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object CDF extends Error

The CDF object contains methods for computing 'F(x)', the Cumulative Distribution Functions 'CDF's for popular distributions: Uniform Exponential Weibel Empirical StandardNormal StudentT ChiSquare Fisher For a given CDF 'F' with argument 'x', compute 'p = F(x)'.

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  4. def _normalCDF(x: Double, pr: Parameters = null): Double

    Compute the Cumulative Distribution Function (CDF) for the Normal distribution.

    Compute the Cumulative Distribution Function (CDF) for the Normal distribution.

    x

    the x coordinate, argument to F(x)

    pr

    parameters for the mean and standard deviation

  5. def _normalCDF(x: Double): Double

    Compute the Cumulative Distribution Function (CDF) 'F(x)' for the Standard Normal distribution using the Hart function.

    Compute the Cumulative Distribution Function (CDF) 'F(x)' for the Standard Normal distribution using the Hart function. Recoded in Scala from C code

    x

    the x coordinate, argument to F(x)

    See also

    stackoverflow.com/questions/2328258/cumulative-normal-distribution-function-in-c-c which was recoded from VB code.

    www.codeplanet.eu/files/download/accuratecumnorm.pdf

  6. final def asInstanceOf[T0]: T0
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  7. def buildEmpiricalCDF(x: VectorD): (VectorD, VectorD)

    Build an empirical CDF from input data vector 'x'.

    Build an empirical CDF from input data vector 'x'. Ex: x = (2, 1, 2, 3, 2) -> cdf = ((1, .2), (2, .8), (3, 1.))

    x

    the input data vector

  8. def chiSquareCDF(x: Double, pr: Parameters = null): Double

    Compute the Cumulative Distribution Function (CDF) for the ChiSquare distribution.

    Compute the Cumulative Distribution Function (CDF) for the ChiSquare distribution.

    x

    the x coordinate, argument to F(x)

  9. def chiSquareCDF(x: Double, df: Int): 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, argument to F(x)

    df

    the degrees of freedom

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  11. def empiricalCDF(x: Double, eCDF: (VectorD, VectorD)): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Empirical distribution 'eCDF'.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Empirical distribution 'eCDF'.

    x

    the x coordinate, argument to F(x)

    eCDF

    the Empirical CDF

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  14. def exponentialCDF(x: Double, pr: Parameters = null): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Exponential distribution.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Exponential distribution.

    x

    the x coordinate, argument to F(x)

  15. def exponentialCDF(x: Double, λ: Double): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Exponential distribution.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Exponential distribution.

    x

    the x coordinate, argument to F(x)

    λ

    the rate parameter

  16. def fisherCDF(x: Double, pr: Parameters = null): 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.

    x

    the x coordinate, argument to F(x)

  17. def fisherCDF(x: 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.

    x

    the x coordinate, argument to F(x)

    df

    the pair of degrees of freedom ('df1', 'df2')

  18. def fisherCDF(x: 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.

    x

    the x coordinate, argument to F(x)

    df1

    the degrees of freedom 1 (numerator)

    df2

    the degrees of freedom 2 (denominator)

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  24. def noncentralTCDF(x: Double, mu: Double, df: Double): Double

    Compute the Cumulative Distribution Function (CDF) for "Noncentral t" distribution.

    Compute the Cumulative Distribution Function (CDF) for "Noncentral t" distribution.

    x

    the x coordinate, argument to F(x)

    mu

    the noncentrality parameter (or mean)

    df

    the degrees of freedom (must be > 0.0)

    See also

    https://en.wikipedia.org/wiki/Noncentral_t-distribution

  25. def normalCDF(x: Double, pr: Parameters = null): Double

    Compute the Cumulative Distribution Function (CDF) for the Normal distribution.

    Compute the Cumulative Distribution Function (CDF) for the Normal distribution.

    x

    the x coordinate, argument to F(x)

    pr

    parameters for the mean and standard deviation

  26. def normalCDF(x: Double): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Standard Normal distribution using the Hart function.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Standard Normal distribution using the Hart function. Recoded in Scala from Java code. Apache license given above.

    x

    the x coordinate, argument to F(x)

    See also

    mail-archives.apache.org/mod_mbox/commons-dev/200401.mbox/%3C20040126030431.92035.qmail@minotaur.apache.org%3E

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  29. def studentTCDF(x: Double, pr: Parameters = null): Double

    Compute the Cumulative Distribution Function (CDF) for "Student's t" distribution.

    Compute the Cumulative Distribution Function (CDF) for "Student's t" distribution.

    x

    the x coordinate, argument to F(x)

    pr

    parameter for the degrees of freedom

  30. def studentTCDF(x: Double, df: Double): Double

    Compute the Cumulative Distribution Function (CDF) for "Student's t" distribution.

    Compute the Cumulative Distribution Function (CDF) for "Student's t" distribution.

    x

    the x coordinate, argument to F(x)

    df

    the degrees of freedom (must be > 0.0)

    See also

    [JKB 1995] Johnson, Kotz & Balakrishnan "Continuous Univariate Distributions" (Volume 2) (2nd Edition) (Chapter 28) (1995)

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  33. def uniformCDF(x: Double, pr: Parameters = null): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Uniform distribution.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Uniform distribution.

    x

    the x coordinate, argument to F(x)

    pr

    parameters giving the end-points of the uniform distribution

  34. def uniformCDF(x: Double, a: Double, b: Double): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Uniform distribution.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Uniform distribution.

    x

    the x coordinate, argument to F(x)

    a

    the lower end-point of the uniform distribution

    b

    the upper end-point of the uniform distribution

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  38. def weibullCDF(x: Double, pr: Parameters = null): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Weibull distribution.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Weibull distribution.

    x

    the x coordinate, argument to F(x)

  39. def weibullCDF(x: Double, α: Double, β: Double): Double

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Weibull distribution.

    Compute the Cumulative Distribution Function 'CDF' 'F(x)' for the Weibull distribution.

    x

    the x coordinate, argument to F(x)

    α

    the shape parameter

    β

    the scale parameter

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