Documentation/Calc Functions/LOGINV

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    Function name:

    LOGINV

    Category:

    Statistical Analysis

    Summary:

    Calculates the inverse of a probability value from the cumulative distribution function of a log-normal distribution.

    A random variable [math]\displaystyle{ x }[/math] is log-normally distributed if [math]\displaystyle{ \text{log}(x) }[/math] is normally distributed. The log-normal distribution is a family of continuous probability distributions that are typically used to model positive, right-skewed data. The distribution has two characteristic parameters, usually denoted as mu (μ) and sigma (σ), that control its location and shape respectively. μ represents the mean value of the underlying normal distribution, while σ represents the standard deviation of the underlying normal distribution.

    LOGINV calculates the value [math]\displaystyle{ x }[/math] such that [math]\displaystyle{ \text{LOGNORMDIST}(x;\:\mu;\:\sigma;\:1)\:=\:p }[/math], where the given probability [math]\displaystyle{ p }[/math] lies in the range (0, 1).

    Syntax:

    LOGINV(Number[; Mean[; STDEV]])

    Returns:

    Returns a positive real number, which is the inverse of the given probability value from the cumulative distribution function for the given log-normal distribution.

    Arguments:

    Number is a real number in the range (0, 1), or a reference to a cell containing that number, which is a probability in the cumulative distribution function of the log-normal distribution.

    Mean is a real number, or a reference to a cell containing that number, which is the value of the location parameter (μ) of the log-normal distribution. If omitted, the default value of 0 is utilized.

    STDEV is a positive real number, or a reference to a cell containing that number, which is the value of the shape parameter (σ) of the log-normal distribution. If omitted, the default value of 1 is utilized.

    • If any of Number, Mean, or STDEV is non-numeric, then LOGINV reports a #VALUE! error.
    • If Number is outside the range (0, 1), then LOGINV reports an invalid argument error (Err:502).
    • If STDEV is less than or equal to 0.0, then LOGINV reports an invalid argument error (Err:502).

    Additional details:

    • Calc's LOGINV and LOGNORM.INV functions perform the same calculations. The requirements for LOGINV are specified in ODF 1.2; LOGNORM.INV is provided for interoperability with Microsoft Excel.
    • The following figure shows inverse cumulative distribution function probability plots for four sample log-normal distributions.
    Lognormal distribution inverse CDF probability plots.png

    Examples:

    Formula Description Returns
    =LOGINV(A1; A2; A3) where cells A1:A3 contain the values 0.6, -0.5, and 1.5 respectively. Here the argument values are passed by cell reference. Note that the formula =LOGNORMDIST(LOGINV(A1; A2; A3); A2; A3; 1) returns 0.6, the same as the value in cell A1. 0.886938755985172
    =LOGINV(0.25) Here the Mean and STDEV arguments are omitted and so take their default values of 0 and 1 respectively. Note that the formula =LOGINV(0.25; 0; 1) returns the same value. 0.509416283863278

    Related LibreOffice functions:

    LOGNORM.DIST

    LOGNORM.INV

    LOGNORMDIST

    ODF standard:

    Section 6.18.43, part 2

    Related (or similar) Excel functions:

    LOGINV