Tukey (JDistlib 0.4.1 API)

java.lang.Object
- jdistlib.generic.GenericDistribution
- - jdistlib.Tukey

```
public class Tukey
extends jdistlib.generic.GenericDistribution
```
Computes the probability and quantile that the maximum of rr studentized ranges, each based on cc means and with df degrees of freedom for the standard error, is less than q.
The algorithm is based on that of the reference.
REFERENCE
Copenhaver, Margaret Diponzio & Holland, Burt S. Multiple comparisons of simple effects in the two-way analysis of variance with fixed effects. Journal of Statistical Computation and Simulation, Vol.30, pp.1-15, 1988.
RJ's Note: See Algorithm AS 190 by Lund and Lund

Field Summary

Fields
Modifier and Type Field and Description

protected double cc

protected double df

protected double rr
- Fields inherited from class jdistlib.generic.GenericDistribution
  random

Fields
Modifier and Type	Field and Description
`protected double`	`cc`
`protected double`	`df`
`protected double`	`rr`

Constructor Summary

Constructors
Constructor and Description

Tukey(double rr, double cc, double df)

Constructors
Constructor and Description
`Tukey(double rr, double cc, double df)`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`cumulative(double p, boolean lower_tail, boolean log_p)`
`static double`	`cumulative(double q, double rr, double cc, double df, boolean lower_tail, boolean log_p)` function ptukey() [was qprob() ]: q = value of studentized range rr = no. of rows or groups cc = no. of columns or treatments df = degrees of freedom of error term ir[0] = error flag = 1 if wprob probability > 1 ir[1] = error flag = 1 if qprob probability > 1 qprob = returned probability integral over [0, q] The program will not terminate if ir[0] or ir[1] are raised.
`double`	`density(double x, boolean log)` Density of Tukey HSD distribution using differentials of the cumulative --- WARNING: Untested!
`static double`	`density(double x, double rr, double cc, double df, boolean log_p)`
`static double`	`density(double x, double rr, double cc, double df, boolean log_p, double diff)` Density of Tukey HSD distribution using differentials of the cumulative --- WARNING: Untested!
`double`	`quantile(double q, boolean lower_tail, boolean log_p)`
`static double`	`quantile(double p, double rr, double cc, double df, boolean lower_tail, boolean log_p)` Copenhaver, Margaret Diponzio & Holland, Burt S.
`double`	`random()`
`static double`	`random(double rr, double cc, double df, jdistlib.rng.RandomEngine random)` Tukey RNG by inversion -- WARNING: Untested
`static double[]`	`random(int n, double rr, double cc, double df, jdistlib.rng.RandomEngine random)`

Methods inherited from class jdistlib.generic.GenericDistribution
cumulative_hazard, cumulative_hazard, cumulative, cumulative, cumulative, density, density, getRandomEngine, hazard, hazard, inverse_survival, inverse_survival, quantile, quantile, quantile, random, random, setRandomEngine, survival, survival, survival

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - rr
```
protected double rr
```
  - cc
```
protected double cc
```
  - df
```
protected double df
```
- Constructor Detail
  - Tukey
```
public Tukey(double rr,
             double cc,
             double df)
```
- Method Detail
  - cumulative
```
public static final double cumulative(double q,
                                      double rr,
                                      double cc,
                                      double df,
                                      boolean lower_tail,
                                      boolean log_p)
```
    function ptukey() [was qprob() ]:
    q = value of studentized range
    rr = no. of rows or groups
    cc = no. of columns or treatments
    df = degrees of freedom of error term
    ir[0] = error flag = 1 if wprob probability > 1
    ir[1] = error flag = 1 if qprob probability > 1
    qprob = returned probability integral over [0, q]
    The program will not terminate if ir[0] or ir[1] are raised.
    All references in wprob to Abramowitz and Stegun are from the following reference:
    Abramowitz, Milton and Stegun, Irene A. Handbook of Mathematical Functions. New York: Dover publications, Inc. (1970).
    All constants taken from this text are given to 25 significant digits.
    nlegq = order of legendre quadrature
    ihalfq = int ((nlegq + 1) / 2)
    eps = max. allowable value of integral
    eps1 & eps2 = values below which there is no contribution to integral.
    d.f. <= dhaf: integral is divided into ulen1 length intervals. else
    d.f. <= dquar: integral is divided into ulen2 length intervals. else
    d.f. <= deigh: integral is divided into ulen3 length intervals. else
    d.f. <= dlarg: integral is divided into ulen4 length intervals.
    d.f. > dlarg: the range is used to calculate integral.
    M_LN2 = log(2)
    xlegq = legendre 16-point nodes
    alegq = legendre 16-point coefficients
    The coefficients and nodes for the legendre quadrature used in qprob and wprob were calculated using the algorithms found in:
    Stroud, A. H. and Secrest, D.
    Gaussian Quadrature Formulas.
    Englewood Cliffs,
    New Jersey: Prentice-Hall, Inc, 1966.
    All values matched the tables (provided in same reference) to 30 significant digits.
    f(x) = .5 + erf(x / sqrt(2)) / 2 for x > 0
    f(x) = erfc( -x / sqrt(2)) / 2 for x < 0
    where f(x) is standard normal c. d. f.
    if degrees of freedom large, approximate integral with range distribution.
  - quantile
```
public static final double quantile(double p,
                                    double rr,
                                    double cc,
                                    double df,
                                    boolean lower_tail,
                                    boolean log_p)
```
    Copenhaver, Margaret Diponzio & Holland, Burt S. Multiple comparisons of simple effects in the two-way analysis of variance with fixed effects. Journal of Statistical Computation and Simulation, Vol.30, pp.1-15, 1988.
    Uses the secant method to find critical values.
    p = confidence level (1 - alpha)
    rr = no. of rows or groups
    cc = no. of columns or treatments
    df = degrees of freedom of error term
    ir(1) = error flag = 1 if wprob probability > 1
    ir(2) = error flag = 1 if ptukey probability > 1
    ir(3) = error flag = 1 if convergence not reached in 50 iterations = 2 if df < 2
    qtukey = returned critical value
    If the difference between successive iterates is less than eps, the search is terminated
  - random
```
public static final double random(double rr,
                                  double cc,
                                  double df,
                                  jdistlib.rng.RandomEngine random)
```
    Tukey RNG by inversion -- WARNING: Untested
    
    Parameters:
    
    rr -
    
    cc -
    
    df -
    
    random -
    
    Returns:
    
    random variate
  - random
```
public static final double[] random(int n,
                                    double rr,
                                    double cc,
                                    double df,
                                    jdistlib.rng.RandomEngine random)
```
  - density
```
public static final double density(double x,
                                   double rr,
                                   double cc,
                                   double df,
                                   boolean log_p)
```
  - density
```
public static final double density(double x,
                                   double rr,
                                   double cc,
                                   double df,
                                   boolean log_p,
                                   double diff)
```
    Density of Tukey HSD distribution using differentials of the cumulative --- WARNING: Untested!
    
    Parameters:
    
    x -
    
    rr -
    
    cc -
    
    df -
    
    log_p -
    
    diff - tunable delta (set to 1e-10) in the preceding routine
    
    Returns:
    
    Density value
  - density
```
public double density(double x,
                      boolean log)
```
    Density of Tukey HSD distribution using differentials of the cumulative --- WARNING: Untested!
    
    Specified by:
    
    density in class jdistlib.generic.GenericDistribution
  - cumulative
```
public double cumulative(double p,
                         boolean lower_tail,
                         boolean log_p)
```
    Specified by:
    
    cumulative in class jdistlib.generic.GenericDistribution
  - quantile
```
public double quantile(double q,
                       boolean lower_tail,
                       boolean log_p)
```
    Specified by:
    
    quantile in class jdistlib.generic.GenericDistribution
  - random
```
public double random()
```
    Specified by:
    
    random in class jdistlib.generic.GenericDistribution

Class Tukey

Field Summary

Fields inherited from class jdistlib.generic.GenericDistribution

Constructor Summary

Method Summary

Methods inherited from class jdistlib.generic.GenericDistribution

Methods inherited from class java.lang.Object

Field Detail

rr

cc

df

Constructor Detail

Tukey

Method Detail

cumulative

quantile

random

random

density

density

density

cumulative

quantile

random