Statistics2 -- Statistical Distributions for Ruby

  Author: Shin-ichiro HARA(sinara@blade.nagaokaut.ac.jp)
  Date: 2003.09.26

Requirements
------------

  * ruby-1.8

Installation
------------
  Copy `statistics2.rb' where Ruby can load.

Installation of extension module (if you need)
---------------------------------------------
  This package also contains the C extension module which has the same functions
  in `statistics2.rb'. Enter ext/ directory of the package. Then type:

    $ ruby extconf.rb
    $ make
    $ make test
    $ make install

Usage
-----
    Example:
      require "statistics2"
      puts Statistics2.normaldist(0.27) #=> 0.606419873198039

Class and Methods
-----------------

Modules:
  Statistics2

Methods:

--- Statistics2.normaldist(x)
    Returns the integral of normal distribution over (-Infty, x].

--- Statistics2.pnormaldist(pr)
    Returns the P-value of normaldist(x).

--- Statistics2.normalxXX_(x)
    Returns the integral of normal distribution over (-Infty, x].

--- Statistics2.normal__X_(x)
    Returns the integral of normal distribution over [0, x].

--- Statistics2.normal___x(x)
    Returns the integral of normal distribution over [x, Infty).

--- Statistics2.normalx__x(x)
    Returns the integral of normal distribution over (-Infty, -x] + [x, Infty).

--- Statistics2.pnormalxXX_(pr)
--- Statistics2.pnormal__X_(pr)
--- Statistics2.pnormal___x(pr)
--- Statistics2.pnormalx__x(pr)
    Return the P-value of the corresponding integral.


--- Statistics2.chi2dist(n, x)
    Returns the integral of Chi-squared distribution with n degrees of freedom
    over [0, x].

--- Statistics2.pchi2dist(n, pr)
    Returns the P-value of chi2dist().

--- Statistics2.chi2X_(n, x)
    Returns the integral of Chi-squared distribution with n degrees of freedom
    over [0, x].

--- Statistics2.chi2_x(n, x)
    Returns the integral of Chi-squared distribution with n degrees of freedom
    over [x, Infty).

--- Statistics2.pchi2X_(n, pr)
--- Statistics2.pchi2_x(n, pr)
    Return the P-value of the corresponding integral.

--- Statistics2.tdist(n, x)
    Returns the integral of t-distribution with n degrees of freedom
    over (-Infty, x].

--- Statistics2.ptdist(n, pr)
    Returns the P-value of tdist().

--- Statistics2.txXX_(n, x)
    Returns the integral of t-distribution with n degrees of freedom
    over (-Infty, x].

--- Statistics2.t__X_(n, x)
    Returns the integral of t-distribution with n degrees of freedom
    over [0, x].

--- Statistics2.t___x(n, x)
    Returns the integral of t-distribution with n degrees of freedom
    over [x, Infty).

--- Statistics2.tx__x(n, x)
    Returns the integral of normal distribution with n degrees of freedom
    over (-Infty, -x] + [x, Infty).

--- Statistics2.ptxXX_(n, pr)
--- Statistics2.pt__X_(n, pr)
--- Statistics2.pt___x(n, pr)
--- Statistics2.ptx__x(n, pr)
    Return the P-value of the corresponding integral.

--- Statistics2.fdist(n1, n2, x)
    Returns the integral of F-distribution with n1 and n2 degrees of freedom
    over [0, x].

--- Statistics2.pfdist(n1, n2, pr)
    Returns the P-value of fdist().

--- Statistics2.fX_(n1, n2, x)
    Returns the integral of F-distribution with n1 and n2 degrees of freedom
    over [0, x].

--- Statistics2.f_x(n1, n2, x)
    Returns the integral of F-distribution with n1 and n2 degrees of freedom
    over [x, Infty).

--- Statistics2.pfX_(n1, n2, pr)
--- Statistics2.pf_x(n1, n2, pr)
    Return the P-value of the corresponding integral.

Samples
-------

    ruby sample-tbl.rb norm     ... table of normal distribution
    ruby sample-tbl.rb chi2     ... table of chi-square distribution
    ruby sample-tbl.rb t        ... table of t distribution
    ruby sample-tbl.rb f <num>  ... table of f distribution

License
-------

  Ruby's (see http://www.ruby-lang.org/en/LICENSE.txt)

Changes
-------
  0.53(2008.07.14)
    * fix pt for p < 0.5.

  0.52(2008.02.24)
    * fix p_nor for z < 0.0.

  0.51(2007.06.17)
    * fix p_nor.
    * simplify chi2 n = 1 or 2.