From: pbristow_at_[hidden]
Date: 2007-09-16 11:19:47
Author: pbristow
Date: 2007-09-16 11:19:47 EDT (Sun, 16 Sep 2007)
New Revision: 39320
URL: http://svn.boost.org/trac/boost/changeset/39320
Log:
Corrections & some improvements but more desirable.
Text files modified:
sandbox/math_toolkit/libs/math/example/binomial_quiz_example.cpp | 187 +++------------------------------------
1 files changed, 17 insertions(+), 170 deletions(-)
Modified: sandbox/math_toolkit/libs/math/example/binomial_quiz_example.cpp
==============================================================================
--- sandbox/math_toolkit/libs/math/example/binomial_quiz_example.cpp (original)
+++ sandbox/math_toolkit/libs/math/example/binomial_quiz_example.cpp 2007-09-16 11:19:47 EDT (Sun, 16 Sep 2007)
@@ -50,51 +50,6 @@
using std::setprecision;
//][/binomial_quiz_example1]
-//[binomial_confidence_limits
-void confidence_limits_on_frequency(unsigned trials, unsigned successes)
-{ // trials = Total number of trials, successes = Total number of observed successes.
-
- // Calculate confidence limits for an observed
- // frequency of occurrence that follows a binomial distribution.
- // Print out general info:
- cout <<
- "___________________________________________\n"
- "2-Sided Confidence Limits For Success Ratio\n"
- "___________________________________________\n\n";
- cout << setprecision(7);
- cout << setw(40) << left << "Number of Observations"
- << "= " << trials << "\n";
- cout << setw(40) << left << "Number of successes"
- << "= " << successes << "\n";
- cout << setw(40) << left << "Sample frequency of occurrence"
- << "= " << double(successes) / trials << "\n";
-
- // Define a table of significance levels:
- double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
- //
- // Print table header:
- //
- cout << "\n\n"
- "___________________________________________\n"
- "Confidence Lower Upper\n"
- " Value (%) Limit Limit\n"
- "___________________________________________\n";
-
- for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
- { // Now print out the data for the table rows.
- // Confidence value:
- cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]);
- // Calculate bounds:
- double l = binomial::estimate_lower_bound_on_p(trials, successes, alpha[i]/2);
- double u = binomial::estimate_upper_bound_on_p(trials, successes, alpha[i]/2);
- // And print limits:
- cout << fixed << setprecision(5) << setw(15) << right << l;
- cout << fixed << setprecision(5) << setw(15) << right << u << endl;
- }
- cout << endl;
-} // void confidence_limits_on_frequency()
-//] [/binomial_confidence_limits]
-
//[binomial_quiz_example2
int main()
{
@@ -221,8 +176,6 @@
cout << "Mode (the most frequent) is " << mode(quiz) << endl;
cout << "Skewness is " << skewness(quiz) << endl;
-
-
/*`
Show the use of quantiles (percentiles or percentage points) for a
few probability levels:
@@ -291,41 +244,6 @@
<< quantile(complement(quiz_real, 0.25)) << endl; // Real Quartiles 2.2821 to 4.6212
//] [/discrete_quantile_real]
-
-//[binomial_quiz_example3
-
-/*`
-Now we can repeat the confidence intervals for various confidences 1 - alpha,
-probability as % = 100 * (1 - alpha[i]), so alpha 0.05 = 95% confidence.
-*/
- double alpha[] = {0.5, 0.33, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001};
-
- cout << "\n\n"
- "Confidence % Lower Upper ""\n";
- for (unsigned int i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
- {
- cout << fixed << setprecision(3) << setw(10) << right << 100 * (1 - alpha[i]);
- double l = real_quantile_binomial::estimate_lower_bound_on_p(questions, answers, alpha[i]/2);
- double u = real_quantile_binomial::estimate_upper_bound_on_p(questions, answers, alpha[i]/2);
- cout << fixed << setprecision(5) << setw(15) << right << l;
- cout << fixed << setprecision(5) << setw(15) << right << u << endl;
- }
- cout << endl;
-
- // static RealType estimate_lower_bound_on_p(RealType trials, RealType successes, RealType probability)
- int successes = 11;
- cout << "Success fraction " << quiz.success_fraction() << ", "
- << quiz.trials() << " correct needed, " << successes << " successes " << endl;
- cout << "Lower bound = " << binomial::estimate_lower_bound_on_p(quiz.trials(), successes, 0.05) << endl; // 0.51560
- // Bounds now 0.45165 to 0.86789 ????
- // Or equivalently:
- cout << "Lower bound = " << quiz.estimate_lower_bound_on_p(quiz.trials(), successes, 0.05) << endl; // 0.51560
- cout << "Upper bound = " << quiz.estimate_upper_bound_on_p(quiz.trials(), successes, 0.05) << endl; // 0.86789
-
- // Print a table of showing upper and lower bounds for a range of confidence levels.
- confidence_limits_on_frequency(20, 2); // 20 trials, 2 successes
- confidence_limits_on_frequency(200, 20);
- confidence_limits_on_frequency(2000, 200);
}
catch(const std::exception& e)
{ // Always useful to include try & catch blocks because
@@ -338,7 +256,7 @@
}
return 0;
} // int main()
-//] [/binomial_quiz_example3]
+
/*
@@ -346,10 +264,18 @@
Output is:
Binomial distribution example - guessing in a quiz.
-In a quiz with 16 and with a probability of guessing right of 25 % or 1 in 4
+In a quiz with 16 questions and with a probability of guessing right of 25 % or 1 in 4
Probability of getting none right is 0.010023
-Probability of getting at least one right is 0.98998
+Probability of getting at least one right is 0.94655
+Probability of getting none or one right is 0.063476
Probability of getting exactly one right is 0.053454
+Probability of getting exactly 11 right is 0.00024713
+Probability of getting > 10 right (to pass) is 0.00028524
+The probability of getting all the answers wrong by chance is 0.010023
+The probability of getting all the answers right by chance is 2.3283e-010
+The probability of getting exactly 11 answers right by guessing is 0.00024713
+The probability of getting less then 11(< 11) answers right by guessing is 0.99996
+The probability of getting at least 11(>= 11) answers right by guessing is 0.00028524 only 1 in 3505.8
Guessed right Probability
0 0.010023
1 0.053454
@@ -368,16 +294,6 @@
14 2.5146e-007
15 1.1176e-008
16 2.3283e-010
-By guessing, on average, one can expect to get 4 correct answers.
-Standard deviation is 1.7321
-So about 2/3 will lie within 1 standard deviation and get between 3 and 5 correct.
-Mode (the most frequent) is 4
-Skewness is 0.28868
-The probability of getting all the answers wrong by chance is 0.010023
-The probability of getting all the answers right by chance is 2.3283e-010
-The probability of getting exactly 11 answers right by guessing is 0.00024713
-The probability of getting at most 11(<= 11) answers right by guessing is 0.99996
-The probability of getting at least 11(>= 11) answers right by guessing is 3.8107e-005
At most (<=)
Guessed right Probability
0 0.010023
@@ -421,6 +337,12 @@
The probability of getting between 1 and 6 answers right by guessing is 0.91042
The probability of getting between 1 and 8 answers right by guessing is 0.98251
The probability of getting between 4 and 4 answers right by guessing is 0.2252
+The probability of getting between 3 and 5 answers right by guessing is 0.61323
+By guessing, on average, one can expect to get 4 correct answers.
+Standard deviation is 1.7321
+So about 2/3 will lie within 1 standard deviation and get between 3 and 5 correct.
+Mode (the most frequent) is 4
+Skewness is 0.28868
Quantiles
Quartiles 2 to 5
1 sd 2 to 5
@@ -430,81 +352,6 @@
2 to 98% 0 to 8
If guessing then percentiles 1 to 99% will get 0 to 8 right.
Real Quartiles 2.2821 to 4.6212
-Using quantiles:
- p plim
-0.01 0.010022595757618546
- q qlim
-0.98999999999999999 -0.98997740424238145
-com 99% 0 0
-Confidence % Lower Upper
- 50.000 0.16108 0.36424
- 67.000 0.13651 0.40078
- 75.000 0.12318 0.42258
- 90.000 0.09025 0.48440
- 95.000 0.07266 0.52377
- 99.000 0.04545 0.59913
- 99.900 0.02427 0.68125
- 99.990 0.01329 0.74363
- 99.999 0.00737 0.79236
-Success fraction 0.25000, 16.00000 trials
-Lower bound = 0.45165
-Lower bound = 0.45165
-Upper bound = 0.86789
-___________________________________________
-2-Sided Confidence Limits For Success Ratio
-___________________________________________
-Number of Observations = 20
-Number of successes = 2
-Sample frequency of occurrence = 0.1000000
-___________________________________________
-Confidence Lower Upper
- Value (%) Limit Limit
-___________________________________________
- 50.000 0.04812 0.18675
- 75.000 0.03078 0.23163
- 90.000 0.01807 0.28262
- 95.000 0.01235 0.31698
- 99.000 0.00530 0.38713
- 99.900 0.00164 0.47093
- 99.990 0.00051 0.54084
- 99.999 0.00016 0.60020
-___________________________________________
-2-Sided Confidence Limits For Success Ratio
-___________________________________________
-Number of Observations = 200
-Number of successes = 20
-Sample frequency of occurrence = 0.1000000
-___________________________________________
-Confidence Lower Upper
- Value (%) Limit Limit
-___________________________________________
- 50.000 0.08462 0.11824
- 75.000 0.07580 0.12959
- 90.000 0.06726 0.14199
- 95.000 0.06216 0.15021
- 99.000 0.05293 0.16698
- 99.900 0.04343 0.18756
- 99.990 0.03641 0.20571
- 99.999 0.03095 0.22226
-___________________________________________
-2-Sided Confidence Limits For Success Ratio
-___________________________________________
-Number of Observations = 2000
-Number of successes = 200
-Sample frequency of occurrence = 0.1000000
-___________________________________________
-Confidence Lower Upper
- Value (%) Limit Limit
-___________________________________________
- 50.000 0.09536 0.10491
- 75.000 0.09228 0.10822
- 90.000 0.08916 0.11172
- 95.000 0.08720 0.11399
- 99.000 0.08344 0.11850
- 99.900 0.07921 0.12385
- 99.990 0.07577 0.12845
- 99.999 0.07282 0.13256
-Build Time 0:03
*/