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Fixed some typos, changes 1 title, and fixed markup in normal_misc_examples.cpp.

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[SVN r38947]
This commit is contained in:
John Maddock
2007-08-25 18:05:41 +00:00
parent 401fd9fda1
commit 32c4c33a03
5 changed files with 20 additions and 15 deletions
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2
doc/distributions/negative_binomial_example.qbk
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@@ -230,7 +230,7 @@ and it is also deliberately over-commented.
[endsect] [/section:negative_binomial_example1]
[section:negative_binomial_example2 Negative Binomial example 2.]
[section:negative_binomial_example2 Negative Binomial Table Printing Example.]
Example program showing output of a table of values of cdf and pdf for various k failures.
[import ../../example/negative_binomial_example2.cpp]
[neg_binomial_example2]

2
example/binomial_coinflip_example.cpp
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@@ -91,7 +91,7 @@ Now we show a variety of predictions on the probability of heads:
cout << "Probability of getting no heads is " << pdf(flip, 0) << endl;
cout << "Probability of getting at least one head is " << 1. - pdf(flip, 0) << endl;
/*`
When we want to calculate the probabilty for a range or values we can sum the PDF's:
When we want to calculate the probability for a range or values we can sum the PDF's:
*/
cout << "Probability of getting 0 or 1 heads is "
<< pdf(flip, 0) + pdf(flip, 1) << endl; // sum of exactly == probabilities

4
example/binomial_example3.cpp
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@@ -5,7 +5,7 @@
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
// Simple example of computing probabilitiesfor a binomial random variable.
// Simple example of computing probabilities for a binomial random variable.
// Replication of source nag_binomial_dist (g01bjc).
// Shows how to replace NAG C library calls by Boost Math Toolkit C++ calls.
@@ -32,7 +32,7 @@ int main()
using boost::math::binomial_distribution;
// This replicates the computation of the examples of using nag-binomial_dist
// using g01bjc in section g01 Somple Calculations on Statistical Data.
// using g01bjc in section g01 Sample Calculations on Statistical Data.
// http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf
// Program results section 8.3 page 3.g01bjc.3
//8.2. Program Data

2
example/binomial_example_NAG_C.cpp
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@@ -5,7 +5,7 @@
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
// Simple example of computing probabilitiesfor a binomial random variable.
// Simple example of computing probabilities for a binomial random variable.
// Replication of source nag_binomial_dist (g01bjc).
// Shows how to replace NAG C library calls by Boost Math Toolkit C++ calls.

25
example/normal_misc_examples.cpp
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@@ -57,13 +57,13 @@ int main()
<< setprecision(precision) << setw(12) << pdf(s, z) << endl;
}
cout.precision(6); // default
/*`And the area under the normal curve from -[infin] upto z,
/*`And the area under the normal curve from -[infin] up to z,
the cumulative distribution function (cdf).
*/
// For a standard normal distribution
cout << "Standard normal mean = "<< s.mean()
<< ", standard deviation = " << s.standard_deviation() << endl;
cout << "Integral (area under the curve) from - infinity upto z " << endl;
cout << "Integral (area under the curve) from - infinity up to z " << endl;
cout << " z " " cdf " << endl;
for (double z = -range; z < range + step; z += step)
{
@@ -129,16 +129,16 @@ that the true occurrence frequency lies *inside* the calculated interval.
/*`Notice the distinction between one-sided (also called one-tailed)
where we are using a > *or* < test (and not both)
and considering the area of the tail (integral) from z upto +[infin],
and considering the area of the tail (integral) from z up to +[infin],
and a two-sided test where we are using two > *and* < tests, and thus considering two tails,
from -[infin] upto z low and z high upto +[infin].
from -[infin] up to z low and z high up to +[infin].
So the 2-sided values alpha[i] are calculated using alpha[i]/2.
If we consider a simple example of alpha = 0.05, then for a two-sided test,
the lower tail area from -[infin] upto -1.96 is 0.025 (alpha/2)
and the upper tail area from +z upto +1.96 is also 0.025 (alpha/2),
and the area between -1.96 upto 12.96 is alpha = 0.95.
the lower tail area from -[infin] up to -1.96 is 0.025 (alpha/2)
and the upper tail area from +z up to +1.96 is also 0.025 (alpha/2),
and the area between -1.96 up to 12.96 is alpha = 0.95.
and the sum of the two tails is 0.025 + 0.025 = 0.05,
*/
@@ -165,19 +165,23 @@ easy to remember proportion of values that lie within 1, 2 and 3 standard deviat
/*`
To a useful precision, the 1, 2 & 3 percentages are 68, 95 and 99.7,
and these are worth memorising as useful 'rules of thumb', as, for example, in
[@http://en.wikipedia.org/wiki/Standard_deviation standard deviation]
[@http://en.wikipedia.org/wiki/Standard_deviation standard deviation]:
[pre
Fraction 1 standard deviation within either side of mean is 0.683
Fraction 2 standard deviations within either side of mean is 0.954
Fraction 3 standard deviations within either side of mean is 0.997
]
We could of course get some really accurate values for these
[@http://en.wikipedia.org/wiki/Confidence_interval confidence intervals]
by using cout.precision(15);
[pre
Fraction 1 standard deviation within either side of mean is 0.682689492137086
Fraction 2 standard deviations within either side of mean is 0.954499736103642
Fraction 3 standard deviations within either side of mean is 0.997300203936740
]
But before you get too excited about this impressive precision,
don't forget that the *confidence intervals of the standard deviation* are surprisingly wide,
@@ -220,7 +224,8 @@ we construct a normal distribution called /bulbs/ with these values:
/*`
[note Real-life failures are often very ab-normal,
with a significant number that 'dead-on-arrival' or suffer failure very early in their life:
the lifetime of the suvivors of 'early mortality' may be well described by the normal distribution.]
the lifetime of the survivors of 'early mortality' may be well described by the normal distribution.]
*/
//] [/normal_bulbs_example1 Quickbook end]
}
{
@@ -445,7 +450,7 @@ Probability distribution function values
3 0.0044318484119380075
4 0.00013383022576488537
Standard normal mean = 0, standard deviation = 1
Integral (area under the curve) from - infinity upto z
Integral (area under the curve) from - infinity up to z
z cdf
-4 3.1671241833119979e-005
-3 0.0013498980316300959