (FREE)
There are 2000+ End-to-End Python & R Notebooks are available to build Professional Portfolio as a Data Scientist and/or Machine Learning Specialist. All Notebooks are only $29.95. We would like to request you to have a look at the website for FREE the end-to-end notebooks, and then decide whether you would like to purchase or not.