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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)

Package NAGC

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.).
Comments? gams@nist.gov