Creates a Binomial distribution object (Discrete Distribution).

A random variable X is defined to have a binomial distribution if the discrete density function of X is given by pf= [Combination(n, x)*pow(p, x)*pow(1-p, n-x), for x=0,1...,n] or 0 otherwise.

p lies between 0 and i inclusive, n ranges over the positive integers and q=1-p. The mean of a binomial distribution is n*p, the variance of a binomial distribution is n*p*q. The binomial dsitribution reduces to the Bernoulli distribution when n=1. For example, consider sampling with replacement from an urn containing M balls, K of which are defective.

Let X represent the number of defective balls in a sample of size n. The individual draws are Bernoulli trials where 'defective' corresponds to 'success' and the experiment of taking a sample of size n with replacement consists of n repeated independent Bernoulli trials where p=P[Success] = K/M, so X has the binomial distibution.

The string 'Key' resulting from a successful construction of this distribution object can be passed to the following functions in order to query (mean, std deviation and variance) or execute functions (probability function, cumulative density function etc...) based on this distribution object : DDistributionMean(), DDistributionVar(), DDistributionSTD(), DDistributionPF() or DDistributionCDF(). In addition, the string 'Key' resulting from a successful construction of this distribution object will also allow you to construct a process generator object via a call to PGBinomialDistribution(). A process generator object allows you to generate large amounts of random numbers based on this distribution.

Even though PGBinomialDistribution() is the process generator object, the function RandomBinomial() is the actual function that obtains the random numbers given a count parameter and the process generator string 'key'.

This function creates an object and returns a string-key value to represent this created object.
The TAG value of the string-key returned (second part of the key) is : "Binomial"

String CTStatDistributions.BinomialDistribution( _
String Key, _
Long Reload, _
Long Trials, _
Double prob)

=CT.STAT.BinomialDistribution(
Excel String Cell Key,
Excel Numeric Cell Reload,
Excel Numeric Cell Trials,
Excel Numeric Cell prob)

static std::string BinomialDistribution(
std::string Key,
long Reload,
long Trials,
double prob);

System.String CTStatDistributionsSA.BinomialDistribution(
System.String Key,
System.Int32 Reload,
System.Int32 Trials,
System.Double prob);

The C# example below contains all the sub-function calls leading up to this function call. As a result, the example can contain a lot of code.

The VB.NET, J#, C++.NET, Java, Excel VBA, Visual Basic 6 (via COM) and C++ examples below contain function code stubs for the calls leading up to this function call. However, the function call for this function is displayed.
You can easily reproduce the stub functions code from the C# example.