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The Poisson distribution is a discrete probability distribution. It is the probability that a given number of events occur in a fixed interval when the events occur independently of the time of the last event, and the events occur with a known constant rate.
Returns the value at x of the probability function of a
\({\it Poisson}(m)\)
random variable, with \(m>0\). To make use of this function, write first load("distrib")
.
The pdf is
Returns the value at x of the distribution function of a \({\it Poisson}(m)\) random variable, with \(m>0\).
The cdf is
where \(Q(x,m)\) is the gamma_incomplete_regularized function.
(%i1) load ("distrib")$
(%i2) cdf_poisson(3,5); (%o2) gamma_incomplete_regularized(4, 5)
(%i3) float(%); (%o3) 0.2650259152973619
Returns the q-quantile of a
\({\it Poisson}(m)\)
random variable, with \(m>0\); in other words, this is the inverse of cdf_poisson
. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib")
.
Returns the mean of a
\({\it Poisson}(m)\)
random variable, with \(m>0\). To make use of this function, write first load("distrib")
.
The mean is
Returns the variance of a
\({\it Poisson}(m)\)
random variable, with \(m>0\). To make use of this function, write first load("distrib")
.
The variance is
Returns the standard deviation of a
\({\it Poisson}(m)\)
random variable, with \(m>0\). To make use of this function, write first load("distrib")
.
The standard deviation is
Returns the skewness coefficient of a
\({\it Poisson}(m)\)
random variable, with \(m>0\). To make use of this function, write first load("distrib")
.
The skewness is
Returns the kurtosis coefficient of a Poisson random variable \(Poi(m)\), with \(m>0\). To make use of this function, write first load("distrib")
.
The kurtosis coefficient is
Returns a
\({\it Poisson}(m)\)
random variate, with \(m>0\). Calling random_poisson
with a second argument n, a random sample of size n will be simulated.
The implemented algorithm is the one described in Ahrens, J.H. and Dieter, U. (1982) Computer Generation of Poisson Deviates From Modified Normal Distributions. ACM Trans. Math. Software, 8, 2, June,163-179.
To make use of this function, write first load("distrib")
.
Next: Bernoulli Random Variable, Previous: Binomial Random Variable, Up: Functions and Variables for discrete distributions [Contents][Index]