diff --git a/doc/distributions/negative_binomial_example.qbk b/doc/distributions/negative_binomial_example.qbk index a447be06e..8639fcc32 100644 --- a/doc/distributions/negative_binomial_example.qbk +++ b/doc/distributions/negative_binomial_example.qbk @@ -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] diff --git a/example/binomial_coinflip_example.cpp b/example/binomial_coinflip_example.cpp index 8a467cab1..1d59375ae 100644 --- a/example/binomial_coinflip_example.cpp +++ b/example/binomial_coinflip_example.cpp @@ -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 diff --git a/example/binomial_example3.cpp b/example/binomial_example3.cpp index dcb336cb0..2b0509070 100644 --- a/example/binomial_example3.cpp +++ b/example/binomial_example3.cpp @@ -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 diff --git a/example/binomial_example_NAG_C.cpp b/example/binomial_example_NAG_C.cpp index 0407c055a..1020a8cf5 100644 --- a/example/binomial_example_NAG_C.cpp +++ b/example/binomial_example_NAG_C.cpp @@ -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. diff --git a/example/normal_misc_examples.cpp b/example/normal_misc_examples.cpp index b6f245dbf..1d24c54b7 100644 --- a/example/normal_misc_examples.cpp +++ b/example/normal_misc_examples.cpp @@ -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