Documentation/Calc Functions/GAMMADIST
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Function name:
GAMMADIST
Category:
Statistical Analysis
Summary:
Calculates gamma distribution values from either the probability density function or the cumulative distribution function.
The gamma distribution is a family of continuous probability distributions that are typically used to model positive variables that have right-skewed distributions. The distribution has two characteristic positive real numbers, usually denoted as alpha (α) and beta (β), that control its shape and rate respectively.
Syntax:
GAMMADIST(Number; Alpha; Beta[; Cumulative])
Returns:
Returns a non-negative real number, which is the gamma 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 gamma 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 gamma distribution.
Beta is a positive real number, or a reference to a cell containing that number, which is the value of the rate parameter of the gamma distribution.
Cumulative 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 Cumulative is set to 0 or FALSE, a value from the probability density function is calculated. For any other values of Cumulative, or if omitted, a value from the cumulative distribution function is calculated.
- If any of Number, Alpha, or Beta is non-numeric, then GAMMADIST reports a #VALUE! error.
- If either Alpha or Beta is less than or equal to 0.0, then GAMMADIST reports an invalid argument error (Err:502).
- If Number is negative and other argument values are valid, then GAMMADIST returns 0.
- Other errors may arise depending on the exact combination of values passed as arguments to GAMMADIST.
Additional details:
- Calc's GAMMADIST and GAMMA.DIST functions perform similar calculations. However, there are minor differences between the two functions with respect to their arguments – for GAMMA.DIST the Cumulative argument cannot be omitted and negative Number values are not accepted. The requirements for GAMMADIST are specified in ODF 1.2; GAMMA.DIST is provided for interoperability with Microsoft Excel.
- The formula for the probability density function of the gamma distribution can be written as:
- [math]\displaystyle{ PDF_{gamma}(x, \alpha, \beta)~=~\frac{1}{\beta^\alpha\:\Gamma(\alpha)}\:x^{\alpha-1}\:e^{-\frac{x}{\beta}} }[/math]
- where x ≥ 0, α > 0, and β > 0.
- The formula for the cumulative distribution function of the gamma distribution can be written as:
- [math]\displaystyle{ CDF_{gamma}(x, \alpha, \beta)~=~\frac{1}{\beta^\alpha\:\Gamma(\alpha)}\int_{0}^{x}\:t^{\alpha-1}\:e^{-\frac{t}{\beta}} \:dt }[/math]
- where x ≥ 0, α > 0, and β > 0.
- The following figure shows four sample probability density function plots for the gamma distribution.
- The following figure shows four sample cumulative distribution function plots for the gamma distribution.
- For more information on the gamma distribution, visit Wikipedia's Gamma distribution page.
Examples:
Formula | Description | Returns |
---|---|---|
=GAMMADIST(A1; A2; A3; A4) where cells A1:A4 contain the numbers 4.7, 3.4, 2.7, and 0 respectively. | Here the function calculates the value of the probability density function for the given inputs. | 0.0824160723859134 |
=GAMMADIST(4.7; 3.4; 2.7; 1) | Here the function calculates the value of the cumulative distribution function for the same input values as in the previous example. The formula =GAMMADIST(4.7; 3.4; 2.7) returns the same result because the omitted Cumulative argument defaults to the value TRUE. |
0.178647117849697 |
=GAMMADIST(0; 2; 4; 0) | Here the function returns 0 for Number equal to 0. | 0 |
=GAMMADIST(-2; 2; 4; 0) | Here the function returns the value 0 for a negative value of Number. Contrast this with the formula =GAMMA.DIST(-2; 2; 4; 0) which returns Err:502. |
0 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
GAMMADIST