ATP Definition: POISSON (87862)

   POISSON(x,mean,cumulative)
				

MORE INFORMATION

The POISSON function returns the result of the Poisson probability distribution function for a particular value of the random variable X. It follows the form "Poisson(x,mean,cumulative)", where:

   x = number of events
   mean = expected value or average of the distribution
   cumulative = logical value specifying whether to return the cumulative
   distribution or the probability mass function.
				

The Microsoft Excel function approximates the Poisson distribution with the following code:

   #include  <math.h>

   #define PI 3.141592654

   float poidev(xm,idum)
   float xm;
   int *idum;

   {

           static float sq,alxm,g,oldm=(-1.0)
           float em,t,y;
           float ran1(),gammln();

           if (xm < 12.0) {
                   if (xm != oldm) {
                           oldm=xm;
                           g=exp(-xm);
                   }
                   em = -1;
                   t = 1.0;
                   do {
                           em += 1.0;
                           t *= ran1(idum);
                   } while (t > g);
           } else {
                   if (xm != oldm) {
                           oldm=xm;
                           sq=sqrt(2.0*xm);
                           alxm=log(xm);
                           g=xm*alxm-gammln(xm+1.0);
                   }
                   do {
                           do {
                                   y=tan(PI*ran1(idum));
                                   em=sq*y*xm;
                           } while (em < 0.0);
                           em=floor(em);
                           t=0.9*(1.0+y*y)*exp(em*alxm-gammln(em+1.0)-g);
                   } while ran1(idum) < t);
           }
           return em;

   }
				

NOTE: The corresponding code for the gammln function can be found by querying on keywords "gammln" and "code".

The POISSON function returns the result of the Poisson probability distribution function for a particular value of the random variable X. The Poisson distribution is useful in predicting the number of events over a specific time period; for example the number of ships arriving at a pier between noon and midnight. Given that the mean number of arrivals was 5, to calculate the probability that exactly 3 ships would arrive, use POISSON(3,5,false). To find the probability that 3 or less ships would arrive, use POISSON(3,5,true).