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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 $$ f(x; m) = \cases{ me^{-mx} & for $x \ge 0$ \cr 0 & otherwise } $$
(%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 $$ F(x; m) = \cases{ 1 - e^{-mx} & $x \ge 0$ \cr 0 & otherwise } $$
(%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 $$ E[X] = {1\over m} $$
(%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 $$ V[X] = {1\over m^2} $$
(%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 $$ D[X] = {1\over m} $$
(%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 $$ SK[X] = 2 $$
(%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 $$ KU[X] = 6 $$
(%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]