When is beta distribution bell-shaped or concave? - Cross Validated
By A Mystery Man Writer
Description
Is there some restriction to parameters $( \alpha , \beta)$ that makes the beta distribution concave down? Bell-shaped like e.g. a normal?
For example, the cases in purple and black, but not the red
![When is beta distribution bell-shaped or concave? - Cross Validated](https://ars.els-cdn.com/content/image/3-s2.0-B9780124058880000064-f06-02-9780124058880.jpg)
Beta Distribution - an overview
![When is beta distribution bell-shaped or concave? - Cross Validated](https://miro.medium.com/v2/resize:fit:1400/1*SMfjErlvHpSVlfBGFT9YuA.png)
Beta Distribution — Intuition, Examples, and Derivation, by Ms Aerin
![When is beta distribution bell-shaped or concave? - Cross Validated](https://vaszar.org/wordpress/wp-content/uploads/2020/03/image-6-1024x731.png)
The beta distribution
![When is beta distribution bell-shaped or concave? - Cross Validated](https://vaszar.org/wordpress/wp-content/uploads/2020/03/image.jpeg)
The beta distribution
![When is beta distribution bell-shaped or concave? - Cross Validated](https://www.researchgate.net/publication/351600702/figure/fig1/AS:1023683833364483@1621076653345/Perks-distribution-when-the-number-of-types-of-arrowheads-is-J-3-a-its-projection.png)
Perks' distribution when the number of types of arrowheads is J = 3
![When is beta distribution bell-shaped or concave? - Cross Validated](https://upload.wikimedia.org/wikipedia/commons/thumb/4/42/Median_Beta_Distribution_for_alpha_and_beta_from_0_to_5_-_J._Rodal.jpg/325px-Median_Beta_Distribution_for_alpha_and_beta_from_0_to_5_-_J._Rodal.jpg)
Beta distribution - Wikipedia
![When is beta distribution bell-shaped or concave? - Cross Validated](https://www.mdpi.com/mca/mca-27-00099/article_deploy/html/images/mca-27-00099-g001.png)
MCA, Free Full-Text
![When is beta distribution bell-shaped or concave? - Cross Validated](https://www.bayesrulesbook.com/bookdown_files/figure-html/beta-tuning-1.png)
Chapter 3 The Beta-Binomial Bayesian Model Bayes Rules! An Introduction to Applied Bayesian Modeling
![When is beta distribution bell-shaped or concave? - Cross Validated](https://journals.sagepub.com/cms/10.1177/0272989X15582210/asset/images/large/10.1177_0272989x15582210-fig1.jpeg)
Using Dual Beta Distributions to Create “Proper” ROC Curves Based on Rating Category Data - Douglas Mossman, Hongying Peng, 2016
What is the effect of a high variance on the distribution of data? - Quora
![When is beta distribution bell-shaped or concave? - Cross Validated](http://varianceexplained.org/figs/2014-12-20-beta_distribution_and_baseball/plot2-1.png)
Understanding the beta distribution (using baseball statistics
![When is beta distribution bell-shaped or concave? - Cross Validated](https://miro.medium.com/v2/resize:fit:1400/1*3mhZOScyAOmzufyDTPNoxA.png)
Beta Distribution — Intuition, Examples, and Derivation
![When is beta distribution bell-shaped or concave? - Cross Validated](https://media.springernature.com/m685/springer-static/image/art%3A10.1007%2Fs00170-024-13234-2/MediaObjects/170_2024_13234_Fig16_HTML.png)
Cutting dynamics research on the five-axis machining of thin curved surface with barrel-taper-ball milling cutter
![When is beta distribution bell-shaped or concave? - Cross Validated](https://i.stack.imgur.com/vEOx5m.png)
What is the intuition behind beta distribution? - Cross Validated
![When is beta distribution bell-shaped or concave? - Cross Validated](https://www.statisticshowto.com/wp-content/uploads/2016/03/Logisticpdfunction.svg_.png)
Bell Shaped Distribution - Statistics How To
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