## How to use the BETA.DIST function

**What is the BETA.DIST function?**

The BETA.DIST function calculates the beta distribution. This function was introduced in Excel 2010.

**What is the beta distribution?**

The beta distribution is a continuous probability distribution defined over the interval [0, 1] and parameterized by two positive shape parameters, alpha (α) and beta (β).

**What is a continuous probability distribution?**

A continuous probability distribution is a function defined over a range of continuous values that provides the probability of a random variable falling between any two points, having a density described by an equation rather than discrete probabilities.

### BETA.DIST function Syntax

BETA.DIST(*x,alpha,beta,cumulative,[A],[B]*)

### BETA.DIST function Arguments

x |
Required. |

alpha |
Required. A parameter which determines the shape of the distribution. |

beta |
Required. A parameter which determines the shape of the distribution. |

cumulative |
Required. A boolean value that determines the form of the function. TRUE - Cumulative beta probability distribution function FALSE - Beta probability density function |

[A] |
Optional. Lower bound, default value 0 (zero). |

[B] |
Optional. Upper bound, default value 1. |

**What is a cumulative beta probability distribution?**

The cumulative beta distribution function gives the probability that a beta-distributed random variable with parameters α and β will be less than or equal to a given value x, providing the accumulated area under the probability density curve from 0 to x.

**What is a beta probability density distribution?**

A beta probability density distribution is a function whose shape over [0,1] depends on parameters α and β that gives the relative likelihood of a beta-distributed random variable occurring at different points, whose total area under the curve integrates to 1.

**When to use the beta distribution?**

The beta distribution is used to model random variables limited to intervals of 0 to 1, such as binomial success probabilities, percentage or fraction outcomes, and measurements constrained between limits, making it useful in Bayesian statistics, experimental design, weather forecasting, and other applications.

**What are continuous values?**

Continuous values are numbers that can take on any quantity within a range and can have infinitely many possibilities, unlike discrete values which have distinct separated values; continuous values can use intervals and ranges to describe events rather than fixed outcomes.

**What are discrete probabilities?**

Discrete probabilities are individual separated probabilities assigned to each of a countable number of possible outcomes that sum to 1, like rolling a die where each number has its own exact probability, as opposed to continuous distributions.

**What are binomial success probabilities?**

Binomial success probabilities describe the chance of a certain number of “successes” occurring in a fixed number of independent binary trial events modeled by the binomial distribution, like the probability of getting 3 heads in 10 coin flips.

**What is Bayesian statistics?**

Bayesian statistics is an approach to statistics using Bayes' theorem where prior beliefs about probabilities are updated as new evidence is acquired to determine conditional probabilities and update understanding of likelihood.

### BETA.DIST function example

Formula in cell C10:

### BETA.DIST function not working

The BETADIST function returns

- #VALUE! error value if any argument is non-numeric.
- #NUM! error value if:
- alpha <= 0
- beta <= 0
- x < A
- x >B
- A = B

### How is the BETA.DIST function calculated?

The general equation to calculate the beta distribution:

Useful resources

### Functions in 'Statistical' category

The BETA.DIST function function is one of many functions in the 'Statistical' category.

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