Runif: Random values simulation from various distributions

In rangen: Random Number Generators and Utilities

Random values simulation from various distributions

Description

Functions to simulate random values from different probability distributions: uniform, beta, exponential, chi-squared, gamma, Cauchy, t-distribution, and geometric.

Usage

Runif(n, min = 0, max = 1) 
Rbeta(n, alpha, beta)
Rexp(n, rate = 1)
Rchisq(n, df)
Rgamma(n, shape, rate = 1)
Rcauchy(n, location = 0, scale = 1)
Rt(n, df, ncp)
Rgeom(n, prob)
Rpareto(n, shape = 1, scale = 1)
Rfrechet(n, lambda = 1, mu = 0, sigma = 1)
Rlaplace(n, mu = 0, sigma = 1)
Rgumble(n, mu = 0, sigma = 1)
Rarcsine(n, min = 0, max = 1)
Rnorm(n, mean = 0, sd = 1)
Runif.mat(nrow, ncol, min = 0, max = 1) 
Rbeta.mat(nrow, ncol, alpha, beta)
Rexp.mat(nrow, ncol, rate = 1)
Rchisq.mat(nrow, ncol, df)
Rgamma.mat(nrow, ncol, shape, rate = 1)
Rcauchy.mat(nrow, ncol, location = 0, scale = 1)
Rt.mat(nrow, ncol, df, ncp)
Rgeom.mat(nrow, ncol, prob)
Rpareto.mat(nrow, ncol, shape = 1, scale = 1)
Rfrechet.mat(nrow, ncol, lambda = 1, mu = 0, sigma = 1)
Rlaplace.mat(nrow, ncol, mu = 0, sigma = 1)
Rgumble.mat(nrow, ncol, mu = 0, sigma = 1)
Rarcsine.mat(nrow, ncol, min = 0, max = 1)
Rnorm.mat(nrow, ncol, mean = 0, sd = 1)
colRunif(nrow, ncol, min = rep_len(0, ncol), max = rep_len(1, ncol))
colRbeta(nrow, ncol, alpha, beta)
colRexp(nrow, ncol, rate = rep_len(1, ncol))
colRchisq(nrow, ncol, df)
colRgamma(nrow, ncol, shape, rate = rep_len(1, ncol))
colRgeom(nrow, ncol, prob)
colRcauchy(nrow, ncol, location = rep_len(0, ncol), scale = rep_len(1, ncol))
colRt(nrow, ncol, df, ncp)
colRpareto(nrow, ncol, shape = rep_len(1, ncol), scale = rep_len(1, ncol))
colRfrechet(nrow, ncol, lambda = rep_len(1, ncol), 
mu = rep_len(0, ncol), sigma = rep_len(1, ncol))
colRlaplace(nrow, ncol, mu = rep_len(0, ncol), sigma = rep_len(1, ncol))
colRgumble(nrow, ncol, mu = rep_len(0, ncol), sigma = rep_len(1, ncol))
colRarcsine(nrow, ncol, min = rep_len(0, ncol), max = rep_len(1, ncol))
colRnorm(nrow, ncol, mean = rep_len(0, ncol), sd = rep_len(1, ncol))
setSeed(seed = nanoTime())

Arguments

n	The number of values to generate.
nrow	The number of rows.
ncol	The number of columns.
min	The lower value.
max	The upper value.
alpha	The shape parameter alpha.
beta	The shape parameter beta.
rate	Rgamma: The rate parameter.
df	Rt: The degrees of freedom.
lambda, shape	The shape parameter.
location, mu	The location parameter.
scale, sigma	The scale parameter.
ncp	The non-centrality parameter.
prob	The probability of success on each trial.
seed	A single value, interpreted as an integer.
mean	Vector of means.
sd	Vector of standard deviations.

Details

• Runif, Runif.mat, colRunif: generates random values from the uniform distribution, similar to R's built-in runif function. The type used is min + (max - min) \cdot U, where U is a uniform random variable in the interval (0, 1).

• Rbeta, Rbeta.mat, colRbeta: generates random values from the beta distribution with parameters alpha and beta. The type used involves generating two gamma-distributed variables \( X_1 \) and \( X_2 \), and returning \frac{X_1}{X_1 + X_2}, where \( X_1 \) and \( X_2 \) have the shape parameters alpha and beta, respectively.

• Rexp, Rexp.mat, colRexp: generates random values from the exponential distribution with the specified rate parameter. The type used is -\frac{\log(U)}{\text{rate}}, where U is a uniform random variable in the interval (0, 1).

• Rchisq, Rchisq.mat, colRchisq: generates random values from the chi-squared distribution with df degrees of freedom. The type used is the sum of the squares of df independent standard normal random variables, i.e., Y_1^2 + Y_2^2 + \dots + Y_{df}^2, where each \( Y_i \) is a standard normal random variable.

• Rgamma, Rgamma.mat, colRgamma: generates random values from the gamma distribution with shape and rate parameters. The type used for shape greater than or equal to 1 is the Marsaglia and Tsang method, which involves generating a variable \( V \) and returning d \cdot V \cdot \text{rate}, where \( d \) is a function of the shape and \( V \) is derived from a normal random variable. For shape less than 1, a combination of the uniform and exponential distributions is used, involving an acceptance-rejection method.

• Rcauchy, Rcauchy.mat, colRcauchy: generates random values from the Cauchy distribution with specified location and scale parameters. The type used for this is \text{location} + \text{scale} \cdot \tan(\pi \cdot (U - 0.5)), where U is a uniform random variable.

• Rt, Rt.mat, colRt: generates random values from the t-distribution with specified df degrees of freedom and an optional non-centrality parameter ncp. The type used is \frac{Z}{\sqrt{\frac{Y}{df}}}, where Z is a standard normal random variable and Y is a chi-squared random variable. If ncp is provided, the type used is \frac{Z + ncp}{\sqrt{\frac{Y}{df}}}.

• Rgeom, Rgeom.mat, colRgeom: generates random values from the geometric distribution with the specified probability prob. The type used is \left\lfloor \frac{\log(U)}{\log(1 - prob)} \right\rfloor, where U is a uniform random variable.

• Rpareto, Rpareto.mat, colRpareto: generates random values from the Pareto distribution with parameters shape and scale. The type used is \text{scale} \cdot (1 - U)^{-\frac{1}{\text{shape}}}, where U is a uniform random variable in the interval (0, 1).

• Rfrechet, Rfrechet.mat, colRfrechet: generates random values from the Frechet distribution with parameters shape, mu, and scale. The type used is \mu + \text{scale} \cdot (-\log U)^{1/\text{shape}}, where U is a uniform random variable in (0, 1).

• Rlaplace, Rlaplace.mat, colRlaplace: generates random values from the Laplace distribution with location parameter mu and scale parameter sigma. The type used is \mu - \sigma \cdot \text{sign}(U) \cdot \log(1 - 2 \cdot |U|), where U is a uniform random variable in (0, 1).

• Rgumble, Rgumble.mat, colRgumble: generates random values from the Gumbel (type I extreme value) distribution with parameters mu and sigma. The type used is \mu - \sigma \cdot \log(-\log U), where U is a uniform random variable in (0, 1).

• Rarcsine, Rarcsine.mat, colRarcsine: generates random values from the arcsine distribution over the interval [min, max]. The type used is \text{min} + (\text{max} - \text{min}) \cdot \sin^2(\pi U / 2), where U is a uniform random variable in (0, 1).

• setSeed: Set the seed for the Rngs. Not working with parallel version of column - row sample.

Value

Each function, for example Runif, returns a vector with simulated values from the respective distribution. Each function.mat, for example Runif.mat, returns a matrix with simulated values from the respective distribution. Each colFunction, for example colRunif, returns a matrix with column major simulated values from the respective distribution.

Author(s)

R implementation and documentation: Manos Papadakis <[e-mail]>.

See Also

runif, rbeta, rexp, rchisq, rgamma, rcauchy, rt, rgeom

Examples

# Scalar draws
x_unif     <- Runif(5, 0, 1)
x_beta     <- Rbeta(5, 2, 5)
x_exp      <- Rexp(5, 1.5)
x_chisq    <- Rchisq(5, 4)
x_gamma    <- Rgamma(5, 2, 2)
x_cauchy   <- Rcauchy(5, 0, 1)
x_t        <- Rt(5, df = 5, ncp = 2)
x_geom     <- Rgeom(5, 0.5)
x_pareto   <- Rpareto(5, shape = 2, scale = 1)
x_frechet  <- Rfrechet(5, lambda = 1, mu = 0, sigma = 1)
x_laplace  <- Rlaplace(5, mu = 0, sigma = 1)
x_gumblet  <- Rgumble(5, mu = 0, sigma = 1)
x_arcsine  <- Rarcsine(5, min = 0, max = 1)
x_norm     <- Rnorm(5)

#matrices
x_unif     <- Runif.mat(5,2, 0, 1)
x_beta     <- Rbeta.mat(5,2, 2, 5)
x_exp      <- Rexp.mat(5,2, 1.5)
x_chisq    <- Rchisq.mat(5,2, 4)
x_gamma    <- Rgamma.mat(5,2, 2, 2)
x_cauchy   <- Rcauchy.mat(5,2, 0, 1)
x_t        <- Rt.mat(5,2, df = 5, ncp = 2)
x_geom     <- Rgeom.mat(5,2, 0.5)
x_pareto   <- Rpareto.mat(5,2, shape = 2, scale = 1)
x_frechet  <- Rfrechet.mat(5,2, lambda = 1, mu = 0, sigma = 1)
x_laplace  <- Rlaplace.mat(5,2, mu = 0, sigma = 1)
x_gumblet  <- Rgumble.mat(5,2, mu = 0, sigma = 1)
x_arcsine  <- Rarcsine.mat(5,2, min = 0, max = 1)
x_norm     <- Rnorm.mat(5,2)

# Column-wise (vectorized by column) draws
x_col_unif    <- colRunif(5, 2, min = c(0, 1), max = c(1, 2))
x_col_beta    <- colRbeta(5, 2, alpha = c(2, 5), beta = c(5, 2))
x_col_exp     <- colRexp(5, 2, rate = c(1.5, 2.0))
x_col_chisq   <- colRchisq(5, 2, df = c(4, 5))
x_col_gamma   <- colRgamma(5, 2, shape = c(2, 3), rate = c(2, 1))
x_col_cauchy  <- colRcauchy(5, 2, location = c(0, 1), scale = c(1, 2))
x_col_t       <- colRt(5, 2, df = c(5, 6), ncp = c(2, 1))
x_col_geom    <- colRgeom(5, 2, prob = c(0.5, 0.3))
x_col_pareto  <- colRpareto(5, 2, shape = c(2, 3), scale = c(1, 1))
x_col_frechet <- colRfrechet(5, 2, lambda = c(1, 2), mu = c(0, 0), sigma = c(1, 1))
x_col_laplace <- colRlaplace(5, 2, mu = c(0, 1), sigma = c(1, 2))
x_col_gumble  <- colRgumble(5, 2, mu = c(0, 1), sigma = c(1, 2))
x_col_arcsine <- colRarcsine(5, 2, min = c(0, 0.5), max = c(1, 1.5))
x_col_norm    <- colRnorm(5, 2)

rangen documentation built on March 16, 2026, 5:08 p.m.