Documentation/Calc Functions/WEIBULL

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    Function name:

    WEIBULL

    Category:

    Statistical Analysis

    Summary:

    Calculates Weibull distribution values from either the probability density function or the cumulative distribution function.

    The Weibull distribution is a two-parameter family of continuous probability distributions. Each Weibull distribution is characterized by two positive real numbers, which are denoted as alpha (α) and beta (β) in Calc but may have different designations in other sources. The value of α controls the shape of the distribution and the value of β controls its scale.

    Syntax:

    WEIBULL(Number; Alpha; Beta; C)

    Returns:

    Returns a non-negative real number, which is the Weibull distribution value for the given arguments. For the probability density function, the value returned lies in the range [0, +∞). For the cumulative distribution function, the value returned lies in the range [0, 1].

    Arguments:

    Number is a non-negative real number, or a reference to a cell containing that number, which is the value at which the Weibull distribution is to be evaluated.

    Alpha is a positive real number, or a reference to a cell containing that number, which is the value of the shape parameter of the Weibull distribution.

    Beta is a positive real number, or a reference to a cell containing that number, which is the value of the scale parameter of the Weibull distribution.

    C is a logical value, or a reference to a cell containing that value, that determines whether the required probability is taken from the probability density function or the cumulative distribution function. If C is set to 0 or FALSE, a value from the probability density function is calculated. For any other values of C, a value from the cumulative distribution function is calculated.

    • If any of Number, Alpha, or Beta is non-numeric, then WEIBULL reports a #VALUE! error.
    • If either Alpha or Beta is less than or equal to 0.0, then WEIBULL reports an invalid argument error (Err:502).
    • If Number is less than 0.0, then WEIBULL reports an invalid argument error (Err:502).

    Additional details:

    • Calc's WEIBULL and WEIBULL.DIST functions perform identical calculations. The requirements for WEIBULL are specified in ODF 1.2; WEIBULL.DIST is provided for interoperability with Microsoft Excel.
    • The formula for the probability density function of the Weibull distribution can be written as:
    [math]\displaystyle{ PDF_{Weibull}(x;\:\alpha;\:\beta)~=~\frac{\alpha}{\beta}\left(\frac{x}{\beta}\right)^{\alpha-1}~\text{EXP}\left(-\left( \frac{x}{\beta} \right)^\alpha \right) }[/math]
    where x ≥ 0, α > 0, and β > 0.
    • The formula for the cumulative distribution function of the Weibull distribution can be written as:
    [math]\displaystyle{ CDF_{Weibull}(x;\:\alpha;\:\beta)~=~1-\text{EXP}\left(-\left( \frac{x}{\beta} \right)^\alpha \right) }[/math]
    where x ≥ 0, α > 0, and β > 0.
    • The following figure shows four sample probability density function plots for the Weibull distribution.
    Weibull distribution PDF plots.png
    • The following figure shows four sample cumulative distribution function plots for the Weibull distribution.
    Weibull distribution CDF plots.png

    Examples:

    Formula Description Returns
    =WEIBULL(A1; A2; A3; A4) where cells A1:A4 contain the values 5.8, 2.2, 3.7, and 0 respectively. Here the function calculates the value of the probability density function for the given inputs. 0.0693305576870189
    =WEIBULL(5.8; 2.2; 3.7; 1) Here the function calculates the value of the cumulative distribution function for the given inputs. 0.932012008181695
    =WEIBULL(1; 5; 1; 0) Here the function calculates the value of the probability density function for the given inputs, returning a probability density that is greater than 1. 1.83939720585721

    Related LibreOffice functions:

    EXP

    WEIBULL.DIST

    ODF standard:

    Section 6.18.86, part 2

    Related (or similar) Excel functions:

    WEIBULL