1. What is Standard Beta Distribution?

The standard beta distribution is a continuous probability distribution defined on the interval [0, 1] that is parameterized by two positive shape parameters. The standard beta value represents a normalized value between the minimum and maximum of a range.

2. How Does the Calculator Work?

The calculator uses the standard beta formula:

Where:

• \( x \) — The value to normalize
• \( min \) — Minimum value of the range
• \( max \) — Maximum value of the range

Explanation: The formula normalizes any value within a given range to a value between 0 and 1, where 0 represents the minimum and 1 represents the maximum.

3. Applications of Beta Distribution

Details: The beta distribution is commonly used in Bayesian analysis, project planning, proportion estimation, and other applications where probabilities are modeled.

4. Using the Calculator

Tips: Enter your value (x) and the minimum and maximum of your range. The value must be between the minimum and maximum.

5. Frequently Asked Questions (FAQ)

Q1: What does a beta value of 0.5 mean?
A: A beta of 0.5 means the value is exactly halfway between your minimum and maximum.

Q2: What are valid beta values?
A: Standard beta values range from 0 to 1, where 0 = minimum and 1 = maximum of your range.

Q3: When should I use beta distribution?
A: Use when you need to model probabilities or proportions that are bounded between two values.

Q4: What's the difference between beta and normalized value?
A: They are essentially the same - both represent a value's position within a range scaled to [0,1].

Q5: Can I use this for values outside my min/max range?
A: No, the standard beta formula only works for values between your specified minimum and maximum.