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The generator and analysis classes use the following probability distributions as
described in [Watkins 93] and [Kalvelagen 90].
Some use the function, which is defined as :
The distributions are :
- the uniform distribution, this distribution represents the
situation whereby a random number can take values within a finite
range with equal probability. It is characterized
by the following function :
The method in the library takes the upper and lower limit as parameters.
- the exponential distribution, takes the non-negative mean as parameter. Its function :
This function is used to model purely random events such as the time
between arrivals of a customer.
- the hyperexponential distribution, takes the non-negative means and of two
exponential distributions as parameters. It then generates a variate
from the first distribution with chance p and
a variate of the second with chance 1-p. Its function :
- the normal distribution, the first parameter
to this distribution is the mean , the second is the standard deviation
.
It is characterized by the following probability distribution :
This function is used for the modeling of the additive effect of
several independent trials.
- the lognormal distribution,
It is calculated as the logarithm of the normal distribution with
as mean and as standard deviation. Its
probability function :
- the erlang distribution.
It is used to model service times in a
queuing system that has n servers where each server has
a mean service time of . The overall service time of
this system is given by the erlang distribution.
It is characterized by the following distribution :
- the gamma distribution, this distribution is parameterized
by two values and , both greater then 0.
It has the following probability distribution :
- the poisson distribution, gets the mean as parameter. This function is used to model the number
of occurrences, such as the number of component failures, over a given
period of time. It is characterized by the following distribution :
- the geometric distribution, this distribution is characterized
by p, the chance on success. It is used to model the number of
occurrences between two significant events as the number of
failures to acquire a particular resource until the first success.
Its distribution :
- the hypergeometric distribution.
Suppose that a sample of size n is to be randomly chosen (without
replacements) from an urn containing m balls of which mp
are white and m(1-p) are black. The chance of x white
balls selected follows the hypergeometric distribution and is equal to :
- the weibull distribution, it gets and
as parameters, both greater then 0. It is used for reliability
measures such as the lifetime of components. It is characterized by
the following distribution function :
- the binomial distribution,
gets as parameters p, the chance on a success and n, the
number of trials. It is used to model the number of successes in n
independent Bernoulli trials. It has the following probability distribution :
- the negative binomial distribution,
it is parameterized by p, the chance on a success, and
n, the number of successes. The negative binomial distribution
returns the number of failures before the success. You can
think of the number of retransmissions of a file. The negative binomial
distribution is characterized by the following function :
- the beta distribution, this probability function is characterized by the
two parameters and . It is used to model random proportions
as the fraction of customers that could not be served. It has the
following distribution :
- the laplace distribution.
The laplace distribution looks like
the exponential distribution with a mirror image in the y-axis. It has
the following probability function :
- the distribution,
with n, the degrees of freedom as parameter.
It has as probability distribution function :
The distribution is a special case of the gamma distribution with
and .
- the student's t distribution, it
also gets the degrees of freedom as parameter.
If n is large enough (), it can be approximated by the standard
normal distribution. It has as function :
- the F distribution, returns a value of the F distribution, which
is often used for testing variances. The distribution takes
two positive integers as arguments, defining the degrees of freedom
of the variances being tested.
It has a probability distribution function :
- the triangular distribution, it gets the mode of the distribution as parameter. Dependent on the
mode m the distribution is in the function takes on various triangular shapes.
If the mode is equal to 0.5, the triangular distribution is symmetrical. It has the following probability function :
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Up: SIM : a C++
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A Eliens
Tue Oct 31 09:27:21 MET 1995