scalation.random

Quantile

object Quantile extends Error

The Quantile object contains methods for computing 'Finv', the inverse Cumulative Distribution Functions (iCDF's) for popular sampling distributions: StandardNormal, StudentT, ChiSquare and Fisher. For a given CDF 'F' and quantile 'p', compute 'x' such that the 'F(x) = p'.

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  1. type ICDF = (Double, Array[Int]) ⇒ Double

    Type for inverse Cumulative Distribution Function (iCDF)

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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  4. final def asInstanceOf[T0]: T0

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  5. def chiSquareCDF(x: Double, df: Int = 4): Double

    Compute the Cumulative Distribution Function (CDF) for the ChiSquare distribution by numerically integrating the ChiSquare probability density function (pdf).

    Compute the Cumulative Distribution Function (CDF) for the ChiSquare distribution by numerically integrating the ChiSquare probability density function (pdf). See Variate.scala.

    x

    the x coordinate

    df

    the degrees of freedom

  6. def chiSquareInv(p: Double, df: Int): Double

    Compute the p-th quantile for "ChiSquare distribution" function.

    Compute the p-th quantile for "ChiSquare distribution" function.

    p

    the p-th quantile, e.g., .95 (95%)

    df

    the degrees of freedom

  7. def chiSquareInv(p: Double = .95, _df: Array[Int] = Array (4)): Double

    Compute the p-th quantile for "ChiSquare distribution" function using bisection search of the CDF.

    Compute the p-th quantile for "ChiSquare distribution" function using bisection search of the CDF.

    p

    the p-th quantile, e.g., .95 (95%)

    _df

    the degrees of freedom

  8. def clone(): AnyRef

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  9. final def eq(arg0: AnyRef): Boolean

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  11. def finalize(): Unit

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  12. def fisherCDF(p: Double, df: (Int, Int)): Double

    Compute the Cumulative Distribution Function (CDF) for the Fisher (F) distribution using beta functions.

    Compute the Cumulative Distribution Function (CDF) for the Fisher (F) distribution using beta functions.

    p

    the p-th quantile, e.g., .95 (95%)

    df

    the pair of degrees of freedom (df1, df2)

  13. def fisherCDF(p: Double, df1: Int, df2: Int): Double

    Compute the Cumulative Distribution Function (CDF) for the Fisher (F) distribution using beta functions.

    Compute the Cumulative Distribution Function (CDF) for the Fisher (F) distribution using beta functions.

    p

    the p-th quantile, e.g., .95 (95%)

    df1

    the degrees of freedom 1

    df2

    the degrees of freedom 2

  14. def fisherInv(p: Double, df: (Int, Int)): Double

    Compute the p-th quantile for "Fisher (F) distribution" function.

    Compute the p-th quantile for "Fisher (F) distribution" function.

    p

    the p-th quantile, e.g., .95 (95%)

    df

    the pair of degrees of freedom (df1 and df2)

  15. def fisherInv(p: Double = .95, _df: Array[Int] = Array (4, 5)): Double

    Compute the p-th quantile for "Fisher (F) distribution" function using bisection search of the CDF.

    Compute the p-th quantile for "Fisher (F) distribution" function using bisection search of the CDF.

    p

    the p-th quantile, e.g., .95 (95%)

    _df

    the degrees of freedom

  16. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

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  17. final def getClass(): Class[_]

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  18. def hashCode(): Int

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  19. final def isInstanceOf[T0]: Boolean

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  20. final def ne(arg0: AnyRef): Boolean

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  21. def normalInv(p: Double = .95, _df: Array[Int] = Array ()): Double

    Compute the p-th quantile for the "standard normal distribution" function.

    Compute the p-th quantile for the "standard normal distribution" function. This function returns an approximation of the "inverse" cumulative standard normal distribution function. I.e., given p, it returns an approximation to the x satisfying p = P{Z <= x} where Z is a random variable from the standard normal distribution. The algorithm uses a minimax approximation by rational functions and the result has a relative error whose absolute value is less than 1.15e-9. Author: Peter J. Acklam (Adapted to Scala by John Miller) (Javascript version by Alankar Misra @ Digital Sutras (alankar@digitalsutras.com)) Time-stamp: 2003-05-05 05:15:14 E-mail: pjacklam@online.no WWW URL: http://home.online.no/~pjacklam

    p

    the p-th quantile, e.g., .95 (95%)

    _df

    the degrees of freedom (not used for Normal)

  22. final def notify(): Unit

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  23. final def notifyAll(): Unit

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  24. def studentTInv(p: Double, df: Int): Double

    Compute the p-th quantile for "Student's t distribution" function.

    Compute the p-th quantile for "Student's t distribution" function.

    p

    the p-th quantile, e.g., 95 (95%)

    df

    the degrees of freedom

  25. def studentTInv(p: Double = .95, _df: Array[Int] = Array (10)): Double

    Compute the p-th quantile for "Student's t distribution" function.

    Compute the p-th quantile for "Student's t distribution" function. This function returns an approximation of the "inverse" cumulative Student's t distribution function. I.e., given p, it returns an approximation to the x satisfying p = P{T <= x} where T is a random variable from Student's t distribution. From K. Pawlikowski (www.cosc.canterbury.ac.nz). This function computes the upper p-th quantile of the t distribution (the value of t for which the area under the curve from t to +infinity is equal to p). It is a transliteration of the 'STUDTP' function given in Appendix C of "Principles of Discrete Event Simulation", G. S. Fishman, Wiley, 1978.

    p

    the p-th quantile, e.g., 95 (95%)

    _df

    the degrees of freedom

  26. final def synchronized[T0](arg0: ⇒ T0): T0

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  27. def toString(): String

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