Documentation/Calc Functions/NORM.DIST

    From The Document Foundation Wiki

    Function name:

    NORM.DIST

    Category:

    Statistical Analysis

    Summary:

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

    The normal distribution is also known as the Gaussian distribution. It is a family of continuous probability distributions used in many fields to represent independent, randomly generated variables. Each normal distribution has a curve with the same general bell shape that is symmetric about the mean (often denoted by the lowercase Greek letter mu (μ)), with a spread defined by the standard deviation (often denoted by the lowercase Greek letter sigma (σ)).

    Syntax:

    NORM.DIST(Number; Mean; STDEV; C)

    Returns:

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

    Mean is a real number, or a reference to a cell containing that number, which is the mean of the normal distribution.

    STDEV is a positive real number, or a reference to a cell containing that number, which is the standard deviation of the normal 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, Mean, or STDEV is non-numeric, then NORM.DIST reports a #VALUE! error.
    • If STDEV is less than or equal to 0.0, then NORM.DIST reports an invalid argument error (Err:502).

    Additional details:

    • Calc's NORMDIST and NORM.DIST functions perform similar calculations. However, there are minor differences between the two functions with respect to their arguments – for NORMDIST the C argument may be omitted. The requirements for NORMDIST are specified in ODF 1.2; NORM.DIST is provided for interoperability with Microsoft Excel.
    • The normal distribution with a mean of 0 and standard deviation of 1 is known as the standard normal distribution. This gives rise to the following relationships between relevant Calc functions:
    [math]\displaystyle{ \text{NORM.DIST}(x;\:0;\:1;\:c)\:=\:\text{NORM.S.DIST}(x;\:c)\:=\:\text{NORMSDIST}(x) }[/math]
    and
    [math]\displaystyle{ \text{NORM.DIST}(x;\:0;\:1;\:0)\:=\:\text{NORM.S.DIST}(x;\:0)\:=\:\text{PHI}(x) }[/math]
    • The formula for the probability density function of the normal distribution is:
    [math]\displaystyle{ PDF_{normal}(x; \mu; \sigma)~=~\frac{1}{\sigma\sqrt{2\pi}}~\text{EXP} \left(-\frac{1}{2}\left( \frac{x-\mu}{\sigma} \right)^2 \right) }[/math]
    • The formula for the cumulative distribution function of the normal distribution is:
    [math]\displaystyle{ CDF_{normal}(x; \mu; \sigma)~=~\int_{-\infty }^{x}\frac{1}{\sigma\sqrt{2\pi}}~\text{EXP} \left(-\frac{1}{2}\left( \frac{t-\mu}{\sigma} \right)^2 \right) \:dt }[/math]
    • The following figure shows probability density function plots for five sample normal distributions.
    Normal distribution PDF plots.png
    • The following figure shows cumulative distribution function plots for five sample normal distributions.
    Normal distribution CDF plots.png
    • The name space for NORM.DIST is COM.MICROSOFT.NORM.DIST.
    • For more information on the normal distribution, visit Wikipedia's Normal distribution page.

    Examples:

    Formula Description Returns
    =NORM.DIST(A1; A2; A3; A4) where cells A1:A4 contain the numbers 7.14, 1.5, 3.2, and 1 respectively. Here the function calculates a value from the cumulative distribution function of the normal distribution for the given argument values. 0.961007571808867
    =NORM.DIST(7.14; 1.5; 3.2; FALSE()) Here the function calculates a value from the probability density function of the normal distribution for the given argument values. 0.026376219058927
    =NORM.DIST(2; 0; 0.5; 0) Here the function calculates a value from the probability density function of the normal distribution for the given argument values. Note that the normal distribution is symmetric and so the formula =NORM.DIST(-2; 0; 0.5; 0) returns the same value. 0.000267660451529771
    =NORM.DIST(1; 0; 1.2; 1) Here the function calculates a value from the cumulative distribution function of the normal distribution for the given argument values. Note that the normal distribution is symmetric and so the formula =1-NORM.DIST(-1; 0; 1.2; 1) returns the same value. 0.797671619036357
    =NORM.DIST(0.5; 0; 1; 0) Here the function calculates a value from the probability density function of the standard normal distribution. Note that the formulas =NORM.S.DIST(0.5; 0) and =PHI(0.5) return the same value. 0.3520653267643

    Related LibreOffice functions:

    NORM.INV

    NORM.S.DIST

    NORM.S.INV

    NORMDIST

    NORMINV

    NORMSDIST

    NORMSINV

    PHI

    ODF standard:

    None

    Related (or similar) Excel functions:

    NORM.DIST