Imported Upstream version 1.72.0

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

diff --git a/libs/math/doc/distributions/nc_f.qbk b/libs/math/doc/distributions/nc_f.qbk
index 535a5da..6436c34 100644 (file)
--- a/libs/math/doc/distributions/nc_f.qbk
+++ b/libs/math/doc/distributions/nc_f.qbk
@@ -33,7 +33,7 @@
 The noncentral F distribution is a generalization of the __F_distrib.
 It is defined as the ratio 
 
-   F = (X/v1) / (Y/v2)
+[expression F = (X/v1) / (Y/v2)]
    
 where X is a noncentral [chi][super 2]
 random variable with /v1/ degrees of freedom and non-centrality parameter [lambda], 
@@ -43,7 +43,7 @@ This gives the following PDF:
 
 [equation nc_f_ref1]
 
-where L[sub a][super b](c) is a generalised Laguerre polynomial and B(a,b) is the 
+where ['L[sub a][super b](c)] is a generalised Laguerre polynomial and ['B(a,b)] is the 
 __beta function, or
 
 [equation nc_f_ref2]
@@ -60,7 +60,7 @@ for different values of [lambda]:
 Constructs a non-central beta distribution with parameters /v1/ and /v2/
 and non-centrality parameter /lambda/.
 
-Requires v1 > 0, v2 > 0 and lambda >= 0, otherwise calls __domain_error.
+Requires /v1/ > 0, /v2/ > 0 and lambda >= 0, otherwise calls __domain_error.
 
       RealType degrees_of_freedom1()const;
       
@@ -104,43 +104,43 @@ is the non-centrality parameter,
 [[Function][Implementation Notes]]
 [[pdf][Implemented in terms of the non-central beta PDF using the relation:
 
-f(x;v1,v2;[lambda]) = (v1\/v2) / ((1+y)*(1+y)) * g(y\/(1+y);v1\/2,v2\/2;[lambda])
+[role serif_italic f(x;v1,v2;[lambda]) = (v1\/v2) / ((1+y)*(1+y)) * g(y\/(1+y);v1\/2,v2\/2;[lambda])]
 
-where g(x; a, b; [lambda]) is the non central beta PDF, and:
-
-y = x * v1 \/ v2
+where [role serif_italic g(x; a, b; [lambda])] is the non central beta PDF, and:
+ 
+[role serif_italic y = x * v1 \/ v2]
 ]]
 [[cdf][Using the relation:
 
-p = B[sub y](v1\/2, v2\/2; [lambda])
+[role serif_italic p = B[sub y](v1\/2, v2\/2; [lambda])]
 
-where B[sub x](a, b; [lambda]) is the noncentral beta distribution CDF and
+where [role serif_italic B[sub x](a, b; [lambda])] is the noncentral beta distribution CDF and
 
-y = x * v1 \/ v2
+[role serif_italic y = x * v1 \/ v2]
 
 ]]
 
 [[cdf complement][Using the relation:
 
-q = 1 - B[sub y](v1\/2, v2\/2; [lambda])
+[role serif_italic q = 1 - B[sub y](v1\/2, v2\/2; [lambda])]
 
-where 1 - B[sub x](a, b; [lambda]) is the complement of the 
+where [role serif_italic 1 - B[sub x](a, b; [lambda])] is the complement of the 
 noncentral beta distribution CDF and
 
-y = x * v1 \/ v2
+[role serif_italic y = x * v1 \/ v2]
 
 ]]
 [[quantile][Using the relation:
 
-x = (bx \/ (1-bx)) * (v1 \/ v2)
+[role serif_italic x = (bx \/ (1-bx)) * (v1 \/ v2)]
 
 where
 
-bx = Q[sub p][super -1](v1\/2, v2\/2; [lambda])
+[role serif_italic bx = Q[sub p][super -1](v1\/2, v2\/2; [lambda])]
 
 and 
 
-Q[sub p][super -1](v1\/2, v2\/2; [lambda])
+[role serif_italic Q[sub p][super -1](v1\/2, v2\/2; [lambda])]
 
 is the noncentral beta quantile.
 
@@ -150,18 +150,18 @@ is the noncentral beta quantile.
 from the complement][
 Using the relation:
 
-x = (bx \/ (1-bx)) * (v1 \/ v2)
+[role serif_italic x = (bx \/ (1-bx)) * (v1 \/ v2)]
 
 where
 
-bx = QC[sub q][super -1](v1\/2, v2\/2; [lambda])
+[role serif_italic bx = QC[sub q][super -1](v1\/2, v2\/2; [lambda])]
 
 and 
 
-QC[sub q][super -1](v1\/2, v2\/2; [lambda])
+[role serif_italic QC[sub q][super -1](v1\/2, v2\/2; [lambda])]
 
 is the noncentral beta quantile from the complement.]]
-[[mean][v2 * (v1 + l) \/ (v1 * (v2 - 2))]]
+[[mean][[role serif_italic v2 * (v1 + l) \/ (v1 * (v2 - 2))]]]
 [[mode][By numeric maximalisation of the PDF.]]
 [[variance][Refer to, [@http://mathworld.wolfram.com/NoncentralF-Distribution.html
     Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource.]  ]]