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The Rayleigh distribution coincides with the \(\chi^2\) distribution with two degrees of freedom.
Returns the value at x of the density function of a \({\it Rayleigh}(b)\) random variable, with \(b>0\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
The pdf is
(%i1) load ("distrib")$
(%i2) pdf_rayleigh(x,b); 2 2 2 - b x (%o2) 2 b x %e unit_step(x)
Returns the value at x of the distribution function of a \({\it Rayleigh}(b)\) random variable, with \(b>0\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
The cdf is
(%i1) load ("distrib")$
(%i2) cdf_rayleigh(x,b); 2 2 - b x (%o2) (1 - %e ) unit_step(x)
Returns the q-quantile of a
\({\it Rayleigh}(b)\)
random variable, with \(b>0\); in other words, this is the inverse of cdf_rayleigh
. Argument q must be an element of \([0,1]\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
(%i1) load ("distrib")$
(%i2) quantile_rayleigh(0.99,b); 2.145966026289347 (%o2) ----------------- b
Returns the mean of a \({\it Rayleigh}(b)\) random variable, with \(b>0\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
The mean is
(%i1) load ("distrib")$
(%i2) mean_rayleigh(b); sqrt(%pi) (%o2) --------- 2 b
Returns the variance of a \({\it Rayleigh}(b)\) random variable, with \(b>0\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
The variance is
(%i1) load ("distrib")$
(%i2) var_rayleigh(b); %pi 1 - --- 4 (%o2) ------- 2 b
Returns the standard deviation of a \({\it Rayleigh}(b)\) random variable, with \(b>0\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
The standard deviation is
(%i1) load ("distrib")$
(%i2) std_rayleigh(b); %pi sqrt(1 - ---) 4 (%o2) ------------- b
Returns the skewness coefficient of a \({\it Rayleigh}(b)\) random variable, with \(b>0\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
The skewness coefficient is
(%i1) load ("distrib")$
(%i2) skewness_rayleigh(b); 3/2 %pi 3 sqrt(%pi) ------ - ----------- 4 4 (%o2) -------------------- %pi 3/2 (1 - ---) 4
Returns the kurtosis coefficient of a \({\it Rayleigh}(b)\) random variable, with \(b>0\).
The \({\it Rayleigh}(b)\) random variable is equivalent to the \({\it Weibull}(2,1/b)\) .
The kurtosis coefficient is
(%i1) load ("distrib")$
(%i2) kurtosis_rayleigh(b); 2 3 %pi 2 - ------ 16 (%o2) ---------- - 3 %pi 2 (1 - ---) 4
Returns a
\({\it Rayleigh}(b)\)
random variate, with \(b>0\). Calling random_rayleigh
with a second 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: Laplace Random Variable, Previous: Weibull Random Variable, Up: Functions and Variables for continuous distributions [Contents][Index]