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

In summary, the person is looking for a way to model a U-shaped distribution centered at 0 and spanning from -A to A. They have found that the beta distribution is the closest option, but they want to know if it can be adjusted to have a range from -A to A instead of 0 to 1. They are also asking for suggestions for other distributions that could work. However, more information is needed to provide a better answer.
  • #1
X1088LoD
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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?
 
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  • #2
You're going to need to post more details.
 
  • #3
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
 
  • #4
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.
 

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

What is the Beta distribution?

The Beta distribution is a continuous probability distribution that is often used to model proportions or probabilities. It is defined by two parameters, alpha (α) and beta (β), which determine the shape of the distribution.

What is the relationship between the Beta distribution and the binomial distribution?

The Beta distribution and the binomial distribution are closely related. In fact, the Beta distribution can be thought of as a continuous version of the binomial distribution. The Beta distribution is often used to model the probability of success in a binomial experiment.

How is the Beta distribution different from the normal distribution?

The Beta distribution is different from the normal distribution in several ways. Firstly, the Beta distribution is a continuous distribution while the normal distribution is a continuous distribution. Additionally, the Beta distribution is bounded between 0 and 1, while the normal distribution is unbounded. The shape of the Beta distribution is also different, with a more skewed and asymmetric shape compared to the symmetrical shape of the normal distribution.

What are some common applications of the Beta distribution?

The Beta distribution has many practical applications in various fields, including statistics, economics, and engineering. Some common applications include modeling proportions in surveys or experiments, estimating probabilities in Bayesian analysis, and modeling survival rates in medical research.

How do you calculate the mean and variance of a Beta distribution?

The mean and variance of a Beta distribution can be calculated using the formula:

Mean = α/(α + β)

Variance = (αβ)/[(α + β)^2(α + β + 1)]

Where α and β are the parameters of the Beta distribution. Alternatively, the mean and variance can also be calculated using statistical software or online calculators.

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