Can the Beta Distribution be Adjusted to Range from -A to A?

  • Context: Graduate 
  • Thread starter Thread starter X1088LoD
  • Start date Start date
  • Tags Tags
    Beta Distribution
Click For Summary
SUMMARY

The discussion centers on adjusting the beta distribution to model a U-shaped probability density function (PDF) ranging from -A to A, where A represents the amplitude of a sine wave. The beta distribution, particularly with parameters alpha and beta both less than 1, is identified as the closest match for this U-shaped distribution. The participant expresses a need for additional PDF suggestions that can also produce a U-shaped plot, indicating a search for alternative distributions beyond the beta distribution.

PREREQUISITES
  • Understanding of beta distribution parameters (alpha and beta)
  • Knowledge of probability density functions (PDFs)
  • Familiarity with U-shaped distributions
  • Basic concepts of sine wave characteristics and amplitude
NEXT STEPS
  • Research alternative U-shaped distributions, such as the triangular distribution
  • Explore the properties and applications of the beta distribution in statistical modeling
  • Investigate the uniform distribution and its transformations
  • Learn about the characteristics of the sine wave and its implications in probability modeling
USEFUL FOR

Mathematicians, statisticians, data scientists, and anyone interested in modeling U-shaped distributions in probability theory.

X1088LoD
Messages
21
Reaction score
0
I have is a distribution that is U-shaped, centered at 0, spanning from -A to A, and I want a means to model this, a beta distribution is the closest thing I have found to kinda do this

can the beta distribution be adjusted to range from -A to A as opposed to 0 to 1? any other suggestions as to distributions to use?
 
Physics news on Phys.org
You're going to need to post more details.
 
The probability density function of a sin wave is a U shaped distribution, let's say from -A to A, where A is the amplitude of the sin wave. The beta distribution is the closest thing to a U shaped distribution I have found when the parameters alpha and beta are less than 1. I have found a way to adjust the range of the beta distribution

however, what I want to know are there any other PDF distributions that generate a U shaped plot. Beta is the only one I have found so far, wasnt sure if there was an obscure one out there under my nose
 
Essentially, X~Uniform(domain) so you want to find the distribution of f(X). I can't help you anymore unless you give more information.
 

Similar threads

Graduate Distribution of Range of Samples taken from N(0,1)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Write probability in terms of shape parameters of beta distribution
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Beta Distributed Random Variates
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Distribution of sum of two circular uniform RVs in the range [0, 2 pi)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Parameters of a distribution of a physical variable
  • · Replies 4 ·
Replies
4
Views
2K
High School Central Limit Theorem: How does sample size affect the sampling distribution?
  • · Replies 31 ·
2
Replies
31
Views
4K
Graduate Range of Difference: Bounds for Length of Stay
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Relating Moments from one Distribution to the Moments of Another
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Can a Beta Distribution Model Scores in the Interval [0,1] for Ranked Retrieval?
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Adding Multivariate Normal Distributions
  • · Replies 8 ·
Replies
8
Views
2K