XIV-2. RESULTS OF NEW TESTS ON STATISTICAL DISTRIBUTIONS …

Short Description
Stirling’s Formula (Abramowitz (1963) equations 6.1.40 and 6.1.4) or the … The Excel function as shown in Help, is a two- parameter (alpha and beta) gamma …

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Content
XIV-2. RESULTS OF NEW TESTS ON STATISTICAL DISTRIBUTIONS, CONTINUOUS FUNCTIONS
Section
Outline
Topic/Function
Page Start
Page End
Tables
Figures
14-2
2
Continuous
2
2
14-2
2.1
Component Functions
2
2
14-2
2.1.1
GAMMALN
2
3
14-2
2.2
Density
3
3
14-2
2.2.1
EXPONDIST
3
3
14-2
2.2.2
GAMMADIST
4
6
18, 19
14-2
2.2.3
NORMDIST
6
6
14-2
2.2.4
WEIBULL
6
6
12. CONTINUOUS STATISTICAL DISTRIBUTIONS
2.1 COMPONENT FUNCTIONS
2.1.1 LOG GAMMA DISTRIBUTION: GAMMALN FUNCTION
The function is =GAMMALN(x)
This function provides values of the natural log of the gamma function. The function has never changed from Excel 97.
The gamma function is a restatement of factorials, and allows a definition of factorials for non-integer real numbers. The gamma function is defined for both positive and negative arguments (see Abramowitz (1963), page 255). The log of the gamma function using Stirling’s Formula (Abramowitz (1963) equations 6.1.40 and 6.1.4) or the power series (eq. 6.1.33) cannot be used to obtain log gamma values for negative arguments. When the gamma value for negative arguments is positive (see Abramowitz (1963), figure 6.1), the log gamma function would exist. In this case it is best to use the gamma function recurrence equations (Abramowitz (1963) equations 6.1.5 or 6.1.6) to obtain existent values for negative arguments.
Smith (2002) did not provide a public log gamma function. His private functions and subs related to the log gamma function are not sufficiently clear so as to build a correct full range accurate log gamma function. According…