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Normal random variables (also called Gaussian) is denoted by \({\it Normal}(m, s)\) where \(m\) is the mean and \(s > 0\) is the standard deviation.
Returns the value at x of the density function of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The pdf is
Returns the value at x of the distribution function of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\). This function is defined in terms of Maxima’s built-in error function erf
.
The cdf can be written analytically:
(%i1) load ("distrib")$
(%i2) cdf_normal(x,m,s); x - m erf(---------) sqrt(2) s 1 (%o2) -------------- + - 2 2
See also erf
.
Returns the q-quantile of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\); in other words, this is the inverse of cdf_normal
. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib")
.
(%i1) load ("distrib")$
(%i2) quantile_normal(95/100,0,1); 9 (%o2) sqrt(2) inverse_erf(--) 10
(%i3) float(%); (%o3) 1.644853626951472
Returns the mean of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The mean is
Returns the variance of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The variance is
Returns the standard deviation of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\), namely s. To make use of this function, write first load("distrib")
.
The standard deviation is
Returns the skewness coefficient of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The skewness coefficient is
Returns the kurtosis coefficient of a
\({\it Normal}(m, s)\)
random variable, with \(s>0\), which is always equal to 0. To make use of this function, write first load("distrib")
.
The kurtosis coefficient is
Returns a
\({\it Normal}(m, s)\)
random variate, with \(s>0\). Calling random_normal
with a third argument n, a random sample of size n will be simulated.
This is an implementation of the Box-Mueller algorithm, as described in Knuth, D.E. (1981) Seminumerical Algorithms. The Art of Computer Programming. Addison-Wesley.
To make use of this function, write first load("distrib")
.