asymmetry.measures (version 0.2)

r.sample: Switch between a range of available random number generators.

Description

Generate a random sample of size $n$ out of a range of available distributions.

Usage

r.sample(s, dist, p1=0, p2=1)

Arguments

s

A scalar which specifies the size of the random sample drawn.

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 distribution.

p2

A scalar. Parameter 2 (vector or object) of the selected distribution.

Value

A vector of random values at the user specified points s.

Details

Based on user-specified argument dist, the function returns a random sample of size $s$ from the corresponding distribution.

Supported distributions (along with the corresponding dist values) are:

• weib: The weibull distribution is implemented as $$f(s;p_1,p_2)=\frac{p_1}{p_2}{\left(\frac{s}{p_2}\right)}^{p_1-1}\exp \{-{\left(\frac{s}{p_2}\right)}^{p_1}\}$$ with $s\ge 0$ where $p_1$ is the shape parameter and $p_2$ the scale parameter.

• lognorm: The lognormal distribution is implemented as $$f(s)=\frac{1}{p_{2}s\sqrt{2\pi }}{e}^{-\frac{(logs-p_1{)}^2}{2p_2^2}}$$ 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 $$f(s)=\frac{1}{\pi p_2\{1+(\frac{s-p_1}{p_2}{)}^2\}}$$ where $p_1$ is the location parameter and $p_2$ the scale parameter.

• fnorm: The half normal distribution is implemented as $$2f(s)-1$$ where $$f(s)=\frac{1}{sd\sqrt{2\pi }}{e}^{-\frac{s^2}{2s{d}^2}},$$ 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 $$f(s)=2\varphi (s)\mathrm{\Phi }(p_{1}s)$$.

• fas: The Fernandez and Steel distribution is implemented as $$f(s;p_1,p_2)=\frac{2}{p_1+\frac{1}{p_1}}\{f_t(s/p_1;p_2)I_{\{s\ge 0\}}+f_t(p_{1}s;p_2)I_{\{s<0\}}\}$$ 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 $(0,+\mathrm{\infty })$ and $p_2$ denotes the degrees of freedom.

• shash: The Sinh-Arcsinh distribution is implemented as $$f(s;\mu ,p_1,p_2,\tau )=\frac{c{e}^{-r^2/2}}{\sqrt{2\pi }}\frac{1}{p_2}\frac{1}{2}\sqrt{1+z^2}$$ 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.

References

Bagkavos D., Patil P.N., Wood A.T.A. (2016), A Numerical Study of the Power Function of a New Symmetry Test. In: Cao R., Gonzalez Manteiga W., Romo J. (eds) Nonparametric Statistics. Springer Proceedings in Mathematics and Statistics, vol 175, Springer.

See Also

d.sample, q.sample, p.sample

Examples

# NOT RUN {
selected.r <- "norm" #select Normal as the distribution
shape <- 2  # specify shape parameter
scale <- 1  # specify scale parameter
n <- 100    # specify sample size
r.sample(n,selected.r,shape,scale)  # calculate CDF at the designated point
# }