Database Reference
In-Depth Information
i-r)*Math.pow(1-p, r)*Math.pow(p,
i-r);
[[CLOSE-LW-CODE80]]
}
These distributions have a variety of applications. From the descriptions,
you can probably guess that they are useful in quality control and
monitoring applications.
Poisson Distribution
The final distribution covered in this section is the
Poisson distribution
. It
models the distribution of the number of events that occur in a finite period
of time—for example, the number of phone calls received per hour or the
number of cars that arrive at a light while it is red:
public static double dpois(int i,double p) {
return Math.
pow
(p, i)*Math.
exp
(-p)
/Arithmetic.
factorial
(i);
}
The Poisson distribution is also used as an approximation of the binomial
distribution when p stays constant but n gets very large. When this happens,
it is often more convenient to work with the Poisson distribution than the
binomial distribution in these settings, and when n ≥ 100 and n×p ≤ 10 the
Poisson is considered to be a very good approximation.
Continuous Distributions
When the distribution is concerned with something truly continuous, such
as the distribution of heights in a population, things are a little bit different.
Unlike the discrete case, it is difficult to talk about P(X = i). When someone
says they are six feet tall, they are not exactly six feet tall. They are perhaps
six feet tall plus some quantization factor (say, half an inch).
To get around this problem for continuous distributions, rather than
working with P(X=i), the distribution is defined in terms of P(X≤x), which is
called the
cumulative distribution function
(
CDF
). To get back to something
more like the continuous case, take P(X≤x+h) - P(X≤x) and then let h
become infinitesimally small. If this sounds like taking a derivative in
calculus, that's because it is. This function, usually written p(x), is called
