KSLCore/ksl.utilities.distributions/Gamma/Companion

Companion

object Companion(source)

Properties

CHISQ_CDF_SERIES_MAX_ITERATIONS

const val CHISQ_CDF_SERIES_MAX_ITERATIONS: Int = 500

The maximum number of iterations permitted in the chi-square cdf computation

DEFAULT_MAX_ITERATIONS

const val DEFAULT_MAX_ITERATIONS: Int

The maximum number of terms permitted when summing the incomplete gamma series.

INC_GAMMA_MAX_ITERATIONS

const val INC_GAMMA_MAX_ITERATIONS: Int

The maximum number of iterations permitted for the incomplete gamma function evaluation process.

SMALL_P_ASYMPTOTIC_THRESHOLD

const val SMALL_P_ASYMPTOTIC_THRESHOLD: Double = 1.0E-12

Below this probability, invCDF uses the closed-form lower-tail asymptotic seed instead of AS 91. The asymptotic x ~ scale * (p * shape * Gamma(shape))^(1/shape) has leading-order error O(p^(1/shape)), which is below 1e-3 once p drops below ~1e-12 for typical shape values.

X_BIG

const val X_BIG: Double = 40.0

Functions

digamma

fun digamma(argX: Double): Double

Computes the digamma function Mark Johnson, 2nd September 2007

diGammaFunction

fun diGammaFunction(x: Double): Double

Computes the digamma function using AS 103

gammaFunction

fun gammaFunction(x: Double): Double

Computes the gamma function at x

incompleteGammaFunction

fun incompleteGammaFunction(x: Double, alpha: Double, maxIterations: Int = INC_GAMMA_MAX_ITERATIONS, eps: Double = KSLMath.defaultNumericalPrecision): Double

Computes the incomplete gamma function at x

invChiSquareDistribution

fun invChiSquareDistribution(p: Double, dof: Double, maxSeriesIterations: Int = CHISQ_CDF_SERIES_MAX_ITERATIONS, maxIncGammaIterations: Int = INC_GAMMA_MAX_ITERATIONS, EPS: Double = KSLMath.defaultNumericalPrecision): Double

Algorithm AS 91 Appl. Statist. (1975) Vol.24, P.35

logGammaFunction

fun logGammaFunction(x: Double): Double

Computes the natural logarithm of the gamma function at x. Useful when x gets large.

parametersFromMeanAndVariance

fun parametersFromMeanAndVariance(mean: Double, variance: Double): DoubleArray

Computes the parameters (shape and scale) by matching to mean and variance element0 = shape element1 = scale

parametersFromMoments

fun parametersFromMoments(vararg moments: Double): DoubleArray

Computes the parameters (shape and scale) by matching to mean and variance element0 = shape element1 = scale