Package 'rangen'

Title: Random Number Generators and Utilities
Description: Provides a collection of random number generators for common and custom distributions, along with utility functions for sampling and simulation.
Authors: Manos Papadakis [aut, cre, cph], Michail Tsagris [ctb], Omar Alzeley [ctb]
Maintainer: Manos Papadakis <[email protected]>
License: GPL-3
Version: 0.0.1
Built: 2026-09-10 12:10:57 UTC
Source: https://github.com/manospapadakis95/rangen

Help Index

Random Number Generators and Utilities

Description

Provides a collection of random number generators for common and custom distributions, along with utility functions for sampling and simulation.

Details

Package: rangen
Type: Package
Version: 0.0.1
Date: 2026-03-09
License: GPL-3

Maintainers

Manos Papadakis <[email protected]>

Author(s)

Angular central Gaussian random values simulation

Description

Angular central Gaussian random values simulation.

Usage

racg(n, sigma, seed = rangen::new.seed())

Arguments

n

The sample size, a numerical value.

sigma

The covariance matrix in RdR^d.

seed

If you want the same to be generated again use a seed for the generator, an integer number.

Details

The algorithm uses univariate normal random values and transforms them to multivariate via a spectral decomposition. The vectors are then scaled to have unit length.

Value

A matrix with the simulated data.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]>

References

Tyler D. E. (1987). Statistical analysis for the angular central Gaussian distribution on the sphere. Biometrika 74(3): 579-589.

See Also

acg.mle, rmvnorm, rmvlaplace, rmvt

Examples

s <- cov( iris[, 1:4] )
#x <- racg(100, s)
#res<-acg.mle(x)  
#res<-vmf.mle(x)  ## the concentration parameter, kappa, is very low, close to zero, as expected.

Multivariate Laplace random values simulation

Description

Multivariate Laplace random values simulation.

Usage

rmvlaplace(n, lam, mu, G, seed = rangen::new.seed())

Arguments

n

The sample size, a numerical value.

lam

The the parameter of the exponential distribution, a positive number.

mu

The mean vector.

G

A d×dd \times d covariance matrix with determinant 1.

seed

If you want the same to be generated again use a seed for the generator, an integer number.

Details

The algorithm uses univariate normal random values and transforms them to multivariate via a spectral decomposition.

Value

A matrix with the simulated data.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]>

References

Eltoft T., Kim T., and Lee T.W. (2006). On the multivariate laplace distribution. Signal Processing Letters, IEEE, 13(5):300-303.

See Also

rmvnorm, racg, rmvt

Examples

m <- colMeans(as.matrix(iris[, 1:4]))
s <- cov(iris[, 1:4])
s <- s / det(s)^0.25
lam <- 3
x <- rmvlaplace(100, lam, m, s)

Multivariate normal and t random values simulation

Description

Multivariate normal and t random values simulation.

Usage

rmvnorm(n, mu, sigma, seed = rangen::new.seed())
rmvt(n, mu, sigma, v, seed = rangen::new.seed())

Arguments

n

The sample size, a numerical value.

mu

The mean vector in RdR^d.

sigma

The covariance matrix in RdR^d.

v

The degrees of freedom.

seed

If you want the same to be generated again use a seed for the generator, an integer number.

Details

The algorithm uses univariate normal random values and transforms them to multivariate via a spectral decomposition. It is faster than the command "mvrnorm" available from MASS, and it allows for singular covariance matrices.

Value

A matrix with the simulated data.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]>

References

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

See Also

racg, rmvlaplace, rmvt

Examples

x <- as.matrix(iris[, 1:4])
m <- colMeans(x)
s <- cov(x)
y <- rmvnorm(1000, m, s)
res <- colMeans(y)
res <- cov(y)
y <- NULL

Random integer values simulation

Description

Random integer values simulation.

Usage

Sample.int(n, size = n, replace = FALSE, seed = new.seed())
Sample(x, size = length(x), replace = FALSE, seed = new.seed())
colSample(x, size = rep_len(nrow(x), ncol(x)), replace = rep_len(FALSE, ncol(x)),
  parallel = FALSE, cores = 0, seed = new.seed())
rowSample(x, size = rep_len(ncol(x), nrow(x)), replace = rep_len(FALSE, nrow(x)),
  parallel = FALSE, cores = 0, seed = new.seed())

Arguments

x

A numeric vector for sampling or a matrix for column-row sampling.

n

This must be an integer value. The function will then draw random integer values from 1:n.

size

The number of integer values to sample.

replace

Do you want to sample with replacement? If yes, set this equal to TRUE.

parallel

Do you want to do it in parallel, for column - row major, in C++? TRUE or FALSE.

cores

Number of cores to use for parallelism. Valid only when argument parallel is set to TRUE. Default value is 0, which uses the OpenMP default number of threads..

seed

A seed object created by new.seed. To reproduce results, pass new.seed(x) with the same x. Not supported by the parallel versions.

Details

These functions provide flexible sampling utilities similar in purpose to R's base functions sample.int and sample. Each function operates on a different structure:

  • Sample.int: Generates a random sample of integers from 1 to n.

  • Sample: Samples elements from the vector x.

  • colSample: Performs column-wise sampling on a matrix or data frame, selecting size[i] elements from each column i.

  • rowSample: Performs row-wise sampling on a matrix or data frame, selecting size[i] elements from each row i.

All functions support sampling with or without replacement. Parallel versions do not support seeding.

Value

Sample.int, Sample

A vector of sampled values.

colSample, rowSample

A matrix or data frame containing the sampled elements.

Author(s)

R implementation and documentation: Manos Papadakis <[email protected]>.

See Also

sample, sample.int

Examples

# Sample integers from 1 to 10 with replacement (faster than base::sample.int)
x <- Sample.int(10, 1000, replace = TRUE)

# Sample from the vector 'x' (faster than base::sample)
xs <- Sample(x)

# Create a matrix and perform column-wise sampling
# 'size' must have the same length as the number of columns
mat <- matrix(1:20, nrow = 5, ncol = 4)
colSample(mat, size = rep(5, ncol(mat)), replace = rep(TRUE, ncol(mat)))

# Create a matrix and perform row-wise sampling
# 'size' must have the same length as the number of rows
rowSample(mat, size = rep(4, nrow(mat)), replace = rep(FALSE, nrow(mat)))

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

For new.seed: a number used as the initial state of the generator. For all other functions: a seed object created by new.seed. To reproduce results, pass new.seed(x) with the same x.

parallel

colRunif only: should the columns be generated in parallel in C++? TRUE or FALSE.

cores

colRunif only: number of cores to use when parallel = TRUE. Default value is 0, which uses the OpenMP default number of threads.

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)⋅Umin + (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 X1X1+X2\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 −log⁡(U)rate-\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., Y12+Y22+⋯+Ydf2Y_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⋅V⋅rated \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 location+scale⋅tan⁡(π⋅(U−0.5))\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 ZYdf\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 Z+ncpYdf\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 ⌊log⁡(U)log⁡(1−prob)⌋\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 scale⋅(1−U)−1shape\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 μ+scale⋅(−log⁡U)1/shape\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 μ−σ⋅sign(U)⋅log⁡(1−2⋅∣U∣)\mu - \sigma \cdot \text{sign}(U) \cdot \log(1 - 2 \cdot |U|), where U is a uniform random variable in (0, 1).

  • Rgumbel, Rgumbel.mat, colRgumbel: generates random values from the Gumbel (type I extreme value) distribution with parameters mu and sigma. The type used is μ−σ⋅log⁡(−log⁡U)\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 min+(max−min)⋅sin⁡2(πU/2)\text{min} + (\text{max} - \text{min}) \cdot \sin^2(\pi U / 2), where U is a uniform random variable in (0, 1).

  • new.seed: creates and returns a seed object of class "seed" that holds the generator state. Its fields initialState and state can be read and set with $. Seeding is not supported by the parallel versions of column and row sampling.

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. new.seed returns an object of class "seed".

Author(s)

R implementation and documentation: Manos Papadakis <[email protected]>.

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_gumbelt  <- Rgumbel(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_gumbelt  <- Rgumbel.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_gumbel  <- colRgumbel(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)

Dirichlet random values simulation

Description

Simulates random values from a Dirichlet distribution.

Usage

rdiri(n, a, b = rep(1, length(a)), seed = new.seed())

Arguments

n

The number of observations (rows) to generate.

a

A numeric vector of positive concentration parameters, one per component.

b

A numeric vector of positive rate parameters for the underlying gamma draws, one per component.

seed

A seed object created by new.seed.

Details

For each row, independent values Xj∼Gamma(aj,bj)X_j \sim Gamma(a_j, b_j) are drawn and divided by their sum. With the default b, the result follows a Dirichlet(a) distribution. Unequal values in b give a scaled Dirichlet distribution, not a Dirichlet.

Value

A matrix with n rows and length(a) columns. Each row sums to 1.

Author(s)

Manos Papadakis <[email protected]>.

See Also

Rgamma, colRgamma

Examples

x <- rdiri(10, c(2, 3, 5))
rowSums(x)

Simulating from a Bingham distribution

Description

Simulation from a Bingham distribution using the code suggested by Kent et al. (2013).

Usage

rbing(n, lam)

Arguments

n

Sample size.

lam

Eigenvalues of the diagonal symmetric matrix of the Bingham distribution. See details for more information on this.

Details

The user must have calculated the eigenvalues of the diagonal symmetric matrix of the Bingham distribution. The function accepts the q-1 eigenvalues only. This means, that the user must have subtracted the lowest eigenvalue from the rest and give the non zero ones. The function uses rejection sampling.

Value

A matrix with the simulated data.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]> and Manos Papadakis <[email protected]>

References

Kent J.T., Ganeiber A.M. and Mardia K.V. (2013). A new method to simulate the Bingham and related distributions in directional data analysis with applications. http://arxiv.org/pdf/1310.8110v1.pdf

C.J. Fallaize and T. Kypraios (2014). Exact Bayesian Inference for the Bingham Distribution. Statistics and Computing (No volum assigned yet). http://arxiv.org/pdf/1401.2894v1.pdf

See Also

Rnorm

Examples

x <- rbing( 100, c(1, 0.6, 0.1) )
x

Simulation of random values from a Bingham distribution with any symmetric matrix

Description

Simulation of random values from a Bingham distribution with any symmetric matrix.

Usage

rbingham(n, A)

Arguments

n

Sample size.

A

A symmetric matrix.

Details

The eigenvalues of the q x q symmetric matrix A are calculated and the smallest of them is subtracted from the rest. The q - 1 non zero eiqenvalues are then passed to rbing. The generated data are then right multiplied by VTV^T, where V is the matrix of eigenvectors of the matrix A.

Value

A matrix with the simulated data.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]> and Manos Papadakis <[email protected]>

References

Kent J.T., Ganeiber A.M. and Mardia K.V. (2013). A new method to simulate the Bingham and related distributions in directional data analysis with applications. http://arxiv.org/pdf/1310.8110v1.pdf

C.J. Fallaize and T. Kypraios (2014). Exact Bayesian Inference for the Bingham Distribution. Statistics and Computing (No volum assigned yet). http://arxiv.org/pdf/1401.2894v1.pdf

See Also

Rnorm

Examples

A <- cov( iris[, 1:4] )
x <- rbingham(100, A)
x

Time functions

Description

Functions to get the current time in different units.

Usage

nanoTime()

Details

  • nanoTime: The current nanoseconds of the system.

Value

Each function returns a numeric value.

Author(s)

Manos Papadakis <[email protected]>.

See Also

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

Examples

x <- nanoTime()