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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 probability/quantile 'p', compute 'x' such that 'F(x) = p'. The iCDF may be thought of as giving value of 'x' for which the area under the curve from -infinity to 'x' of the probability density function (pdf) is equal to 'p'.

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  5. def check(p: Double, x_min: Double = NEGATIVE_INFINITY): (Boolean, Double)

    Check whether the probability 'p' is out of range (giving NaN) or extreme, either close to 0 (giving -infinity) or 1 (giving +infinity).

    Check whether the probability 'p' is out of range (giving NaN) or extreme, either close to 0 (giving -infinity) or 1 (giving +infinity). Return (true, special-value) for these cases.

    p

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

    x_min

    the smallest value in the distribution's domain

  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, pr: Parameters = null): 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. FIX: need a faster algorithm

    p

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

    pr

    parameter for the degrees of freedom

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  9. def empiricalInv(p: Double, data: Parameters): Double

    Compute the 'p'-th quantile for the Empirical distribution function.

    Compute the 'p'-th quantile for the Empirical distribution function.

    p

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

    data

    parameters as data

  10. def empiricalInv(p: Double, eCDF: (VectorD, VectorD)): Double

    Compute the 'p'-th quantile for the Empirical distribution function.

    Compute the 'p'-th quantile for the Empirical distribution function.

    p

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

    eCDF

    the empirical CDF

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  13. def exponentialInv(p: Double, pr: Parameters = null): Double

    Compute the 'p'-th quantile for the Exponential distribution function.

    Compute the 'p'-th quantile for the Exponential distribution function.

    p

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

    pr

    parameter for the rate

  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, pr: Parameters = null): 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. FIX: need a faster algorithm

    p

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

    pr

    parameters for the degrees of freedom (numerator, denominator)

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  21. def normalInv(p: Double = .95, pr: Parameters = null): Double

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

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

    p

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

    pr

    parameter for the distribution (currently not used)

    See also

    home.online.no/~pjacklam/notes/invnorm/impl/sprouse/ltqnorm.c -------------------------------------------------------------------------

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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, pr: Parameters = null): 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%)

    pr

    parameter for the degrees of freedom

    See also

    wp.csiro.au/alanmiller/toms/cacm396.f90 -------------------------------------------------------------------------

  26. def studentTInv2(p: Double = .95, pr: Parameters = null): Double

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

    Compute the 'p'-th quantile for "Student's t" distribution function. This algorithm is less accurate than the one above. ------------------------------------------------------------------------- It is a transliteration of the 'STUDTP' function given in Appendix C

    p

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

    pr

    parameter for the degrees of freedom

    See also

    "Principles of Discrete Event Simulation", G. S. Fishman, Wiley, 1978. -------------------------------------------------------------------------

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  29. def uniformInv(p: Double, pr: Parameters = null): Double

    Compute the 'p'-th quantile for the Uniform distribution function.

    Compute the 'p'-th quantile for the Uniform distribution function.

    p

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

    pr

    parameters for the end-points of the Uniform distribution

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