BETA.INV function

The BETA.INV function in Excel returns the inverse of the cumulative beta probability density function (also known as the quantile function) for a specified probability. This is useful when you have a probability and want to determine the corresponding value of the beta distribution.

Syntax

=BETA.INV(probability, alpha, beta, [A], [B])

Arguments

• probability: The probability at which to evaluate the inverse beta distribution. It must be a value between 0 and 1.
• alpha: A parameter of the distribution, often referred to as the shape parameter.
• beta: Another parameter of the distribution, also referred to as a shape parameter.
• A (optional): The lower bound of the interval of x. If omitted, it defaults to 0.
• B (optional): The upper bound of the interval of x. If omitted, it defaults to 1.

Return Value

• BETA.INV returns the value x such that the cumulative beta distribution function (BETA.DIST) evaluated at x equals the given probability.

Description

• The BETA.INV function is essentially the inverse of the BETA.DIST function when BETA.DIST is used in cumulative mode.
• It calculates the value x associated with a cumulative probability, given the shape parameters alpha and beta.
• This function can be used in scenarios such as quality control, where you may know the likelihood of a particular event but need to know the value at which that event occurs.

Example Usage

Example 1: Basic Inverse Beta Distribution

To find the value of x corresponding to a cumulative probability of 0.8, with alpha = 2 and beta = 5 on the interval [0, 1]:

=BETA.INV(0.8, 2, 5)

Result:

This returns the x value that corresponds to an 80% cumulative probability in the beta distribution.

Example 2: Custom Interval

To find the value of x for a cumulative probability of 0.6, with alpha = 3, beta = 4, and the interval [1, 10]:

=BETA.INV(0.6, 3, 4, 1, 10)

Result:

This will return the value of x within the interval [1, 10] corresponding to a 60% cumulative probability.

Applications

• The BETA.INV function is useful in scenarios where the beta distribution is applied, such as decision analysis, Bayesian statistics, and project management (PERT charts).
• It can also be used for estimating percentiles of bounded data, for example, modeling the time to complete a task when times are not fixed but vary.

Notes

• probability must be between 0 and 1, inclusive. If the probability is outside this range, the function returns an error.
• alpha and beta must both be positive, or the function returns an error.
• If A and B are omitted, the function assumes a standard beta distribution over the interval [0, 1].

Error Handling

• If alpha ≤ 0 or beta ≤ 0, BETA.INV returns the #NUM! error.
• If probability is outside the range 0 to 1, it returns the #NUM! error.
• If non-numeric arguments are provided, BETA.INV returns the #VALUE! error.