Documentation/Calc Functions/EXPON.DIST

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    Function name:

    EXPON.DIST

    Category:

    Statistical Analysis

    Summary:

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

    Exponential distributions are a family of continuous probability distributions that are defined for non-negative real numbers. Each distribution is characterised by a positive rate parameter, usually represented by the Greek letter λ.

    Syntax:

    EXPON.DIST(Number; Lambda; C)

    Returns:

    Returns a non-negative real number, which is the exponential distribution value for the given arguments. For the probability density function, the value returned lies in the range [0, λ]. 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 exponential distribution is to be evaluated.

    Lambda is a positive real number, or a reference to a cell containing that number, which is the rate parameter of the exponential 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, Lambda, or C is non-numeric, then EXPON.DIST reports a #VALUE! error.
    • If Number is less than 0.0, then EXPON.DIST returns the value 0.
    • If Lambda is less than or equal to 0.0, then EXPON.DIST reports an invalid argument error (Err:502).

    Additional details:

    • Calc's EXPONDIST and EXPON.DIST functions perform the same calculations. The requirements for EXPONDIST are specified in ODF 1.2; EXPON.DIST is provided for interoperability with Microsoft Excel.
    • The formula for EXPON.DIST when C is set to 0 or FALSE (probability density function) is:
    [math]\displaystyle{ \text{EXPON.DIST}(x;\:\lambda;\:FALSE)~=~\lambda e^{-\lambda x} }[/math]
    where x is greater than or equal to 0.0.
    • The formula for EXPON.DIST when C is set to any value other than 0 and FALSE (cumulative density function) is:
    [math]\displaystyle{ \text{EXPON.DIST}(x;\:\lambda;\:TRUE)~=~1\:-\: e^{-\lambda x} }[/math]
    where x is greater than or equal to 0.0.
    • For valid values of the Lambda argument, EXPON.DIST returns 0 for negative values of the Number argument.
    • For more information on the exponential distribution, visit Wikipedia's Exponential distribution page.

    Examples:

    Formula Description Returns
    =EXPON.DIST(A1; A2; A3) where cells A1:A3 contain the values 0, 7.89, and FALSE respectively. Here the function calculates a value of the probability density function. Notice that with the Number argument set to 0, the probability density is equal to λ. The formula =EXPONDIST(A1; A2; A3) returns the same value. 7.89
    =EXPON.DIST(-3; 0.5; 0) Here the function calculates a value of the probability density function. However, EXPON.DIST returns 0 for any negative Number argument. 0
    =EXPON.DIST(10; 0.5; 0) Here the function calculates a value of the probability density function for a larger value of the Number argument. It is a feature of exponential distributions that small values have relatively high probabilities, which reduce as data values increase. 0.00336897349954273
    =EXPON.DIST(0; 2; TRUE) Here the function calculates a value of the cumulative distribution function. Notice that with the Number argument set to 0, the cumulative probability is always equal to 0. The formula =EXPONDIST(0; 2; TRUE) returns the same value. 0
    =EXPON.DIST(10; 2; TRUE) Here the function calculates a value of the cumulative distribution function. The cumulative probability increase towards 1 as the value of the Number argument increases. 0.999999997938846

    Related LibreOffice functions:

    EXPONDIST

    ODF standard:

    None

    Related (or similar) Excel functions:

    EXPON.DIST