Imported Upstream version 1.72.0

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

diff --git a/libs/math/doc/distributions/fisher.qbk b/libs/math/doc/distributions/fisher.qbk
index f09388d..bd62dfb 100644 (file)
--- a/libs/math/doc/distributions/fisher.qbk
+++ b/libs/math/doc/distributions/fisher.qbk
@@ -27,11 +27,11 @@
    }} //namespaces
 
 The F distribution is a continuous distribution that arises when testing
-whether two samples have the same variance.  If [chi][super 2][sub m][space] and
-[chi][super 2][sub n][space] are independent variates each distributed as 
+whether two samples have the same variance.  If [chi][super 2][sub m] and
+[chi][super 2][sub n] are independent variates each distributed as 
 Chi-Squared with /m/ and /n/ degrees of freedom, then the test statistic:
 
-F[sub n,m][space] = ([chi][super 2][sub n][space] / n) / ([chi][super 2][sub m][space] / m)
+[expression F[sub n,m] = ([chi][super 2][sub n] / n) / ([chi][super 2][sub m] / m)]
 
 Is distributed over the range \[0, [infin]\] with an F distribution, and
 has the PDF:
@@ -100,13 +100,13 @@ Direct differentiation of the CDF expressed in terms of the incomplete beta func
 
 led to the following two formulas:
 
-f[sub v1,v2](x) = y * __ibeta_derivative(v2 \/ 2, v1 \/ 2, v2 \/ (v2 + v1 * x))
+[expression f[sub v1,v2](x) = y * __ibeta_derivative(v2 \/ 2, v1 \/ 2, v2 \/ (v2 + v1 * x))]
 
 with y = (v2 * v1) \/ ((v2 + v1 * x) * (v2 + v1 * x))
 
 and
 
-f[sub v1,v2](x) = y * __ibeta_derivative(v1 \/ 2, v2 \/ 2, v1 * x \/ (v2 + v1 * x))
+[expression f[sub v1,v2](x) = y * __ibeta_derivative(v1 \/ 2, v2 \/ 2, v1 * x \/ (v2 + v1 * x))]
 
 with y = (z * v1 - x * v1 * v1) \/ z[super 2]
 
@@ -118,11 +118,11 @@ The aim is to keep the /x/ argument to __ibeta_derivative away from 1 to avoid
 rounding error. ]]
 [[cdf][Using the relations:
 
-p = __ibeta(v1 \/ 2, v2 \/ 2, v1 * x \/ (v2 + v1 * x))
+[expression p = __ibeta(v1 \/ 2, v2 \/ 2, v1 * x \/ (v2 + v1 * x))]
 
 and
 
-p = __ibetac(v2 \/ 2, v1 \/ 2, v2 \/ (v2 + v1 * x))
+[expression :p = __ibetac(v2 \/ 2, v1 \/ 2, v2 \/ (v2 + v1 * x))]
 
 The first is used for v1 * x > v2, otherwise the second is used.
 
@@ -131,11 +131,11 @@ avoid rounding error. ]]
 
 [[cdf complement][Using the relations:
 
-p = __ibetac(v1 \/ 2, v2 \/ 2, v1 * x \/ (v2 + v1 * x))
+[expression p = __ibetac(v1 \/ 2, v2 \/ 2, v1 * x \/ (v2 + v1 * x))]
 
 and
 
-p = __ibeta(v2 \/ 2, v1 \/ 2, v2 \/ (v2 + v1 * x))
+[expression p = __ibeta(v2 \/ 2, v1 \/ 2, v2 \/ (v2 + v1 * x))]
 
 The first is used for v1 * x < v2, otherwise the second is used.
 
@@ -143,15 +143,15 @@ The aim is to keep the /x/ argument to __ibeta well away from 1 to
 avoid rounding error. ]]
 [[quantile][Using the relation: 
 
-x = v2 * a \/ (v1 * b)
+[expression x = v2 * a \/ (v1 * b)]
 
 where:
 
-a = __ibeta_inv(v1 \/ 2, v2 \/ 2, p)
+[expression a = __ibeta_inv(v1 \/ 2, v2 \/ 2, p)]
 
 and
 
-b = 1 - a
+[expression b = 1 - a]
 
 Quantities /a/ and /b/ are both computed by __ibeta_inv without the
 subtraction implied above.]]
@@ -159,15 +159,15 @@ subtraction implied above.]]
 
 from the complement][Using the relation:
 
-x = v2 * a \/ (v1 * b)
+[expression x = v2 * a \/ (v1 * b)]
 
 where
 
-a = __ibetac_inv(v1 \/ 2, v2 \/ 2, p)
+[expression a = __ibetac_inv(v1 \/ 2, v2 \/ 2, p)]
 
 and
 
-b = 1 - a
+[expression b = 1 - a]
 
 Quantities /a/ and /b/ are both computed by __ibetac_inv without the
 subtraction implied above.]]
@@ -180,7 +180,7 @@ subtraction implied above.]]
     Weisstein, Eric W. "F-Distribution." From MathWorld--A Wolfram Web Resource.]  ]]
 ]
 
-[endsect][/section:f_dist F distribution]
+[endsect] [/section:f_dist F distribution]
 
 [/ fisher.qbk
   Copyright 2006 John Maddock and Paul A. Bristow.