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revision 1.1.2.1 by jstover, Sat Dec 7 06:01:11 2002 UTC revision 1.1.2.2 by jstover, Thu Jan 9 15:47:34 2003 UTC
# Line 7  The functions described in this section Line 7  The functions described in this section
7  @file{gsl_cdf.h}.  @file{gsl_cdf.h}.
8    
9  @menu  @menu
10    * Cumulative Distribution Function Usage::
11    * The gsl_cdf_result struct::
12  * The Gaussian CDF::    * The Gaussian CDF::  
13  * CDF Examples::  * CDF Examples::
14  * CDF References and Further Reading::  * CDF References and Further Reading::
15  @end menu  @end menu
16    
17    @node Cumulative Distribution Function Usage
18    @section Usage
19    
20    Following the design of the GSL special functions, the cumulative
21    distribution functions are available in two calling conventions, a
22    @dfn{natural form} which returns the numerical value of the function
23    and
24    an @dfn{error-handling form} which returns an error code.  The two
25    types
26    of function provide alternative ways of accessing the same underlying
27    code.
28    
29    The @dfn{natural form} returns only the value of the function and can be
30    used directly in mathematical expressions.  For example, the following
31    function call will compute the value of the Gamma cdf with
32    scale parameter alpha and shape parameter beta.
33    
34    @example
35    double y = gsl_cdf_gamma (x, alpha, beta, GSL_CDF_LOWER);
36    @end example
37    @noindent
38    There is no way to access an error code or to estimate the error using
39    this method.  To allow access to this information the alternative
40    error-handling form stores the value and error in a modifiable argument,
41    
42    @example
43    gsl_cdf_result result;
44    int status = gsl_cdf_gamma_e (x, alpha, beta, GSL_CDF_UPPER, &result);
45    @end example
46    @noindent
47    The error-handling functions have the suffix @code{_e}. The returned
48    status value indicates error conditions such as overflow, underflow or
49    loss of precision.  If there are no errors the error-handling functions
50    return @code{GSL_SUCCESS}.
51    
52    @node The gsl_cdf_result struct
53    @section The gsl_cdf_result struct
54    @cindex gsl_cdf_result
55    @cindex gsl_cdf_result_e10
56    
57    The error handling form of the special functions always calculate an
58    error estimate along with the value of the result.  Therefore,
59    structures are provided for amalgamating a value and error estimate.
60    These structures are declared in the header file @file{gsl_cdf_result.h}.
61    
62    The @code{gsl_cdf_result} struct contains value and error fields.
63    
64    @example
65    typedef struct
66    @{
67      double val;
68      double err;
69    @} gsl_cdf_result;
70    @end example
71    @noindent
72    The field @var{val} contains the value and the field @var{err} contains
73    an estimate of the absolute error in the value.
74    
75    In some cases, an overflow or underflow can be detected and handled by a
76    function.  In this case, it may be possible to return a scaling exponent
77    as well as an error/value pair in order to save the result from
78    exceeding the dynamic range of the built-in types.  The
79    @code{gsl_cdf_result_e10} struct contains value and error fields as well
80    as an exponent field such that the actual result is obtained as
81    @code{result * 10^(e10)}.
82    
83    @example
84    typedef struct
85    @{
86      double val;
87      double err;
88      int    e10;
89    @} gsl_cdf_result_e10;
90    @end example
91    
92  @page  @page
93  @node The Gaussian CDF  @node The Gaussian CDF
94  @section The Gaussian Cumulative Distribution Function  @section The Gaussian Cumulative Distribution Function

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