Creates a Poisson distribution object.

A random variable X is defined to have a Poisson distribution if the density of X is given by pf = [ (exp(-L)*pow(L,x))/factorial(x) for x=0,1,2,.. ] 0 otherwise.

The parameter L (lamda) is greater than 0. The mean of a Poisson distribution is L (lamda), the variance of a Poisson distribution is also L (lamba).

The Poisson distribution provides a realistic model for many random phenomena.

Since the values of a Poisson random variable are the non-negative integers, any random phenomenon for which a count of some sort is of interest is a candidate for modelling assuming a Poisson distribution.

For example the number of fatal traffic accidents per week in a given town, the number of telephone calls per hour coming into the switchboard of a large business or the number of defects per unit of some material.

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 PGPoissonDistribution(). A process generator object allows you to generate large amounts of random numbers based on this distribution.

Even though PGPoissonDistribution() is the process generator object, the function RandomPoisson() 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 : "Poisson"

String CTStatDistributions.PoissonDistribution( _
String Key, _
Long Reload, _
Double mu)

=CT.STAT.PoissonDistribution(
Excel String Cell Key,
Excel Numeric Cell Reload,
Excel Numeric Cell mu)

static std::string PoissonDistribution(
std::string Key,
long Reload,
double mu);

System.String CTStatDistributionsSA.PoissonDistribution(
System.String Key,
System.Int32 Reload,
System.Double mu);

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.