Database Reference
In-Depth Information
public static double dchisq(double x,double k) {
return (Math.
pow
(x,k/2.0 - 1.0)
*Math.
exp
(-x/2.0))
/(Math.
pow
(2,k/2.0)*Gamma.
gamma
(k/2.0));
}
The
Gamma.gamma()
function in the previous density function is
essentially a continuous version of the factorial distribution. In fact,
Arithmetic.factorial(n)
is equal to
Gamma.gamma(n-1)
.
Exponential, Gamma, and Beta Distributions
If the Poisson distribution is the number of events that occur within a given
time frame, the
exponential distribution
models the waiting time between
theseevents. ItisoftenusedalongwiththePoisson distribution inmodeling
queues. The distribution has a fairly simple density function with a single
parameter:
public static double dexp(double x,double
p
) {
return
p
*Math.
exp
(-x*
p
);
}
The distribution of the waiting time from the first event until the k
th
event,
when the waiting time between each event is exponentially distributed,
is the
gamma distribution
. This distribution takes two parameters, the
p
parameter (called the rate) from the exponential distribution, and a second
parameter
k
(called the shape), which represents the number of events.
The density function clearly shows the relationship between the two
distributions:
public static
double
dgamma(double x,double k,double
p) {
return
Math.pow(p,k)*Math.pow(x,k-1)*Math.exp(-p*x)/
Gamma.gamma(k);
}
The relationship is similar to the one between the geometric distribution
and the negative binomial. Essentially, the exponential distribution is a
special case of the gamma distribution. The chi-square distribution is also
