DiscreteDistribution-class is the mother-class of the classes
Poisson. Further discrete distributions can be defined either by
declaration of own random number generator, density and cumulative distribution and quantile functions, or as result of a
convolution of two discrete distributions or by application of a mathematical operator to a discrete distribution. An
additional way is, to specify only the random number generator. The function
RtoDPQ.d then approximates the three
q by random sampling.
Working with a computer, we use a finite interval as support which carries at least mass
Objects from the Class
Objects can be created by calls of the form
new("DiscreteDistribution", r, d, p, q).
The result of this call is a discrete distribution.
"Distribution", by class
B = Binom(prob=0.1,size=10) # B is a Binomial distribution with prob=0.1 and size=10. P = Pois(lambda=1) # P is a Poisson distribution with lambda=1. D1 = B+1 # a new discrete distributions with exact slots d, p, q D2 = D1*3 # a new discrete distributions with exact slots d, p, q D3 = B+P # a new discrete distributions with approximated slots d, p, q D4 = D1+P # a new discrete distributions with approximated slots d, p, q support(D4) # the (approximated) support of this distribution is 1, 2, ..., 21 r(D4)(1) # one random number generated from this distribution, e.g. 4 d(D4)(1) # The (approximated) density for x=1 is 0.1282716. p(D4)(1) # The (approximated) probability that x<=1 is 0.1282716. q(D4)(.5) # The (approximated) 50 percent quantile is 3.