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

Maintainers

Manos Papadakis <papadakm95@gmail.com>

Author(s)

• Manos Papadakis <papadakm95@gmail.com>

• Michail Tsagris <mtsagris@uoc.gr>

Random integer values simulation

Description

Random integer values simulation.

Usage

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

Arguments

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

Author(s)

R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.

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) 
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

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 <papadakm95@gmail.com>.

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)

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 <papadakm95@gmail.com>.

See Also

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

Examples

x <- nanoTime()