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Title: Discrete Tempered Stable Distributions
Version: 0.1.1
Description: Methods for evaluating the probability mass function, cumulative distribution function, and generating random samples from discrete tempered stable distributions. For more details see Grabchak (2021) <doi:10.1007/s11009-021-09904-3>.
License: GPL (≥ 3)
Encoding: UTF-8
RoxygenNote: 7.3.2
Imports: actuar, expint, stats
NeedsCompilation: no
Packaged: 2025-05-21 16:31:30 UTC; sinasaba
Author: Sina Saba [aut, cre, cph]
Maintainer: Sina Saba <sabasina22@gmail.com>
Repository: CRAN
Date/Publication: 2025-05-26 12:50:06 UTC

The probability mass function of the discrete tempered stable distribution.

Description

The probability mass function of the discrete tempered stable distribution.

Usage

ddts(x, alpha, eta, tp = c(1, 1), tf = "poisson-tweedie", zt = FALSE)

Arguments

x

vector of points.

alpha

Index of stability; Number in (0,1)

eta

A parameter, eta>0.

tp

A vector of tempering parameters.

tf

Tempering function. It can be one of the "discrete-stable", "discrete-truncated-stable", "discrete-pRDTS", "poisson-tweedie", "exp-tempering", "beta-prime-tempering", "Pareto-tempering".

zt

Logical. If True it calculates zero-truncated probabilities.

Value

A vector of probabilities.

References

M. Grabchak. Discrete tempered stable distributions. Methodology and Computing in Applied Probability, 24(3):1877-1890, 2021.

Examples

x <- 0:10
ddts(x, 0.5, 1)

Log-likelihood function for a discrete tempered stable distribution.

Description

Log-likelihood function for a discrete tempered stable distribution.

Usage

edts(pv, smpl, tf = "poisson-tweedie", zt = FALSE)

Arguments

pv

A vector of parameters.

smpl

A sample data to be used for estimation.

tf

Tempering function. It can be one of the "discrete-stable", "discrete-truncated-stable", "discrete-pRDTS", "poisson-tweedie", "exp-tempering", "beta-prime-tempering", "Pareto-tempering".

zt

Logical. If True it calculates zero-truncated probabilities.

Value

A number. Negative of likelihood function.

References

M. Grabchak. Discrete tempered stable distributions. Methodology and Computing in Applied Probability, 24(3):1877-1890, 2021.

Examples

pv <- c(0.5, 1, 1)
n <- 100
smpl <- rdts(n, 0.5, 1)
edts(pv, smpl)

The probability distribution of the discrete tempered stable distribution.

Description

The probability distribution of the discrete tempered stable distribution.

Usage

pdts(x, alpha, eta, tp = c(1, 1), tf = "poisson-tweedie", zt = FALSE)

Arguments

x

vector of points.

alpha

Index of stability; Number in (0,1)

eta

A parameter, eta>0.

tp

A vector of tempering parameters.

tf

Tempering function. It can be one of the "discrete-stable", "discrete-truncated-stable", "discrete-pRDTS", "poisson-tweedie", "exp-tempering", "beta-prime-tempering", "Pareto-tempering".

zt

Logical. If True it calculates zero-truncated probabilities.

Value

A vector of numbers.

References

M. Grabchak. Discrete tempered stable distributions. Methodology and Computing in Applied Probability, 24(3):1877-1890, 2021.

Examples

x <- 0:10
pdts(x, 0.5, 1)

Simulation from a discrete tempered stable distribution.

Description

Simulation from a discrete tempered stable distribution.

Usage

rdts(n, alpha, eta, tp = c(1, 1), tf = "poisson-tweedie", c = 1, zt = FALSE)

Arguments

n

Number of observations.

alpha

Index of stability; Number in (0,1)

eta

A parameter, eta>0.

tp

A vector of tempering parameters.

tf

Tempering function. It can be one of the "discrete-stable", "discrete-truncated-stable", "discrete-pRDTS", "poisson-tweedie", "exp-tempering", "beta-prime-tempering", "Pareto-tempering".

c

The essential supremum of the tempering function.

zt

Logical. If True it calculates zero-truncated probabilities.

Value

A vector of observations from a DTS distributions.

References

M. Grabchak. Discrete tempered stable distributions. Methodology and Computing in Applied Probability, 24(3):1877-1890, 2021.

Examples

n <- 10
rdts(n, 0.5, 1)

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