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Returns the value at x of the density function of a
\({\it Gumbel}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The pdf is
Returns the value at x of the distribution function of a
\({\it Gumbel}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The cdf is
Returns the q-quantile of a
\({\it Gumbel}(a,b)\)
random variable, with \(b>0\); in other words, this is the inverse of cdf_gumbel
. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib")
.
Returns the mean of a \({\it Gumbel}(a,b)\) random variable, with \(b>0\).
The mean is
(%i1) load ("distrib")$
(%i2) mean_gumbel(a,b); (%o2) %gamma b + a
where symbol %gamma
stands for the Euler-Mascheroni constant. See also %gamma
.
Returns the variance of a
\({\it Gumbel}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The variance is
Returns the standard deviation of a
\({\it Gumbel}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The standard deviation is
Returns the skewness coefficient of a \({\it Gumbel}(a,b)\) random variable, with \(b>0\).
The skewness coefficient is
(%i1) load ("distrib")$
(%i2) skewness_gumbel(a,b); 3/2 2 6 zeta(3) (%o2) -------------- 3 %pi
where zeta
stands for the Riemann’s zeta function.
Returns the kurtosis coefficient of a
\({\it Gumbel}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The kurtosis coefficient is
Returns a
\({\it Gumbel}(a,b)\)
random variate, with \(b>0\). Calling random_gumbel
with a third argument n, a random sample of size n will be simulated.
The implemented algorithm is based on the general inverse method.
To make use of this function, write first load("distrib")
.