Returns the value of the selected cumulative distribution function at user supplied grid points.
p.sample(s,dist, p1,p2)A scalar or vector: the x-axis grid points where the cumulative distribution function is be evaluated.
Character string, used as a switch to the user selected distribution function (see details below).
A scalar. Parameter 1 (vector or object) of the selected distribution.
A scalar. Parameter 2 (vector or object) of the selected distribution.
A vector containing the cumulative distribution function values at the user specified points s.
Based on the user-specified argument dist, the function returns the value of the cumulative distribution function at s.
Supported distributions (along with the corresponding dist values) are:
weib: The Weibull distribution is implemented as $$F(s) = 1 - \exp \left \{- \left ( \frac{s}{p_2} \right )^{p_1} \right \} $$ with \(s > 0\) where \(p_1\) is the shape parameter and \(p_2\) the scale parameter.
lognorm: The lognormal distribution is implemented as $$F(s)=\Phi \left ( \frac{\ln s-p_1 }{p_2} \right )$$ where \(p_1\) is the mean,\(p_2\) is the standard deviation and \(\Phi\) is the cumulative distribution function of the standard normal distribution.
norm: The normal distribution is implemented as $$\Phi(s)={\frac {1}{\sqrt {2\pi}p_2 }}\int_{-\infty }^s e^{-\frac{(t-p_1)^2}{2p_2^2}}\,dt$$ where \(p_1\) is the mean and the \(p_2\) is the standard deviation.
uni: The uniform distribution is implemented as $$F(s)=\frac{s-p_1}{p_2-p_1}$$ for \(p_1 \le s \le p_2.\)
cauchy: The cauchy distribution is implemented as $$F(s;p_1,p_2)=\frac{1}{\pi}\arctan \left ( \frac{s-p_1}{p_2} \right ) + \frac{1}{2} $$ where \(p_1\) is the location parameter and \(p_2\) the scale parameter.
fnorm: The half normal distribution is implemented as $$F_S(s;\sigma)=\int_0^s \frac{\sqrt{2/\pi}}{\sigma} \exp \left \{ -\frac{x^2}{2\sigma^2} \right \} \,dx $$ where \(mean=0\) and \(sd=\sqrt{\pi/2}/p_1\).
normmixt: The normal mixture distribution is implemented as $$F(s)=p_1\frac{1}{p_2[2]\sqrt{2\pi}}\int_{-\infty }^{s}e^{-\frac{(t - p_2[1])^2}{2p_2[2]^2}}\,dt + (1-p_1) \frac{1}{p_2[4]\sqrt{2\pi}} \int_{-\infty }^s e^{-\frac{(t - p2[3])^2}{2p_2[4]^2}}\,dt$$ where \(p_1\) 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 is implemented as $$F(y; p_1) = \Phi \left ( \frac{y-\xi}{\omega} \right )-2 T \left ( \frac{y-\xi}{\omega},p_1 \right ) $$ where \(location=\xi=0\), \(scale=\omega=1\), \(parameter=p_1\) and \(T(h, a)\) is the Owens T function, defined by $$T(h,a) = \frac{1}{2\pi}\int_{0}^{a} \exp \left \{ \frac{- 0.5 h^2 (1+x^2) }{1+x^2} \right \} \,dx, -\infty \le h, a \le \infty $$
fas: The Fernandez and Steel distribution is implemented as $$F(s;p_1,p_2) = \frac{2}{p_1+\frac{1}{p_1}} \left \{ \int_{-\infty}^s f_t(x/p_1; p_2)I_{\{x \ge 0\}} \,dx + \int_{-\infty}^s f_t(p_1 x; p_2)I_{\{x<0\}}\, dx \right \} $$ 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 \(p_2\) is the degrees of freedom.
shash: The Sinh-Arcsinh distribution is implemented as $$F(s;\mu, p_2, p_1, \tau) =\int_{-\infty}^s \frac{ce^{-r^2/2}}{\sqrt{2\pi }} \frac{1}{p_2} \frac{1}{2} \sqrt{1+z^2}\,dz $$
where \(r=\sinh(\sinh(z)- p_1)\), \(c=\cosh(\sinh(z)- p_1)\) and \(z=(s-\mu)/p_2\). \(p_1\) is the vector of skewness, \(p_2\) is the scale parameter, \(\mu=0\) is the location parameter and \(\tau=1\) the kurtosis parameter.
# NOT RUN {
selected.d <- "weib" #select Weibull as the CDF
shape <- 2 # specify shape parameter
scale <- 1 # specify scale parameter
xout <- seq(0.1,5,length=50) #design point where the CDF is evaluated
p.sample(xout,selected.d,shape,scale) # calculate CDF at xout
# }
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