Next: Cauchy Random Variable, Previous: Rayleigh Random Variable, Up: Functions and Variables for continuous distributions [Contents][Index]
The Laplace distribution is a continuous probability distribution that is sometimes called the double exponential distribution because it can be thought of as two exponential distributions spliced back to back.
Returns the value at x of the density function of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
Here, \(a\) is the location parameter (or mean), and \(b\) is the scale parameter, related to the variance.
The pdf is $$ f(x; a, b) = {1\over 2b}\exp\left(-{|x-a|\over b}\right) $$
Returns the value at x of the distribution function of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The cdf is $$ F(x; a, b) = \cases{ \displaystyle{1\over 2} \exp\left({x-a\over b}\right) & for $x < a$\cr \cr 1-\displaystyle{1\over 2} \exp\left({x-a\over b}\right) & for $x \ge a$ } $$
Returns the q-quantile of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\); in other words, this is the inverse of cdf_laplace
. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib")
.
Returns the mean of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The mean is $$ E[X] = a $$
Returns the variance of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The variance is $$ V[X] = 2b^2 $$
Returns the standard deviation of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The standard deviation is $$ D[X] = \sqrt{2} b $$
Returns the skewness coefficient of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The skewness coefficient is $$ SK[X] = 0 $$
Returns the kurtosis coefficient of a
\({\it Laplace}(a,b)\)
random variable, with \(b>0\). To make use of this function, write first load("distrib")
.
The kurtosis coefficient is $$ KU[X] = 3 $$
Returns a
\({\it Laplace}(a,b)\)
random variate, with \(b>0\). Calling random_laplace
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")
.
Next: Cauchy Random Variable, Previous: Rayleigh Random Variable, Up: Functions and Variables for continuous distributions [Contents][Index]