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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- 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
- 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
- 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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- 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
- 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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- 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
- 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')
- 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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- 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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- 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
- 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 -------------------------------------------------------------------------
- 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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- 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
Uniformdistribution
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