This class generates Bernoulli
random variates.
This class generates Bernoulli
random variates.
This discrete RV models the one trial (success is 1, failure is 0).
the probability of success
the random number stream
http://www.math.uah.edu/stat/bernoulli/Introduction.html
This class generates Beta
random variates.
This class generates Beta
random variates.
This continuous RV models random proportions.
Beta = Gamma1 / (Gamma1 + Gamma2).
the shape parameter for Gamma1
the shape parameter for Gamma2
the random number stream
http://www.math.uah.edu/stat/special/Beta.html
This class generates Binomial
random variates.
This class generates Binomial
random variates.
This discrete RV models the number of successes in n trials.
the probability of success
the number of independent trials
the random number stream
http://www.math.uah.edu/stat/bernoulli/Binomial.html
This class generates Cauchy
(or Lorentz) random variates.
This class generates Cauchy
(or Lorentz) random variates.
This continuous RV models data with heavier tails than normally distributed.
the location parameter (median)
the scale parameter
the random number stream
http://www.math.uah.edu/stat/special/Cauchy.html
This class generates ChiSquare
random variates.
This class generates ChiSquare
random variates.
This continuous RV models the variance of a distribution.
http://www.math.uah.edu/stat/special/ChiSquare.html
the degrees of freedom
the random number stream
This class generates Dice
random variates for a given distribution specified
using a cumulative distribution function (cdf).
This class generates Dice
random variates for a given distribution specified
using a cumulative distribution function (cdf). This discrete RV models the
roll of dice numbered 0, 1, ..., n-1. Add 1 for 1 to n.
the distribution function (cdf)
the random number stream
This class generates generalized Discrete
random variates for a given
distribution specified using either a probability mass function (pmf)
or a cumulative distribution function (cdf).
This class generates generalized Discrete
random variates for a given
distribution specified using either a probability mass function (pmf)
or a cumulative distribution function (cdf).
This discrete RV models arbitrary experiments with discrete outcomes.
the distribution function (pdf or cdf)
the x-coordinate values (mass points)
whether dist is cumulative (cdf) or not (pmf)
the random number stream
This class generates Erlang
random variates.
This class generates Erlang
random variates.
This continuous RV models the time until k stages complete.
the mean of exponential samples (Erlang mean = mu * k)
the number of stages (or Exponential samples)
the random number stream
http://www.math.uah.edu/stat/poisson/Gamma.html
This class generates Exponential
random variates.
This class generates Exponential
random variates.
This continuous RV models the time until an event occurs.
http://www.math.uah.edu/stat/poisson/Exponential.html
the mean
the random number stream
This class generates Fisher
(F-Distribution) random variates.
This class generates Fisher
(F-Distribution) random variates.
This continuous RV models the ratio of variances.
the degrees of freedom for numerator Chi-Square
the degrees of freedom for denominator Chi-Square
the random number stream
http://www.math.uah.edu/stat/special/Fisher.html
This class generates Gamma
random variates.
This class generates Gamma
random variates.
This continuous RV models the time until an event occurs.
Note: variance = alpha * beta ^ 2.
the shape parameter
the scale parameter
the random number stream
http://www.math.uah.edu/stat/poisson/Gamma.html
This class generates Geometric
random variates.
This class generates Geometric
random variates.
This discrete RV models the number of failures before the first success.
the probability of success
the random number stream
http://www.math.uah.edu/stat/bernoulli/Geometric.html
This class generates HyperExponential
random variates (two rates).
This class generates HyperExponential
random variates (two rates).
This continuous RV models the time until an event occurs (higher coefficient
of variation than exponential distribution).
the probability of first vs. second rates
the first mean (1 / lambda1)
the second mean (1 / lambda2)
the random number stream
This class generates HyperGeometric
random variates.
This class generates HyperGeometric
random variates.
This discrete RV models the number of successes in n draws from a finite population.
the probability of success (red balls)
the number of draws (balls drawn)
the size of the finite population (total number of balls)
the random number stream
http://www.math.uah.edu/stat/urn/Hypergeometric.html
This class generates LogNormal
random variates.
This class generates LogNormal
random variates.
This continuous RV models data that is normally distributed after a log transformation.
the mean for underlying Normal
the variance (sigma squared) for underlying Normal
the random number stream
http://www.math.uah.edu/stat/special/LogNormal.html
This class generates Logistic
random variates.
This class generates Logistic
random variates.
This continuous RV models logisticlly distributed data (stretched Normal).
the location parameter
the scale parameter
the random number stream
http://www.math.uah.edu/stat/special/Logistic.html
This class generates Multinomial
random variates vectors.
This class generates Multinomial
random variates vectors.
This discrete RV models the ...?
array of probabilities
the number of independent trials
the random number stream
http://www.math.uah.edu/stat/bernoulli/Multinomial.html
This class generates arrival times according to a NHPoissonProces
, an
Non-Homogeneous Process Process (NHPP), where the arrival rate function
'lambda(t)' is piecewise constant.
This class generates arrival times according to a NHPoissonProces
, an
Non-Homogeneous Process Process (NHPP), where the arrival rate function
'lambda(t)' is piecewise constant. Rates are constant over basic time
intervals of length 'dt'.
the vector of arrival rates
the length the basic time intervals
the random number stream
http://en.wikipedia.org/wiki/Poisson_process#Non-homogeneous
This class generates NegativeBinomial
random variates.
This class generates NegativeBinomial
random variates.
This discrete RV models the number of failures before s-th success.
the probability of success
the number of successes
the random number stream
http://www.math.uah.edu/stat/bernoulli/NegativeBinomial.html
This class generates Normal
(Gaussian) random variates.
This class generates Normal
(Gaussian) random variates.
This continuous RV models normally distributed data (bell curve).
When summed, most distributions tend to Normal (Central Limit Theorem).
the mean
the variance (sigma squared)
the random number stream
http://www.math.uah.edu/stat/special/Normal.html
The NormalVec
class generates Normal (Gaussian) random variate vectors according
to the Multivariate Normal distribution with mean 'mu' and covariance 'cov'.
The NormalVec
class generates Normal (Gaussian) random variate vectors according
to the Multivariate Normal distribution with mean 'mu' and covariance 'cov'.
This continuous RVV models normally distributed multidimensional data.
the mean vector
the covariance matrix
the random number stream
http://www.statlect.com/mcdnrm1.htm
http://onlinelibrary.wiley.com/doi/10.1111/1467-9639.00037/pdf
This class generates Pareto
random variates.
This class generates Pareto
random variates.
This continuous RV models Pareto distributed data.
the shape parameter
the scale parameter
the random number stream
http://www.math.uah.edu/stat/special/Pareto.html
The PermutedVecD
class generates random permutations of a vector of doubles.
The PermutedVecD
class generates random permutations of a vector of doubles.
the vector of doubles to permute
the random number stream
maths-people.anu.edu.au/~brent/pd/Arndt-thesis.pdf
The PermutedVecI
class generates random permutations of a vector of integers.
The PermutedVecI
class generates random permutations of a vector of integers.
the vector of integers to permute
the random number stream
maths-people.anu.edu.au/~brent/pd/Arndt-thesis.pdf
This class generates Poisson
random variates (discrete).
This class generates Poisson
random variates (discrete).
This discrete RV models the number of events in a time interval of unit length.
the mean
the random number stream
http://www.math.uah.edu/stat/poisson/Poisson.html
This class generates arrival times according to a PoissonProcess
.
This class generates arrival times according to a PoissonProcess
.
Given the current arrival time 't', generate the next arrival time.
the arrival rate (arrivals per unit time)
the random number stream
http://en.wikipedia.org/wiki/Poisson_process
The ProbabilityVec
class generates a probability vector where the ith
probability is '1/n' with a +/- randomizing displacement of at most 'd'.
The ProbabilityVec
class generates a probability vector where the ith
probability is '1/n' with a +/- randomizing displacement of at most 'd'.
Note, the probability vector must add to one.
the dimension/size of the probability vector
the randomizing displacement, must be in [0, 1]
The RNG
abstract class is the base class for all ScalaTion Random Number
Generators (RNGs).
The RNG
abstract class is the base class for all ScalaTion Random Number
Generators (RNGs). The subclasses must implement a 'gen' method that generates
random real numbers in the range (0, 1). They must also implement an 'igen'
methods to return stream values.
This class generates Randi
random variates (random integers: a, ..., b).
This class generates Randi
random variates (random integers: a, ..., b).
This discrete RV models equiprobable integral outcomes.
the lower bound (inclusive)
the upper bound (inclusive)
the random number stream
http://www.math.uah.edu/stat/special/UniformDiscrete.html
This class generates Randi0
random variates (random integers: 0, ..., b).
This class generates Randi0
random variates (random integers: 0, ..., b).
This discrete RV models equiprobable integral outcomes starting with 0.
the upper bound (>= 0) (inclusive)
the random number stream
The Random
class generates random real numbers in the range (0, 1).
The Random
class generates random real numbers in the range (0, 1).
It implements, using 64-bit integers (Long's), the 'MRG31k3p' generator
developed by L'Ecuyer and Touzin, described in "FAST COMBINED MULTIPLE
RECURSIVE GENERATORS WITH MULTIPLIERS OF THE FORM a = 2q +/- 2r".
MRG31k3p is a Combined Multiple Recursive Generator (CMRG) shown to have good
performance and statistical properties for simulations. It has a period of
about 2185 and is considered to be a faster alternative to the popular
'MRG32k3' generator. MRG31k3p combines MRG1 and MRG2.
MRG1: x_i = (0 + a_12 x_i-2 + a_13 x_i-3) % M1
MRG2: x_i = (a_21 x_i-1 + 0 + a_23 x_i-3) % M2
where a_12 = 222, a_13 = 27+1, a_21 = 215 and a_23 = 2^15+1.
the random number stream index
http://www.iro.umontreal.ca/~simardr/ssj/doc/pdf/guiderng.pdf
http://www.informs-sim.org/wsc00papers/090.PDF
The Random2
class generates random real numbers in the range (0, 1).
The Random2
class generates random real numbers in the range (0, 1).
It implements, using 32-bit integers (Int's), the 'MRG31k3p' generator
developed by L'Ecuyer and Touzin, described in "FAST COMBINED MULTIPLE
RECURSIVE GENERATORS WITH MULTIPLIERS OF THE FORM a = 2q +/- 2r".
MRG31k3p is a Combined Multiple Recursive Generator (CMRG) shown to have good
performance and statistical properties for simulations. It has a period of
about 2185 and is considered to be a faster alternative to the popular
'MRG32k3' generator. MRG31k3p combines MRG1 and MRG2.
MRG1: x_i = (0 + a_12 x_i-2 + a_13 x_i-3) % M1
MRG2: x_i = (a_21 x_i-1 + 0 + a_23 x_i-3) % M2
where a_12 = 222, a_13 = 27+1, a_21 = 215 and a_23 = 2^15+1.
the random number stream index
http://www.iro.umontreal.ca/~simardr/ssj/doc/pdf/guiderng.pdf
http://www.informs-sim.org/wsc00papers/090.PDF
The Random3
class generates random real numbers in the range (0, 1).
The Random3
class generates random real numbers in the range (0, 1).
It implements, using 64-bit integers (Int's), the 'MINSTD' generator, which
is a multiplicative Linear Congruential Generator (LCG).
These generators were commonly used in the last century.
x_i = a x_i-1 % m
the random number stream index
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.1024
Random
http://random.mat.sbg.ac.at/results/karl/server/node4.html#SECTION00042000000000000000 In case a better generator is needed, a Multiple Recursive Generator (MRG) or Composite Multiple Recursive Generator (CMRG) should be used.
This class generates Sharp
(Deterministic) random variates.
This class generates Sharp
(Deterministic) random variates.
This discrete RV models the case when the variance is 0.
the value for this constant distribution
the random number stream
This class generates StudentT
random variates.
This class generates StudentT
random variates.
This continuous RV models cases where data are normally distributed, but
variability increases since the variance is unknown.
the degrees of freedom
the random number stream
http://www.math.uah.edu/stat/special/Student.html
The TimeVariate
abstract class serves as a superclass for time-based
random variates such Poisson Processes.
This class generates Trapezoidal
random variates.
This class generates Trapezoidal
random variates.
This continuous RV models cases where outcomes cluster between two modes.
Both Uniform and
Triangular are special cases of
Trapezoidal.
the minimum
the first mode
the second mode
the maximum
the random number stream
http://iopscience.iop.org/0026-1394/44/2/003/pdf/0026-1394_44_2_003.pdf
This class generates simple Triangular
random variates with the mode in the middle.
This class generates simple Triangular
random variates with the mode in the middle.
This continuous RV models cases where outcomes cluster around the mode.
the lower bound
the upper bound
the mode
the random number stream
http://www.math.uah.edu/stat/special/Triangle.html
This class generates Trinomial
random variates.
This class generates Trinomial
random variates. While Binomial is based on
trials with two outcomes, success (1) or failure (0). Trinomial is based on
trials with three outcomes, high (2), medium (1) or low (0).
This discrete RV models the result of 'n' trials.
the probability of high (2)
the probability of medium (1)
the number of independent trials
the random number stream
https://onlinecourses.science.psu.edu/stat414/node/106
This class generates Uniform
random variates in the range (a, b).
This class generates Uniform
random variates in the range (a, b).
This continuous RV models equiprobable outcomes.
the lower bound
the upper bound
the random number stream
http://www.math.uah.edu/stat/special/UniformContinuous.html
The Variate
abstract class serves as a base class for all the random variate
(RV) generators.
The Variate
abstract class serves as a base class for all the random variate
(RV) generators. They use one of the Random Number Generators (RNG's) from
Random
to generate numbers following their particular distribution.
Random Variate Generators (RVG's) for thirty popular probability distributions
are implemented as extensions of Variate. Still need to add one.
VariateVec
for Random MultiVariate Generators (RMVG's).
http://www.math.uah.edu/stat/special/index.html
The VariateVec
abstract class serves as a base class for all the random
variate vector (RVV) generators.
The VariateVec
abstract class serves as a base class for all the random
variate vector (RVV) generators. They use one of the Random Number Generators
(RNG's) from Random.scala to generate numbers following their particular
multivariate distribution.
This class generates Weibull
random variates.
This class generates Weibull
random variates.
This continuous RV models the time for an event to occur.
the shape parameter
the scale parameter
the random number stream
http://www.math.uah.edu/stat/special/Weibull.html
This class generates HyperExponential
random variates.
This class generates HyperExponential
random variates.
This continuous RV models the time until an event occurs (higher coefficient
of variation than exponential distribution). FIX
the mean
the standard deviation
the random number stream
The PoissonProcessTest
object is used to test both the PoissonProcess
and
NHPoissonProcess
classes.
The Quantile
object contains methods for computing 'Finv', the inverse
Cumulative Distribution Functions (iCDF's) for popular sampling distributions:
StandardNormal, StudentT, ChiSquare and Fisher.
The Quantile
object contains methods for computing 'Finv', the inverse
Cumulative Distribution Functions (iCDF's) for popular sampling distributions:
StandardNormal, StudentT, ChiSquare and Fisher.
For a given CDF 'F' and quantile 'p', compute 'x' such that the 'F(x) = p'.
The QuantileTest
object tests the Quantile
object.
The RNGTest
object conducts three simple tests of the Random Number
Generators: (1) Spped Test, (2) Means Test and (3) Chi-square Goodness of Fit Test.
The RNGTest
object conducts three simple tests of the Random Number
Generators: (1) Spped Test, (2) Means Test and (3) Chi-square Goodness of Fit Test.
FIX: need to add (3) Variance Test and (4) K-S Goodness of Fit Test.
The first 1000 seeds for the 'MRG31k3p' random number generator.
The first 1000 seeds for the LCG random number generator.
The StreamMaker
object computes seeds for Random
and Random2
, both
of which implement the 'MRG31k3p' random number generator.
The StreamMaker
object computes seeds for Random
and Random2
, both
of which implement the 'MRG31k3p' random number generator. This generator
has a period length around 2^185. Each seed is a 6-dimensional vector of
32-bit integers.
http://www.iro.umontreal.ca/~simardr/ssj/indexe.html
The StreamMaker3
object finds seeds for the Random3
random number generator.
The StreamMaker3
object finds seeds for the Random3
random number generator.
This generator has a period length around 2^31. Each seed is a 32-bit integer.
The StreamMakerGen
object generates and prints the first 'k' seeds for the
the 'MRG31k3p' random number generator's streams.
The VariateTest
object conducts two simple tests of the Random Variate
Generators: (1) Means Test and (2) Chi-square Goodness of Fit Test.
The VariateTest
object conducts two simple tests of the Random Variate
Generators: (1) Means Test and (2) Chi-square Goodness of Fit Test.
FIX: need to add (3) Variance Test and (4) K-S Goodness of Fit Test.
The VariateVecTest
object is used to test the Random Variate Vector (RVV)
generators from the classes derived from VariateVec
.
The random package contains classes, traits and objects for the generation of random numbers.