pdfsqcdf {asymmetry.measures} | R Documentation |
f^2(x)F(x)
Return the product f^2(x)F(x)
pdfsqcdf(s,dist, p1,p2)
s |
A scalar or vector: the x-axis grid points where the probability density function will be evaluated. |
dist |
Character string, used as a switch to the user selected distribution function (see details below). |
p1 |
A scalar. Parameter 1 (vector or object) of the selected density. |
p2 |
A scalar. Parameter 2 (vector or object) of the selected density. |
Based on user-specified argument dist
, the function returns the value of f^2(x)F(x)dx
, used in the definitions of \rho_p^*
, \rho_p
and their exact versions.
Supported distributions (along with the corresponding dist
values) are:
weib: The weibull distribution is implemented as
f(s;p_1,p_2)= \frac{p_1}{p_2} \left (\frac{s}{p_2}\right )^{p_1-1} \exp \left \{- \left (\frac{s}{p_2}\right )^{p_1} \right \}
with s \ge 0
where p_1
is the shape parameter and p_2
the scale parameter.
lognorm: The lognormal distribution is implemented as
f(s) = \frac{1}{p_2s\sqrt{2\pi}}e^{-\frac{(log s -p_1)^2}{2p_2^2}}
where p_1
is the mean and p_2
is the standard deviation of the distirbution.
norm: The normal distribution is implemented as
f(s) = \frac{1}{p_2\sqrt{2 \pi}}e^{-\frac{ (s - p_1)^2 }{ 2p_2^2 }}
where p_1
is the mean and the p_2
is the standard deviation of the distirbution.
uni: The uniform distribution is implemented as
f(s) = \frac{1}{p_2-p_1}
for p_1 \le s \le p_2
.
cauchy: The cauchy distribution is implemented as
f(s)=\frac{1}{\pi p_2 \left \{1+( \frac{s-p_1}{p_2})^2\right \} }
where p_1
is the location parameter and p_2
the scale parameter.
fnorm: The half normal distribution is implemented as
2 f(s)-1
where
f(s) = \frac{1}{sd\sqrt{2 \pi} }e^{-\frac{s^2}{2 sd^2 }},
and sd=\sqrt{\pi/2}/p_1
.
normmixt:The normal mixture distribution is implemented as
f(s)=p_1\frac{1}{p_2[2] \sqrt{2\pi} } e^{- \frac{ (s - p_2[1])^2}{2p_2[2]^2}} +(1-p_1)\frac{1}{p_2[4]\sqrt{2\pi}} e^{-\frac{(s - p_2[3])^2}{2p_2[4]^2 }}
where p1
is a mixture component(scalar) and p_2
a vector of parameters for the mean and variance of the two mixture components p_2= c(mean1, sd1, mean2, sd2)
.
skewnorm: The skew normal distribution with parameter p_1
is implemented as
f(s)=2\phi(s)\Phi(p_1s)
.
fas: The Fernandez and Steel distribution is implemented as
f(s; p_1, p_2) = \frac{2}{p_1+\frac{1}{p_1}} \left \{ f_t(s/p_1; p_2) I_{\{s \ge 0\}} + f_t(p_1s; p_2)I_{\{s<0 \}}\right \}
where f_t(x;\nu)
is the p.d.f. of the t
distribution with \nu = 5
degrees of freedom. p_1
controls the skewness of the distribution with values between (0, +\infty)
and p_2
denotes the degrees of freedom.
shash: The Sinh-Arcsinh distribution is implemented as
f(s;\mu, p_1, p_2, \tau) = \frac{ce^{-r^2/2}}{\sqrt{2\pi }} \frac{1}{p_2} \frac{1}{2} \sqrt{1+z^2}
where r=\sinh(\sinh(z)-(-p_1))
, c=\cosh(\sinh(z)-(-p_1))
and z=((s-\mu)/p2)
. p_1
is the vector of skewness, p_2
is the scale parameter, \mu=0
is the location parameter and \tau=1
the kurtosis parameter.
A vector containing the user selected density values at the user specified points s
.
Dimitrios Bagkavos and Lucia Gamez Gallardo
R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com> ,Lucia Gamez Gallardo <gamezgallardolucia@gmail.com>
selected.dens <- "weib" #select Weibull
shape <- 2 # specify shape parameter
scale <- 1 # specify scale parameter
xout <- seq(0.1,5,length=50) #design point
pdfsqcdf(xout,selected.dens,shape,scale) # calculate pdfsqcdf function at xout