Class C8a: Error functions, their inverses, integrals, including the normal distribution function
General Information
- Parent Class
- C8
- Top of Tree
- GAMS
- Keywords
- Complementary error, Complementary error function, Erf, Erfc, Error, Error function, Error integrals, Inverse error, Inverse error function, Mathematical Functions, Normal distribution, Normal distribution function
Modules
Package CEPHES (Downloadable)
- CPROB
- C routines for evaluation of probability distribution functions and their complements, inverses, and related functions. Among the distributions included are binomial, negative binomial, Beta, Chi-square, F, Gamma, normal, Poisson, and Student''s t. .
- LDOUBLE
- C routines for long double precision evaluation of mathematical functions, including Bessel, beta, exponentials, gamma, incomplete gamma, hyperbolics, Jacobian elliptic, log, and trig. Also elliptic integrals. Also binomial, Chi square, F, gamma, normal, Poisson and Student''s t distributions. Test programs and makefiles included.
Package CMLIB (Downloadable; Installed on ITL, ARNO)
- DERF
- Double precision error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- DERFC
- Double precision complementary error function, = (2 / square root of pi) * the integral from x to infinity of exp(-t**2)dt.
- ERF
- Error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- ERFC
- Complementary error function, = (2 / square root of pi) * the integral from x to infinity of exp(-t**2)dt.
Package FDLIBM (Downloadable)
- ERF
- Erf(x) and Erfc(x). A portable C implementation for machines that support IEEE 754 floating point arithmetic or other standards such as SVID, X/OPEN, and POSIX/ANSI.
Package FN (Downloadable)
- DERF
- Double precision error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- DERFC
- Double precision complementary error function, = (2 / square root of pi) * the integral from x to infinity of exp(-t**2)dt.
- ERF
- Error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- ERFC
- Complementary error function, = (2 / square root of pi) * the integral from x to infinity of exp(-t**2)dt.
Package IMSLM (Installed on ITL)
- CERFE
- Complex scaled complementary error function.
- DERF
- Double precision error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- DERFC
- Double precision complementary error function, = (2 / square root of pi) * the integral from x to infinity of exp(-t**2)dt.
- DERFCE
- Exponentially scaled complementary error function.
- DERFCI
- Inverse complementary error function.
- DERFI
- Inverse error function.
- ERF
- Error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- ERFC
- Complementary error function, = (2 / square root of pi) * the integral from x to infinity of exp(-t**2)dt.
- ERFCE
- Exponentially scaled complementary error function.
- ERFCI
- Inverse complementary error function.
- ERFI
- Inverse error function.
Package IMSLS (Installed on ITL)
- ANORDF
- Normal (Gaussian) distribution function.
- ANORIN
- Inverse of the normal (Gaussian) distribution function.
- DNORDF
- Normal (Gaussian) distribution function.
- DNORIN
- Inverse of the normal (Gaussian) distribution function.
Package NAG
- S15ABF
- Cumulative Normal distribution function P(x)
- S15ACF
- Complement of cumulative Normal distribution function Q(x)
- S15ADF
- Complement of error function erfc(x)
- S15AEF
- Error function erf(x)
- S15AGF
- Scaled complement of error function, erfcx(x)
- S15DDF
- Scaled complex complement of error function, exp(-z2)erfc(-iz)
- s15abc
- Cumulative Normal distribution function P(x)
- s15acc
- Complement of cumulative Normal distribution function Q(x)
- s15adc
- Complement of error function erfc(x)
- s15aec
- Error function erf(x)
- s15ddc
- Scaled complex complement of error function, exp(-z2)erfc(-iz)
Package NMS (Installed on ITL)
- DERF
- Double precision error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- DERFC
- Complementary error function.
- ERF
- Error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t**2)dt.
- ERFC
- Double precison complementary error function, = (2 / square root of pi) * the integral from x to infinity of exp(-t**2)dt.
Package SLATEC (Downloadable; Installed on ITL, ARNO)
- DERF
- Compute the error function.
- DERFC
- Compute the complementary error function.
- ERF
- Compute the error function.
- ERFC
- Compute the complementary error function.
Package SPECFN (Installed on ITL)
- ERRINT
- Error function and complementary error function.
Package SPECFUN (Downloadable)
- ERF
- Evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) for a real argument x. Uses rational functions that theoretically approximate erf(x) and erfc(x) to at least 18 significant decimal digits.
Package TOMS (Downloadable)
- 521
- INERFC: a Fortran subroutine for evaluating repeated integrals of the coerror function. (See W. Gautschi, ACM TOMS 3 (1977) pp. 301-302.).
- 680
- A Fortran subroutine for evaluating the complex error function. (See G.P.M. Poppe and C.M.J. Wijers, ACM TOMS 16 (1990) pp. 47.).