Statistics for Beginners in Excel – Gumbel Distribution

Hits: 237

(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

Gumbel pdf

where β > 0. The cdf is

Gumbel cdf

The inverse of the Gumbel distribution is

Gumbel inverse function

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:

Gumbel distribution propertiesFigure 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.

Gumbel distribution chart

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

Personal Career & Learning Guide for Data Analyst, Data Engineer and Data Scientist

Applied Machine Learning & Data Science Projects and Coding Recipes for Beginners

A list of FREE programming examples together with eTutorials & eBooks @ SETScholars

95% Discount on “Projects & Recipes, tutorials, ebooks”

Projects and Coding Recipes, eTutorials and eBooks: The best All-in-One resources for Data Analyst, Data Scientist, Machine Learning Engineer and Software Developer

Topics included: Classification, Clustering, Regression, Forecasting, Algorithms, Data Structures, Data Analytics & Data Science, Deep Learning, Machine Learning, Programming Languages and Software Tools & Packages.
(Discount is valid for limited time only)

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

Please do not waste your valuable time by watching videos, rather use end-to-end (Python and R) recipes from Professional Data Scientists to practice coding, and land the most demandable jobs in the fields of Predictive analytics & AI (Machine Learning and Data Science).

The objective is to guide the developers & analysts to “Learn how to Code” for Applied AI using end-to-end coding solutions, and unlock the world of opportunities!