# Boost-Commit :

From: pbristow_at_[hidden]
Date: 2007-08-06 08:10:59

Author: pbristow
Date: 2007-08-06 08:10:58 EDT (Mon, 06 Aug 2007)
New Revision: 38472
URL: http://svn.boost.org/trac/boost/changeset/38472

Log:
Problem with find_minimum_number_of_trials - needs attention?
Text files modified:
sandbox/math_toolkit/libs/math/example/negative_binomial_example1.cpp | 96 ++++++++++++++++++++++++++++++++++-----
1 files changed, 83 insertions(+), 13 deletions(-)

Modified: sandbox/math_toolkit/libs/math/example/negative_binomial_example1.cpp
==============================================================================
--- sandbox/math_toolkit/libs/math/example/negative_binomial_example1.cpp (original)
+++ sandbox/math_toolkit/libs/math/example/negative_binomial_example1.cpp 2007-08-06 08:10:58 EDT (Mon, 06 Aug 2007)
@@ -72,8 +72,11 @@
using std::cout;
using std::endl;
using std::noshowpoint;
+ using std::fixed;
+ using std::right;
#include <iomanip>
- using std::setprecision;
+ using std::setprecision;
+ using std::setw;

int main()
{
@@ -166,25 +169,81 @@
cout << "If the confidence of meeting sales quota is " << 0.
<< ", then the finishing house is " << quantile(nb, 0.) + sales_quota << endl;

+ cout << "If the confidence of meeting sales quota is " << 0.5
+ << ", then the finishing house is " << quantile(nb, 0.5) + sales_quota << endl;
+
cout << "If the confidence of meeting sales quota is " << 1 - 0.00151 // 30 th
<< ", then the finishing house is " << quantile(nb, 1 - 0.00151) + sales_quota << endl;

// If the opposite is true, we don't want to assume any confidence, then
- // this is tantamount to assuming that the first sales_quota will be successful.
+ // this is tantamount to assuming that all the first sales_quota will be successful sales.
cout << "If confidence of meeting quota is zero (we assume all houses are successful sales)"
", then finishing house is " << sales_quota << endl;

-
- int const pssize = 11;
- double ps[pssize] = {0., 0.001, 0.01, 0.05, 0.1, 0.5, 0.9, 0.95, 0.99, 0.999, 1.};
- for (int i = 0; i < pssize; i++)
+ //int const pssize = 11;
+ double ps[] = {0., 0.001, 0.01, 0.05, 0.1, 0.5, 0.9, 0.95, 0.99, 0.999, 1.};
+ // Confidence as fraction = 1-alpha, as percent = 100 * (1-alpha[i])
+ for (int i = 0; i < sizeof(ps)/sizeof(ps[0]); i++)
{
cout << "If confidence of meeting quota is " << ps[i]
- << ", then finishing house is " << ceil(quantile(nb, ps[i])) + sales_quota << endl;
+ << ", then finishing house is " << ceil(quantile(nb, ps[i])) + sales_quota
+ << endl;
+ }
+ cout << "If we demand a confidence of meeting sales quota of unity"
+ ", then we can never be certain of selling 5 bars, so the finishing house is infinite!" << endl;
+
+ // Define a table of significance levels:
+ double alpha[] = { 1., 0.99999, 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 , 0.000000001};
+
+ // Now turn the question on its head as ask how many houses for a given confidence.
+
+ cout << "\n"
+ "Confidence (%) Minimum houses for " << sales_quota << " sales" << endl;
+ for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
+ { // Confidence values %:
+ cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]) << " "
+ // find_minimum_number_of_trials
+ << setw(6) << right
+ << (int)ceil(negative_binomial::find_minimum_number_of_trials(sales_quota, success_fraction, alpha[i]))
+ << endl;
}
+ cout << endl;
+
+ /*
+ Notes:
+Confidence (%) Minimum houses for 5 sales
+ 0.000 5 only if confidence is really zero can we assume that all visits will be successful.
+ 0.001 6 So even a tiny increase means we must allow for one failure to sell.
+ 50.000 10
+
+ But above using quantile(nb, 0.5) + sales_quota
+
+" If the confidence of meeting sales quota is 0.5, then the finishing house is 12 "
+
+Probability of selling his quota of 5 candy bars
+on or before the 10th house is 0.3669
+
+Probability that Pat finishes on the 11th house is 0.10033
+Probability of selling his quota of 5 candy bars
+on or before the 11th house is 0.46723
+
+Probability that Pat finishes on the 12th house is 0.094596
+Probability of selling his quota of 5 candy bars
+on or before the 12th house is 0.56182
+
+So is this formula wrong / over optimistic?
+
+ 75.000 11
+ 90.000 13
+ 95.000 15
+ 99.000 18
+ 99.900 21
+ 99.990 25
+ 99.999 28
+
+ */
+

- cout << "If we demand a confidence of meeting sales quota of unity"
- ", then we can never be certain of selling 5 bars, so the finishing house is infinite!" << endl;
}
catch(const std::exception& e)
{
@@ -244,7 +303,8 @@
negative_binomial_example1.cpp
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\negative_binomial_example1.exe"
-Example 1 using the Negative Binomial Distribution. ..\..\..\..\..\..\boost-sandbox\math_toolkit\libs\math\example\negative_binomial_example1.cpp Fri Aug 3 14:13:05 2007 140050727
+Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\negative_binomial_example1.exe"
+Example 1 using the Negative Binomial Distribution. ..\..\..\..\..\..\boost-sandbox\math_toolkit\libs\math\example\negative_binomial_example1.cpp Mon Aug 6 12:57:09 2007 140050727
Selling candy bars - an example of using the negative binomial distribution.
An example by Dr. Diane Evans,
Professor of Mathematics at Rose-Hulman Institute of Technology,
@@ -278,6 +338,7 @@
If the confidence of meeting sales quota is 0.17367, then the finishing house is 8
If the confidence of meeting sales quota is 1, then the finishing house is 1.#INF
If the confidence of meeting sales quota is 0, then the finishing house is 5
+If the confidence of meeting sales quota is 0.5, then the finishing house is 12
If the confidence of meeting sales quota is 0.99849, then the finishing house is 31
If confidence of meeting quota is zero (we assume all houses are successful sales), then finishing house is 5
If confidence of meeting quota is 0, then finishing house is 5
@@ -291,9 +352,18 @@
If confidence of meeting quota is 0.99, then finishing house is 25
If confidence of meeting quota is 0.999, then finishing house is 32
If confidence of meeting quota is 1, then finishing house is 1.#INF
-If we demand a confidence of meeting sales quota of unity,
-then we can never be certain of selling 5 bars, so the finishing house is infinite!
-
+If we demand a confidence of meeting sales quota of unity, then we can never be certain of selling 5 bars, so the finishing house is infinite!
+Confidence (%) Minimum houses for 5 sales
+ 0.000 5
+ 0.001 6
+ 50.000 10
+ 75.000 11
+ 90.000 13
+ 95.000 15
+ 99.000 18
+ 99.900 21
+ 99.990 25
+ 99.999 28

*/