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Beta inv

BETA.INV Function

The BETA.INV function in Excel calculates the inverse of the cumulative beta probability density function for a given probability. In other words, it determines the value x such that the cumulative beta distribution function with specified parameters equals the given probability.

This function is primarily used in statistics and probability calculations, especially when working with data modeled by the beta distribution.

Key Features of BETA.INV:

  • Computes the value associated with a given cumulative probability for the beta distribution.
  • Supports specifying bounds of the interval where the beta distribution applies (lower_bound and upper_bound).

Syntax:

BETA.INV(probability, alpha, beta, [lower_bound], [upper_bound])
  • probability: A numeric value between 0 and 1 that specifies the cumulative probability.
  • alpha: Positive shape parameter of the beta distribution that determines its skewness.
  • beta: Positive shape parameter of the beta distribution that determines its skewness.
  • [lower_bound] (optional): The minimum value of the x range. Defaults to 0 if omitted.
  • [upper_bound] (optional): The maximum value of the x range. Defaults to 1 if omitted.

Examples:

  1. Basic Calculation
    =BETA.INV(0.6, 2, 5)
    Calculates the inverse beta distribution for the cumulative probability 0.6 with alpha = 2, beta = 5, and the default interval [0, 1].
    Result: 0.428571.

  2. Custom Boundaries
    =BETA.INV(0.75, 3, 4, 0, 10)
    Finds the value of x within the interval [0, 10] for a cumulative probability of 0.75 with alpha = 3 and beta = 4.
    Result: 6.875.

  3. Negative Bounds
    =BETA.INV(0.2, 1, 2, -10, 0)
    Computes the inverse beta distribution for probability 0.2 with alpha = 1, beta = 2, over the interval [-10, 0].
    Result: -8.

Notes:

  • If alpha ≤ 0, beta ≤ 0, or probability is outside the range [0, 1], the function returns an error (#NUM! or #VALUE!).
  • If lower_bound and upper_bound are omitted, the function assumes the default interval of [0, 1].
  • The function is closely related to the BETA.DIST function but applies inversely.

Tip: Use BETA.INV for reverse probability calculations, such as finding the threshold value corresponding to a given cumulative probability in beta-distributed data.