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ERFC.PRECISE function
::: warning Note: This draft page is under construction 🚧 :::
Overview
ERFC.PRECISE (ERror Function Complementary) is a function of the Engineering category that calculates a value for the complementary error function, defined by \text{erfc}(x) = 1 - \text{erf}(x). Also known as the complementary Gauss error function, the complementary error function represents the probability of a random variable falling outside a certain range, given that it follows a specified normal distribution.
ERFC.PRECISE is provided for compatibility with other spreadsheets. For all real values of x, \text{ERFC.PRECISE}(x)=\text{ERFC}(x).
Usage
Syntax
ERFC.PRECISE(X) => erfc.precise
Argument descriptions
- X (number, required). The lower integration limit to be used to calculate the complementary error function. ERFC.PRECISE integrates over the range [X,
\infty).
Additional guidance
None.
Returned value
ERFC.PRECISE returns a number that is the complementary error function probability for the specified argument. The returned value lies in range [0, 2].
Error conditions
- In common with many other IronCalc functions, ERFC.PRECISE propagates errors that are found in its argument.
- If no argument, or more than one argument, is supplied, then ERFC.PRECISE returns the
#ERROR!error. - If the value of any argument is not (or cannot be converted to) a number, then ERFC.PRECISE returns the
#VALUE!error. - For some argument values, ERFC.PRECISE may return the
#DIV/0!error.
Details
- The complementary error function arises in many scientific, engineering, and mathematical fields and is commonly defined by the following equation (applicable for any real number
x):
\text{erfc}(x) = \frac{2}{\sqrt{\pi} }\: \int_{x}^{\infty} e^{-t^2}\:dt
- The figure below illustrates the output of the ERFC.PRECISE function for values of
xin the range -3 to +3.
-
This figure illustrates some of the key characteristics of the complementary error function:
\text{erfc}(0) = 1\text{erfc}(-x) = 2-\text{erfc}(x)- As
x \rightarrow \infty,\text{erfc}(x) \rightarrow 0 - As
x \rightarrow -\infty,\text{erfc}(x) \rightarrow 2
-
The complementary error function is a transcendental, non-algebraic mathematical function. IronCalc implements the ERFC.PRECISE function by numerical approximation using a power series.
Examples
See some examples in IronCalc.
Links
- See also IronCalc's ERF, ERFC and ERF.PRECISE functions.
- Visit Microsoft Excel's ERFC.PRECISE function page.
- Both Google Sheets and LibreOffice Calc provide versions of the ERFC.PRECISE function.