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Compute the log of the gamma function for a given alpha. Comments from Z. Yang: Returns ln(gamma(alpha)) for alpha>0, accurate to 10 decimal places. Stirling's formula is used for the central polynomial part of the procedure. Pike MC & Hill ID (1966) Algorithm 291: Logarithm of the gamma function. Communications of the Association for Computing Machinery, 9:684 |
Compute an incomplete gamma ratio. Comments from Z. Yang: Returns the incomplete gamma ratio I(x,alpha) where x is the upper limit of the integration and alpha is the shape parameter. returns (-1) if in error ln_gamma_alpha = ln(Gamma(alpha)), is almost redundant. (1) series expansion if alpha>x or x<=1 (2) continued fraction otherwise RATNEST FORTRAN by Bhattacharjee GP (1970) The incomplete gamma integral. Applied Statistics, 19: 285-287 (AS32) |
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