Next: Lognormal Random Variable, Previous: F Random Variable, Up: Functions and Variables for continuous distributions [Contents][Index]
The exponential distribution is the probablity distribution of the time between events in a process where the events occur continuously and independently at a constant average rate.
Returns the value at x of the density function of an \({\it Exponential}(m)\) random variable, with \(m>0\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
The pdf is
(%i1) load ("distrib")$
(%i2) pdf_exp(x,m); - m x (%o2) m %e unit_step(x)
Returns the value at x of the distribution function of an \({\it Exponential}(m)\) random variable, with \(m>0\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
The cdf is
(%i1) load ("distrib")$
(%i2) cdf_exp(x,m); - m x (%o2) (1 - %e ) unit_step(x)
Returns the q-quantile of an
\({\it Exponential}(m)\)
random variable, with \(m>0\); in other words, this is the inverse of cdf_exp
. Argument q must be an element of \([0,1]\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
(%i1) load ("distrib")$
(%i2) quantile_exp(0.56,5); (%o2) 0.1641961104139661
(%i3) quantile_exp(0.56,m); 0.8209805520698303 (%o3) ------------------ m
Returns the mean of an \({\it Exponential}(m)\) random variable, with \(m>0\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
The mean is
(%i1) load ("distrib")$
(%i2) mean_exp(m); 1 (%o2) - m
Returns the variance of an \({\it Exponential}(m)\) random variable, with \(m>0\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
The variance is
(%i1) load ("distrib")$
(%i2) var_exp(m); 1 (%o2) -- 2 m
Returns the standard deviation of an \({\it Exponential}(m)\) random variable, with \(m>0\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
The standard deviation is
(%i1) load ("distrib")$
(%i2) std_exp(m); 1 (%o2) - m
Returns the skewness coefficient of an \({\it Exponential}(m)\) random variable, with \(m>0\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
The skewness coefficient is
(%i1) load ("distrib")$
(%i2) skewness_exp(m); (%o2) 2
Returns the kurtosis coefficient of an \({\it Exponential}(m)\) random variable, with \(m>0\).
The \({\it Exponential}(m)\) random variable is equivalent to the \({\it Weibull}(1,1/m)\) .
The kurtosis coefficient is
(%i1) load ("distrib")$
(%i2) kurtosis_exp(m); (%o2) 6
Returns an
\({\it Exponential}(m)\)
random variate, with \(m>0\). Calling random_exp
with a second argument k, a random sample of size k will be simulated.
The simulation algorithm is based on the general inverse method.
To make use of this function, write first load("distrib")
.
Next: Lognormal Random Variable, Previous: F Random Variable, Up: Functions and Variables for continuous distributions [Contents][Index]