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Statistics.Math | Portability | portable | Stability | experimental | Maintainer | bos@serpentine.com |
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Description |
Mathematical functions for statistics.
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Synopsis |
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Functions
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:: Double | Parameter of each function.
| -> Vector Double | Coefficients of each polynomial
term, in increasing order.
| -> Double | | Evaluate a series of Chebyshev polynomials. Uses Clenshaw's
algorithm.
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The binomial coefficient.
7 `choose` 3 == 35
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Factorial functions
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Compute the factorial function n!. Returns ∞ if the
input is above 170 (above which the result cannot be represented by
a 64-bit Double).
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Compute the natural logarithm of the factorial function. Gives
16 decimal digits of precision.
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Gamma functions
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:: Double | s
| -> Double | x
| -> Double | | Compute the incomplete gamma integral function γ(s,x).
Uses Algorithm AS 239 by Shea.
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Compute the logarithm of the gamma function Γ(x). Uses
Algorithm AS 245 by Macleod.
Gives an accuracy of 10–12 significant decimal digits, except
for small regions around x = 1 and x = 2, where the function
goes to zero. For greater accuracy, use logGammaL.
Returns ∞ if the input is outside of the range (0 < x
≤ 1e305).
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Compute the logarithm of the gamma function, Γ(x). Uses a
Lanczos approximation.
This function is slower than logGamma, but gives 14 or more
significant decimal digits of accuracy, except around x = 1 and
x = 2, where the function goes to zero.
Returns ∞ if the input is outside of the range (0 < x
≤ 1e305).
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References
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- Clenshaw, C.W. (1962) Chebyshev series for mathematical
functions. National Physical Laboratory Mathematical Tables 5,
Her Majesty's Stationery Office, London.
- Lanczos, C. (1964) A precision approximation of the gamma
function. SIAM Journal on Numerical Analysis B
1:86–96. http://www.jstor.org/stable/2949767
- Macleod, A.J. (1989) Algorithm AS 245: A robust and reliable
algorithm for the logarithm of the gamma function.
Journal of the Royal Statistical Society, Series C (Applied Statistics)
38(2):397–402. http://www.jstor.org/stable/2348078
- Shea, B. (1988) Algorithm AS 239: Chi-squared and incomplete
gamma integral. Applied Statistics
37(3):466–473. http://www.jstor.org/stable/2347328
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