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The beta distribution is a family of distributions defined over \([0,1]\) parameterized by two positive shape parameters \(a\), and \(b\).
Returns the value at x of the density function of a
\({\it Beta}(a,b)\)
random variable, with \(a,b>0\). To make use of this function, write first load("distrib")
.
The pdf is
Returns the value at x of the distribution function of a \({\it Beta}(a,b)\) random variable, with \(a,b>0\).
The cdf is
(%i1) load ("distrib")$
(%i2) cdf_beta(1/3,15,2); 11 (%o2) -------- 14348907
(%i3) float(%); (%o3) 7.666089131388195e-7
Returns the q-quantile of a
\({\it Beta}(a,b)\)
random variable, with \(a,b>0\); in other words, this is the inverse of cdf_beta
. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib")
.
Returns the mean of a
\({\it Beta}(a,b)\)
random variable, with \(a,b>0\). To make use of this function, write first load("distrib")
.
The mean is
Returns the variance of a
\({\it Beta}(a,b)\)
random variable, with \(a,b>0\). To make use of this function, write first load("distrib")
.
The variance is
Returns the standard deviation of a
\({\it Beta}(a,b)\)
random variable, with \(a,b>0\). To make use of this function, write first load("distrib")
.
The standard deviation is
Returns the skewness coefficient of a
\({\it Beta}(a,b)\)
random variable, with \(a,b>0\). To make use of this function, write first load("distrib")
.
The skewness coefficient is
Returns the kurtosis coefficient of a
\({\it Beta}(a,b)\)
random variable, with \(a,b>0\). To make use of this function, write first load("distrib")
.
The kurtosis coefficient is
Returns a
\({\it Beta}(a,b)\)
random variate, with \(a,b>0\). Calling random_beta
with a third argument n, a random sample of size n will be simulated.
The implemented algorithm is defined in Cheng, R.C.H. (1978). Generating Beta Variates with Nonintegral Shape Parameters. Communications of the ACM, 21:317-322
To make use of this function, write first load("distrib")
.