Generate Binomial random numbers.
The binomial distribution is calculated by first calculating the natural logarithm of each term and then applying the exponential function to the result. (See java source code for real function Binomial). Generate each binomial random number using a uniform random number as a search key into the cumulative density function to locate the integer value. (See java source code for real function BinomialRandom.) As a check for this calculation, count the number of random numbers for each value of k using real function BinomialRandomCnt. The binomial Distribution is plotted (See plot page BinomialDist) with the counts of the random numbers normalized by the total number of random numbers generated. For p=0.5, the Bernoulli numbers are calculated as a check. It is not necessary to include or call the BinomialRandomCnt java code if the checking routine is not counted. The program is demonstrated for n=8, p=0.5. As t.max is increased, the difference between Binomial(k,n,p) and the distribution of the generated binomial random numbers equal to k becomes smaller and smaller. Try setting t.max to 1.0E5
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
We welcome comments and feedback for this model. Please use the button below to send comments:
Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.