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Beta inv

BETAINV Function

The BETAINV function in Excel returns the inverse of the beta cumulative probability density function for a specified probability. In simpler terms, it computes the value x such that BETADIST(x, alpha, beta, lower_bound, upper_bound) equals the given probability.

This function is useful in statistical and probability analyses, especially when modeling data that follows a beta distribution.

Key Features of BETAINV:

  • Requires input of probability for which you want to find the corresponding value.
  • Allows flexibility in defining the boundaries (lower_bound and upper_bound) of the beta distribution.

Syntax:

BETAINV(probability, alpha, beta, [lower_bound], [upper_bound])
  • probability: The probability corresponding to the beta distribution. Must be between 0 and 1.
  • alpha: A positive parameter of the distribution that shapes the curve.
  • beta: A positive parameter of the distribution that shapes the curve.
  • [lower_bound] (optional): The minimum value of the interval of x. Defaults to 0 if omitted.
  • [upper_bound] (optional): The maximum value of the interval of x. Defaults to 1 if omitted.

Examples:

  1. =BETAINV(0.5, 2, 5)
    Calculates the value of x for the beta distribution with alpha = 2 and beta = 5, assuming the interval [0, 1] by default.
    Result: 0.392857.

  2. =BETAINV(0.8, 3, 4, 0, 10)
    Computes the value of x for the beta distribution with alpha = 3, beta = 4, and interval [0, 10].
    Result: 6.532.

  3. =BETAINV(0.25, 1, 1, -5, 5)
    Calculates the value of x for a uniform beta distribution (alpha = beta = 1) with interval [-5, 5].
    Result: -2.5.

Notes:

  • If any of the arguments alpha ≤ 0, beta ≤ 0, or probability is not between 0 and 1, the function returns an error (#NUM! or #VALUE!).
  • The function is closely related to the BETADIST function but works inversely.
  • When lower_bound and upper_bound are omitted, the beta distribution is applied to the standard range [0, 1].

Tip: Use BETAINV when performing reverse beta distribution calculations, particularly for solving statistical problems involving probability thresholds.