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#Statistical

GAMMALN.PRECISE

Excel Functions

To calculate the natural logarithm of the gamma function.

Syntax

EXCEL 
=GAMMALN.PRECISE(x)

Arguments

Parameter Description
x A positive real number for which you want to calculate the natural logarithm of the gamma function.

Return Value

A number representing the natural logarithm of the gamma function.

Details

The GAMMALN.PRECISE function returns the natural logarithm of the gamma function, ln(Γ(n)), for a given number. This is useful in statistical calculations, such as those involving probability distributions, where the gamma function appears in the denominator and direct computation could result in very large or very small numbers. For positive integers n, GAMMALN.PRECISE(n) is equivalent to LN((n-1)!). For example, the following formula calculates the natural logarithm of the gamma value for 5: The GAMMALN.PRECISE function takes a single argument as input like this: The argument x is the value for which you want to calculate the natural logarithm of the gamma function. Here are some basic examples showing both integer and non-integer inputs: In general, the GAMMALN.PRECISE function is equiv

Examples

Example 1

For positive integers n, GAMMALN.PRECISE(n) is equivalent to LN((n-1)!). For example, the following formula calculates the natural logarithm of the ga

EXCEL 
=GAMMALN.PRECISE(5) // returns 3.17805383
Example #1 - Basic calculations

The GAMMALN.PRECISE function takes a single argument as input like this:

EXCEL 
=GAMMALN.PRECISE(x)
Example #1 - Basic calculations

The argument x is the value for which you want to calculate the natural logarithm of the gamma function. Here are some basic examples showing both int

EXCEL 
=GAMMALN.PRECISE(0.5) // returns 0.57236494...
=GAMMALN.PRECISE(2.0) // returns 0
=GAMMALN.PRECISE(2.5) // returns 0.28468287...
=GAMMALN.PRECISE(4.0) // returns 1.79175947...
Example #2 - Relationship to gamma and factorials

In general, the GAMMALN.PRECISE function is equivalent to the natural logarithm of the gamma function:

EXCEL 
=GAMMALN.PRECISE(x) // returns LN(GAMMA(x))
Example #2 - Relationship to gamma and factorials

This relationship makes the GAMMALN.PRECISE function useful for calculations involving large factorials, as it avoids direct computation of large numb

EXCEL 
=GAMMA(172) // returns #NUM! error
Example #3 - Error conditions

The GAMMALN.PRECISE function returns #NUM! for zero and negative numbers, and #VALUE! for non-numeric inputs.

EXCEL 
=GAMMALN.PRECISE(0) // returns #NUM! error
=GAMMALN.PRECISE(-1) // returns #NUM! error
=GAMMALN.PRECISE(-2.5) // returns #NUM! error
=GAMMALN.PRECISE("text") // returns #VALUE! error

See Also

GAMMA LN GAMMALN