Imported Upstream version 1.72.0

[platform/upstream/boost.git] / libs / math / doc / distributions / inverse_chi_squared.qbk

diff --git a/libs/math/doc/distributions/inverse_chi_squared.qbk b/libs/math/doc/distributions/inverse_chi_squared.qbk
index 4c1f9f9..7bc75a8 100644 (file)
--- a/libs/math/doc/distributions/inverse_chi_squared.qbk
+++ b/libs/math/doc/distributions/inverse_chi_squared.qbk
@@ -38,7 +38,7 @@ A second version has an implicit scale = 1/degrees of freedom and gives the 1st
 The 2nd Wikipedia inverse chi_squared distribution definition can be implemented
 by  explicitly specifying a scale = 1.
 
-Both definitions are also available in Wolfram Mathematica and in __R (geoR) with default scale = 1/degrees of freedom.
+Both definitions are also available in __Mathematica and in __R (geoR) with default scale = 1/degrees of freedom.
 
 See 
 
@@ -60,7 +60,7 @@ See also __inverse_gamma_distrib and __chi_squared_distrib.
 The inverse_chi_squared distribution is a special case of a inverse_gamma distribution
 with [nu] (degrees_of_freedom) shape ([alpha]) and scale ([beta]) where
 
-__spaces [alpha]= [nu] /2 and [beta] = [frac12].
+[expression [alpha]= [nu] /2 and [beta] = [frac12]]
 
 [note This distribution *does* provide the typedef:
 
@@ -75,20 +75,20 @@ or you can write `inverse_chi_squared my_invchisqr(2, 3);`]
 For degrees of freedom parameter [nu],
 the (*unscaled*) inverse chi_squared distribution is defined by the probability density function (PDF):
 
-__spaces f(x;[nu]) = 2[super -[nu]/2] x[super -[nu]/2-1] e[super -1/2x] / [Gamma]([nu]/2)
+[expression f(x;[nu]) = 2[super -[nu]/2] x[super -[nu]/2-1] e[super -1/2x] / [Gamma]([nu]/2)]
 
 and Cumulative Density Function (CDF)
 
-__spaces  F(x;[nu]) = [Gamma]([nu]/2, 1/2x) / [Gamma]([nu]/2)
+[expression F(x;[nu]) = [Gamma]([nu]/2, 1/2x) / [Gamma]([nu]/2)]
 
 For degrees of freedom parameter [nu] and scale parameter [xi],
 the *scaled* inverse chi_squared distribution is defined by the probability density function (PDF):
 
-__spaces f(x;[nu], [xi]) = ([xi][nu]/2)[super [nu]/2] e[super -[nu][xi]/2x] x[super -1-[nu]/2] / [Gamma]([nu]/2)
+[expression f(x;[nu], [xi]) = ([xi][nu]/2)[super [nu]/2] e[super -[nu][xi]/2x] x[super -1-[nu]/2] / [Gamma]([nu]/2)]
 
 and Cumulative Density Function (CDF)
 
-__spaces  F(x;[nu], [xi]) = [Gamma]([nu]/2, [nu][xi]/2x) / [Gamma]([nu]/2)
+[expression  F(x;[nu], [xi]) = [Gamma]([nu]/2, [nu][xi]/2x) / [Gamma]([nu]/2)]
 
 The following graphs illustrate how the PDF and CDF of the inverse chi_squared distribution
 varies for a few values of parameters [nu] and [xi]:
@@ -148,8 +148,8 @@ are used for the inverse gamma function: [alpha] = [nu]/2 and [beta] = [nu] * [x
 [[pdf][Using the relation: pdf = __gamma_p_derivative([alpha], [beta]/ x, [beta]) / x * x ]]
 [[cdf][Using the relation: p = __gamma_q([alpha], [beta] / x) ]]
 [[cdf complement][Using the relation: q = __gamma_p([alpha], [beta] / x) ]]
-[[quantile][Using the relation: x = [beta][space]/ __gamma_q_inv([alpha], p) ]]
-[[quantile from the complement][Using the relation: x = [alpha][space]/ __gamma_p_inv([alpha], q) ]]
+[[quantile][Using the relation: x = [beta]/ __gamma_q_inv([alpha], p) ]]
+[[quantile from the complement][Using the relation: x = [alpha]/ __gamma_p_inv([alpha], q) ]]
 [[mode][[nu] * [xi] / ([nu] + 2) ]]
 [[median][no closed form analytic equation is known, but is evaluated as quantile(0.5)]]
 [[mean][[nu][xi] / ([nu] - 2) for [nu] > 2, else a __domain_error]]