- beta
- cdf-standard-normal
- digamma
- erf
- erf-derivative
- erf-diff
- erfc
- euler-mascheroni-constant
- exact-stirling-errors
- gamma
- gamma-derivative
- incomplete-beta
- inv-cdf-standard-normal
- inv-erf
- inv-erfc
- inv-probit
- lanczos-coefficients
- log-beta
- log-gamma
- log-gamma-derivative
- log-sum-exp
- logistic
- logit
- lower-gamma
- multivariate-gamma
- multivariate-log-gamma
- probit
- rational-approximation-coefficients
- regularized-beta
- regularized-gamma-p
- regularized-gamma-q
- trigamma
- upper-gamma
- upper-gamma-derivative-x
provisdom.math.special-functions
betaclj
(beta x y)Returns the beta of x and y:
integral[0, 1] (t ^ (x - 1) × (1 - t) ^ (y - 1) * dt.
Returns the beta of `x` and `y`: integral[0, 1] (t ^ (`x` - 1) × (1 - t) ^ (`y` - 1) * dt.
cdf-standard-normalclj
(cdf-standard-normal x)Returns the standard Normal cdf.
Returns the standard Normal cdf.
erfclj
(erf x)Returns the error function:
2 / (sqrt PI) × integral[0, x] (e ^ - (t ^ 2) × dt).
Returns the error function: 2 / (sqrt PI) × integral[0, `x`] (e ^ - (t ^ 2) × dt).
erf-derivativeclj
(erf-derivative x)Returns the derivative of the error function.
Returns the derivative of the error function.
erfcclj
(erfc x)Returns the complementary error function.
Returns the complementary error function.
exact-stirling-errorsclj
Expansion error for values 0.0 through 15.0 by 0.5.
Expansion error for values 0.0 through 15.0 by 0.5.
gammaclj
(gamma a)Returns the gamma function: integral[0, inf] (t ^ (a- 1) × e ^ -t × dt).
Although gamma is defined for positive a, this function also allows for all
non-roughly-round-non+ a.
Returns the gamma function: integral[0, inf] (t ^ (`a`- 1) × e ^ -t × dt). Although gamma is defined for positive `a`, this function also allows for all non-roughly-round-non+ `a`.
gamma-derivativeclj
(gamma-derivative a)Returns the derivative of the gamma of a. a > -3e8 because it becomes
slow.
Returns the derivative of the gamma of `a`. `a` > -3e8 because it becomes slow.
incomplete-betaclj
(incomplete-beta c x y)Returns the lower beta:
integral[0, c] (t ^ (x - 1) × (1 - t) ^ (y - 1) × dt. If Apache's
solution doesn't converge, then NaN is returned.
Returns the lower beta: integral[0, `c`] (t ^ (`x` - 1) × (1 - t) ^ (`y` - 1) × dt. If Apache's solution doesn't converge, then NaN is returned.
inv-cdf-standard-normalclj
(inv-cdf-standard-normal cumulative-prob)Returns the standard Normal inverse cdf.
Returns the standard Normal inverse cdf.
inv-erfclj
(inv-erf x)Returns the inverse error function.
Returns the inverse error function.
inv-erfcclj
(inv-erfc x)Returns the inverse complementary error function.
Returns the inverse complementary error function.
log-betaclj
(log-beta x y)Returns the log-beta of x and y.
Returns the log-beta of `x` and `y`.
log-gammaclj
(log-gamma a)Returns the log gamma of a.
Returns the log gamma of `a`.
log-gamma-derivativeclj
(log-gamma-derivative a)Returns the derivative of the log gamma of a. a > -3e8 because
it becomes slow. Taken from Apache. Could use a better algorithm.
Returns the derivative of the log gamma of `a`. `a` > -3e8 because it becomes slow. Taken from Apache. Could use a better algorithm.
log-sum-expclj
(log-sum-exp numbers)Special function for taking the log of the sum of the exponent of numbers that are either very large or very small.
Special function for taking the log of the sum of the exponent of numbers that are either very large or very small.
lower-gammaclj
(lower-gamma a x)Returns the lower incomplete gamma function:
integral[0, x] (t ^ (a - 1) × e ^ -t × dt).
Returns the lower incomplete gamma function: integral[0, `x`] (t ^ (`a` - 1) × e ^ -t × dt).
multivariate-gammaclj
(multivariate-gamma a p)Returns the multivariate gamma of a with dimension p.
Returns the multivariate gamma of `a` with dimension `p`.
multivariate-log-gammaclj
(multivariate-log-gamma a p)Returns the multivariate log gamma of a with dimension p.
Returns the multivariate log gamma of `a` with dimension `p`.
regularized-betaclj
(regularized-beta c x y)Returns the regularized beta. Equal to incomplete beta function divided by beta function. If Apache's solution doesn't converge, then NaN is returned.
Returns the regularized beta. Equal to incomplete beta function divided by beta function. If Apache's solution doesn't converge, then NaN is returned.
regularized-gamma-pclj
(regularized-gamma-p a x)Returns the regularized gamma function P(a, x) = 1 - Q(a, x). Equal
to lower-gamma function (a, x) divided by gamma function (a).
Returns the regularized gamma function P(`a`, `x`) = 1 - Q(`a`, `x`). Equal to [[lower-gamma]] function (a, x) divided by [[gamma]] function (`a`).
regularized-gamma-qclj
(regularized-gamma-q a x)Returns the regularized gamma function Q(a, x) = 1 - P(a, x). Equal
to upper-gamma function (a, x) divided by gamma function (a).
Returns the regularized gamma function Q(`a`, `x`) = 1 - P(`a`, `x`). Equal to [[upper-gamma]] function (`a`, `x`) divided by [[gamma]] function (`a`).
trigammaclj
(trigamma a)Returns the trigamma (2nd derivative of log-gamma) of a. Approximated for
a < -1e7 because it becomes slow. Taken from Apache. Could use a better
algorithm.
Returns the trigamma (2nd derivative of log-gamma) of `a`. Approximated for `a` < -1e7 because it becomes slow. Taken from Apache. Could use a better algorithm.
upper-gammaclj
(upper-gamma a x)Returns the upper incomplete gamma function:
integral[x, inf] (t ^ (a - 1) × e ^ -t × dt).
Returns the upper incomplete gamma function: integral[`x`, inf] (t ^ (`a` - 1) × e ^ -t × dt).
upper-gamma-derivative-xclj
(upper-gamma-derivative-x a x)Returns the upper gamma derivative x.
Returns the upper gamma derivative `x`.
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