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The lognormal distribution is distribution for a random variable whose logarithm is normally distributed.
Returns the value at x of the density function of a
\({\it Lognormal}(m,s)\)
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
\({\it Lognormal}(m,s)\)
random variable, with \(s>0\). This function is defined in terms of Maxima’s built-in error function erf
.
The cdf is
(%i1) load ("distrib")$
(%i2) cdf_lognormal(x,m,s); log(x) - m erf(----------) sqrt(2) s 1 (%o2) unit_step(x) (--------------- + -) 2 2
See also erf
.
Returns the q-quantile of a
\({\it Lognormal}(m,s)\)
random variable, with \(s>0\); in other words, this is the inverse of cdf_lognormal
. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib")
.
(%i1) load ("distrib")$
(%i2) quantile_lognormal(95/100,0,1); sqrt(2) inverse_erf(9/10) (%o2) %e
(%i3) float(%); (%o3) 5.180251602233015
Returns the mean of a
\({\it Lognormal}(m,s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The mean is
Returns the variance of a
\({\it Lognormal}(m,s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The variance is
Returns the standard deviation of a
\({\it Lognormal}(m,s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The standard deviation is
Returns the skewness coefficient of a
\({\it Lognormal}(m,s)\)
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
\({\it Lognormal}(m,s)\)
random variable, with \(s>0\). To make use of this function, write first load("distrib")
.
The kurtosis coefficient is
Returns a
\({\it Lognormal}(m,s)\)
random variate, with \(s>0\). Calling random_lognormal
with a third argument n, a random sample of size n will be simulated.
Log-normal variates are simulated by means of random normal variates. See random_normal
for details.
To make use of this function, write first load("distrib")
.
Next: Gamma Random Variable, Previous: Exponential Random Variable, Up: Functions and Variables for continuous distributions [Contents][Index]