goose-ref.texi

非常著名的曲线拟合程序

range is defined to be the difference of the third and first
quartiles.
@end deftypemethod

@deftypemethod RealSet double decile (int @var{i})
Returns the @var{i}th decile of the RealSet.
@end deftypemethod

@deftypemethod RealSet double mean_trimmed (int @var{l}, int @var{r})
Returns the mean of the elements of the RealSet, excluding the @var{l}
smallest and @var{r} largest values.  (Here the letters @var{l} and
@var{r} refer to the ``left'' and ``right'' sides of the data.  If we
imagine the data to be sorted from high to low and lined up in a single
row across a page, we would be removing @var{l} from the left side and
@var{r} from the right.)
@end deftypemethod

@deftypemethod RealSet double mean_trimmed (int @var{t})
Returns the mean of the elements of the RealSet, excluding
the @var{t} smallest and @var{t} largest values.
@end deftypemethod

@deftypemethod RealSet double mean_winsorized (int @var{l}, int @var{r})
Return the (@var{l},@var{r})-Winsorized mean of the RealSet.

In statistics, to winsorize a data set means to replacing the
@var{l} smallest and @var{r} largest values of the data set by the
@var{(l+1)}st smallest and @var{(r+1)}st largest elements, respectively.
This operation throws out the most extreme values in the data and
replaces them by certain values that are presumed to be ``more
representative''.
@tex
In mathematical notation, this function returns the quantity
$$
{l x_{(l+1)} + \sum_{i=l+1}^{N-r} x_{(i)} + r x_{(N-r)} \over N}.
$$
@end tex
@end deftypemethod

@deftypemethod RealSet double mean_winsorized (int @var{t})
@end deftypemethod

@deftypemethod RealSet double moment (int @var{k}, int @var{x})
@end deftypemethod

@deftypemethod RealSet double moment (int @var{k})
@end deftypemethod

@deftypemethod RealSet double gmean ()
@end deftypemethod

@deftypemethod RealSet double hmean ()
@end deftypemethod

@deftypemethod RealSet double rms ()
@end deftypemethod

@deftypemethod RealSet double meandev ()
@end deftypemethod

@deftypemethod RealSet double meddev ()
@end deftypemethod

@deftypemethod RealSet double kurtosis ()
@end deftypemethod

@deftypemethod RealSet double skewness ()
@end deftypemethod

@deftypemethod RealSet double excess_kurtosis ()
@end deftypemethod

@deftypemethod RealSet double momental_skewness ()
@end deftypemethod

@deftypemethod RealSet double durbin_watson ()
Returns the Durbin-Watson statistic for the RealSet.  Unlike most of
statistics discussed so far, this depends on the order of the elements.
@tex
The Durbin-Watson statistic is defined to be the expression
$$ {\sum_{i=2}^N (x_i - x_{i-1})^2 \over \sum_{i=1}^N x_i^2}. $$
@end tex
@end deftypemethod

@deftypemethod RealSet double AR1_independence_z ()
@end deftypemethod

@deftypemethod RealSet double autocorr (int @var{lag})
@end deftypemethod

@deftypemethod RealSet double autocorr_z (int @var{lag})
@end deftypemethod

@deftypemethod RealSet double covar (const RealSet& @var{rs})
@end deftypemethod

@deftypemethod RealSet double corr (const RealSet& @var{rs})
@end deftypemethod

@deftypemethod RealSet double pooled_mean (const RealSet& @var{rs})
@end deftypemethod

@deftypemethod RealSet double pooled_var (const RealSet& @var{rs})
@end deftypemethod

@deftypemethod RealSet double weighted_mean (const RealSet& @var{rs})
@end deftypemethod

@deftypemethod RealSet size_t greater_than (double @var{x})
Returns the number of elements of the RealSet that are strictly greater than
@var{x}.
@end deftypemethod

@deftypemethod RealSet size_t less_than (double @var{x})
Returns the number of elements of the RealSet that are strictly less than
@var{x}.
@end deftypemethod

@deftypemethod RealSet size_t between (double @var{a}, double @var{b})
Returns the number of elements of the RealSet that are between @var{a} and
@var{b}, inclusive.
@end deftypemethod

@deftypemethod RealSet size_t equal_to (double @var{x})
Returns the number of elements of the RealSet that are equal to @var{x}.
@end deftypemethod

@section Global Transformations on a RealSet

@deftypemethod RealSet void apply(FunctionObject @var{f})
This is a template function that takes any function object @var{f} and
applies it to each element of the RealSet, replacing the elements with
the calculated values.
@end deftypemethod

@deftypemethod RealSet void linear_transform(double @var{a}, double @var{b})
Iterates across the elements of the RealSet, replacing each element @var{x} by
@var{a}@var{x}+@var{b}.
@end deftypemethod

@deftypemethod RealSet void log_transform ()
Iterates across the elements of the RealSet, replacing each elements by
its natural logarithm.  An exception is thrown if any element is less
than or equal to zero.
@end deftypemethod

@deftypemethod RealSet void exp_transform ()
Iterates across the elements of the RealSet, applying the exponential
function to each element.
@end deftypemethod

@deftypemethod RealSet void logit_transform ()
Iterates across the elements, applying the logit transform to each element.
@tex
The logit transform maps $x$ to $\log(x/(1-x))$.
@end tex
@end deftypemethod

@deftypemethod RealSet void reverse ()
Reverses the order of the elements in the RealSet.
@end deftypemethod

@deftypemethod RealSet void sort (int @var{dir} = 1)
If @var{dir} is greater than zero, sorts the elements of the RealSet in
ascending order.  If @var{dir} is less than zero, the sort is performed
in descending order.
@end deftypemethod

@deftypemethod RealSet void scramble ()
Randomly permutes the elements of the RealSet.
@end deftypemethod

@deftypemethod RealSet void rank ()
Replaces each element of the RealSet by its rank within that RealSet.
In the case of ties, ranks are averages, following the usual statistical
convention.
@end deftypemethod

@c ***************************************************************************

@node Linear Regression, Bootstrapping Functions, The RealSet Class, Top
@chapter Linear Regression

@section Simple Linear Regression

@section Multiple Regression

Multiple Regression currently not implemented in Goose.

@c ***************************************************************************

@node Bootstrapping Functions, Special Functions, Linear Regression, Top
@chapter Bootstrapping Functions

@section Optimized Resampling Functions

@deftypefun RealSet bootstrap_mean (size_t @var{N}, const RealSet& @var{data}, int @var{threads}=1)
@deftypefunx RealSet bootstrap_median (size_t @var{N}, const RealSet& @var{data}, int @var{threads}=1)
@deftypefunx RealSet bootstrap_sdev (size_t @var{N}, const RealSet& @var{data}, int @var{threads}=1)
@deftypefunx RealSet bootstrap_skewness (size_t @var{N}, const RealSet& @var{data}, int @var{threads}=1)
@deftypefunx RealSet bootstrap_kurtosis (size_t @var{N}, const RealSet& @var{data}, int @var{threads}=1)
Each of these functions returns a RealSet containing a set of @var{N} values,
each of which represents the value of the appropriate statistic
calculated against a resampling of the elements in @var{data}.

Since these resampling calculations are highly parallelizable,
significant performance enhancements are possible in multiprocessor
environments.  If @var{threads} is set greater than one, that many
different threads are created and the computation is split amongst them.
(If your system does not support threads, the @var{threads} argument is
ignored.)
@end deftypefun

@c ***************************************************************************

@node Special Functions, Using Goose from Guile, Bootstrapping Functions, Top
@chapter Special Functions

One important part of Goose is a library called @code{libspecfns}, which
provides mathematical functions that are frequently needed when
performing statistical calculations.  These functions are used
internally by Goose, but you may find them to be useful for your own
programs.

The majority of the code that makes up @code{libspecfns} is derived from
parts of Stephen L. Moshier's Cephes library.  Moshier holds the
copyright on Cephes, but it is distributed with no licensing
restrictions of any kind.  Since @code{libspecfns} is derived from
Cephes, Moshier is still the primary copyright holder.  However, this
library, like Goose, is licensed under the LGPL.

@section General Functions

@deftypefun double factorial (int @var{n})
Returns @var{n} factorial.  For sufficiently small values of @var{n}
(say, @var{n} less than 24), it should be possible to obtain an exact
answer by casting the results to an int.  An exception will be thrown if
@var{n} is negative.
@tex 
Mathematically,
$$\hbox{\tt factorial(n)} = n! = \prod_{i=1}^n i.$$
@end tex
@end deftypefun

@deftypefun double log_factorial (int @var{n})
Returns the natural logarithm of @code{factorial(n)}.  This function is
equivalent to @code{log(factorial(n))}, but is much more numerically
stable for large values of @var{n}.
@end deftypefun

@deftypefun double choose (int @var{n}, int @var{k})
Returns the binomial coefficient of @var{n} and @var{k}, which also
happens to be the number of different possible unordered sets of size
@var{k} that can be chosen (without replacement) from a set of @var{n}
distinct objects.  For sufficiently small values of @var{n} and @var{k}, it should be possible to obtain an exact answer by casting the results to an int.
@tex
Mathematically,
$$\hbox{\tt choose(n,k)} = {n\choose k} = {n!\over k!(n-k)!}.$$
@end tex
@end deftypefun

@deftypefun double log_choose (int @var{n}, int @var{k})
Returns the natural logarithm of @code{choose(n,k)}.
@end deftypefun

@deftypefun double log_gamma (double @var{x})
Returns the logarithms of the value of the gamma function at @var{x}.
@tex
In mathematical notation,
$$ \hbox{\tt log\_gamma(x)} = \log\Gamma(x) =
\log\int_0^\infty t^{x-1}e^{-t}\,dt.$$
@end tex
@end deftypefun

@deftypefun double incomplete_gamma (double @var{a}, double @var{b})
Returns the value of the incomplete gamma integral of @var{a},
integrated from 0 to @var{b}.
@tex
In mathematical notation,
$$ \hbox{\tt incomplete\_gamma(a,b)} = {1\over\Gamma(a)}\int_0^b t^{a-1}e^{-t}\,dt.$$
@end tex
@end deftypefun

@section Statistical Distributions

For the functions that are associated with various statistical
distributions, we have adopted the following convention:  For the Foo
distribution, the cumulative distribution function (or CDF) is always
named @code{foo_cdf}.  The inverse cumulative distribution function is
always named @code{inv_foo_cdf}.

@deftypefun double normal_cdf (double @var{x})
Returns the value at @var{x} of the CDF of a standard normal distribution.
@tex
In mathematical notation,
$$ \hbox{\tt normal\_cdf(x)} = {1\over 2\pi}\int_{-\infty}^x e^{-t^2/2}\,dt.$$
@end tex
@end deftypefun

@deftypefun double normal_cdf (double @var{m}, double @var{s}, double @var{x})
Returns the value at @var{x} of the CDF of a normal distribution with
mean @var{m} and standard deviation @var{s}.
@end deftypefun

@deftypefun double inv_normal_cdf (double @var{p})
Returns the value at @var{p} of the inverse CDF of a standard normal
distribution.
@end deftypefun

@deftypefun double poisson_cdf (int @var{k}, double @var{x})
Returns the value at @var{x} of the CDF of a Poisson distribution with
mean @var{k}.
@end deftypefun

@deftypefun double inv_poisson_cdf (int @var{k}, double @var{p})
Returns the value at @var{p} of the inverse CDF of a Poisson distribution with
mean @var{k}.
@end deftypefun

@deftypefun double chisq_cdf (int @var{df}, double @var{x})
Returns the value at @var{x} of the CDF of a Chi-square distribution
with @var{df} degrees of freedom.
@end deftypefun

@deftypefun double inv_chisq_cdf (int @var{df}, double @var{p})
Returns the value at @var{p} of the inverse CDF of a Chi-square
distribution with @var{df} degrees of freedom.
@end deftypefun

@deftypefun double t_cdf (int @var{df}, double @var{x})
Returns the value at @var{x} of the CDF of a T-distribution
with @var{df} degrees of freedom.
@end deftypefun

@deftypefun double inv_t_cdf (int @var{df}, double @var{p})
Returns the value at @var{p} of the inverse CDF of a T-distribution with
@var{df} degrees of freedom.
@end deftypefun

@deftypefun double F_cdf (int @var{df1}, int @var{df2}, double @var{x})
Returns the value at @var{x} of the CDF of an F-distribution
with @var{df1} and @var{df2} degrees of freedom.
@end deftypefun

@deftypefun double inv_F_cdf (int @var{df}, int @var{df2}, double @var{p})
Returns the value at @var{p} of the inverse CDF of an F-distribution with
@var{df1} and @var{df2} degrees of freedom.
@end deftypefun

@deftypefun double gamma_cdf (double @var{a}, double @var{b}, double @var{x})
@end deftypefun

@deftypefun double binomial_cdf (int @var{k}, int @var{k}, double @var{x})
@end deftypefun

@deftypefun double neg_binomial_cdf (int @var{n}, int @var{k}, double @var{x})
@end deftypefun

@c ***************************************************************************

@node Using Goose from Guile, Using Goose from Perl, Special Functions, Top
@chapter Using Goose from Guile

An incomplete set of guile bindings exist.

@c ***************************************************************************

@node Using Goose from Perl, Concept Index, Using Goose from Guile, Top
@chapter Using Goose from Perl

Perl bindings don't exist yet.  They will someday.

@c ***************************************************************************

@node Concept Index, Function Index, Using Goose from Perl, Top
@unnumbered Concept Index

@printindex cp

@node Function Index,  , Concept Index, Top
@unnumbered Function Index

@printindex fn

@c @shortcontents
@contents
@bye