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Add mapairy document graphs

This commit is contained in:
tk-yoshimura
2024-07-23 22:56:27 +09:00
parent c64db569a0
commit 72afe90646
7 changed files with 2982 additions and 4 deletions

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@@ -29,11 +29,11 @@ This distribution is also defined as [beta] = 1, which is inverted about the
[@http://en.wikipedia.org/wiki/Probability_distribution probability distribution function PDF]
given by:
[equation mapairy_ref1]
[equation mapairy_ref1] [/f(x; \mu=0, c=1/\sqrt[3]{18}) = 2 \exp \left( \frac{2}{3} x^3 \right) \left( -x \mathrm{Ai}(x^2) - \mathrm{Ai}'(x^2) \right)]
The location parameter [mu] is the location of the distribution,
while the scale parameter [c] determines the width of the distribution. If the location is
zero, and the scale 1, then the result is a standard mapairy
zero, and the scale 1, then the result is a standard map-airy
distribution.
The distribution describes the probability distribution of the area under a Brownian excursion over a unit interval.
@@ -55,7 +55,7 @@ the distribution:
Constructs a mapairy distribution, with location parameter /location/
and scale parameter /scale/. When these parameters take their default
values (location = 0, scale = 1)
then the result is a Standard mapairy Distribution.
then the result is a Standard map-airy Distribution.
Requires scale > 0, otherwise calls __domain_error.
@@ -72,7 +72,7 @@ Returns the scale parameter of the distribution.
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
Note however that the mapairy distribution does not have a skewness,
Note however that the map-airy distribution does not have a skewness,
kurtosis, etc. See __math_undefined
[/link math_toolkit.pol_ref.assert_undefined mathematically undefined function]
to control whether these should fail to compile with a BOOST_STATIC_ASSERTION_FAILURE,
@@ -87,6 +87,18 @@ The domain of the random variable is \[-[max_value], +[min_value]\].
The error is within 4 epsilon except for the rapidly decaying left tail.
Errors in the PDF at 64-bit double precision:
[$../graphs/mapairy_pdf_accuracy_64.png]
Errors in the CDF at 64-bit double precision:
[$../graphs/mapairy_cdf_accuracy_64.png]
Errors in the CDF-complement at 64-bit double precision:
[$../graphs/mapairy_ccdf_accuracy_64.png]
[h4 Implementation]
See references.
@@ -100,6 +112,7 @@ DOI: 10.36227/techrxiv.172053942.27675733/v1, 2024.
[endsect][/section:mapairy_dist mapairy]
[/ mapairy.qbk
Copyright Takuma Yoshimura 2024.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).

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@@ -0,0 +1,86 @@
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