Title: | Mainardi-Wright Family of Distributions |
---|---|
Description: | Implements random number generation, plotting, and estimation algorithms for the two-parameter one-sided and two-sided M-Wright (Mainardi-Wright) family. The M-Wright distributions naturally generalize the widely used one-sided (Airy and half-normal or half-Gaussian) and symmetric (Airy and Gaussian or normal) models. These are widely studied in time-fractional differential equations. References: Cahoy and Minkabo (2017) <doi:10.3233/MAS-170388>; Cahoy (2012) <doi:10.1007/s00180-011-0269-x>; Cahoy (2012) <doi:10.1080/03610926.2010.543299>; Cahoy (2011); Mainardi, Mura, and Pagnini (2010) <doi:10.1155/2010/104505>. |
Authors: | Dexter Cahoy |
Maintainer: | Dexter Cahoy <[email protected]> |
License: | GPL (>= 3) |
Version: | 0.3.2 |
Built: | 2024-12-11 06:44:04 UTC |
Source: | CRAN |
Plots the density function.
dmwright1(ah, sh, m, max)
dmwright1(ah, sh, m, max)
ah |
point estimate for shape parameter alpha. |
sh |
point estimate for scale parameter s. |
m |
number of data points (pairs) to use for plotting. |
max |
maximum x-axis value to use for plotting. |
numeric matrix
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
xy=dmwright1(0.45, 2.5, 1000, 10) plot(xy[,1], xy[,2], lwd = 2, type="l",ylab="", xlab="x") mwright1_sided <- rmwright1(1000, 0.45, 2.5) hist(mwright1_sided, br=30, prob=TRUE) lines(xy[,1], xy[,2], lwd=2 )
xy=dmwright1(0.45, 2.5, 1000, 10) plot(xy[,1], xy[,2], lwd = 2, type="l",ylab="", xlab="x") mwright1_sided <- rmwright1(1000, 0.45, 2.5) hist(mwright1_sided, br=30, prob=TRUE) lines(xy[,1], xy[,2], lwd=2 )
Plots the density function.
dmwright2(ah, sh, m, max)
dmwright2(ah, sh, m, max)
ah |
point estimate for shape parameter alpha. |
sh |
point estimate for scale parameter s. |
m |
number of data points (pairs) to use for plotting. |
max |
maximum x-axis value to use for plotting. |
numeric matrix
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
xy=dmwright2(0.45, 2.5, 1000, 10) plot(xy[,1], xy[,2], lwd = 2, type="l",ylab="", xlab="x") mwright2_sided <- rmwright2(1000, 0.45, 2.5) hist(mwright2_sided, br=30, prob=TRUE) lines(xy[,1], xy[,2], lwd=2 )
xy=dmwright2(0.45, 2.5, 1000, 10) plot(xy[,1], xy[,2], lwd = 2, type="l",ylab="", xlab="x") mwright2_sided <- rmwright2(1000, 0.45, 2.5) hist(mwright2_sided, br=30, prob=TRUE) lines(xy[,1], xy[,2], lwd=2 )
Confidence intervals for the model parameters.
int_est1(x, lev)
int_est1(x, lev)
x |
numeric vector |
lev |
confidence level. |
matrix
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
mwright_1sided <- rmwright1(1000, 0.7, 0.4) int_est1(mwright_1sided ,0.95)
mwright_1sided <- rmwright1(1000, 0.7, 0.4) int_est1(mwright_1sided ,0.95)
Confidence intervals for the model parameters.
int_est2(x, lev)
int_est2(x, lev)
x |
numeric vector |
lev |
confidence level. |
matrix
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
mwright_2sided <- rmwright2(1000, 0.7, 0.4) int_est2(mwright_2sided ,0.95)
mwright_2sided <- rmwright2(1000, 0.7, 0.4) int_est2(mwright_2sided ,0.95)
Contains random number generation, plotting, and estimation algorithms for the two-parameter one-sided and two-sided M-Wright (Mainardi-Wright) family. The M-Wright distributions naturally generalize widely used one-sided (Airy and half-normal or half-normal) and symmetric (Airy and Gaussian or normal) models. These are widely studied in time-fractional diffusion processes.
References:
Cahoy and Minkabo (2017)<doi:10.3233/MAS-170388>
Cahoy (2012) <doi:10.1007/s00180-011-0269-x>
Cahoy (2012) <doi:10.1080/03610926.2010.543299>
Cahoy (2011)
Mainardi, Mura, and Pagnini (2010) <doi:10.1155/2010/104505>
Dexter Cahoy [email protected]
Calculates a left-tail probability.
pmwright1(alp, sc, upper)
pmwright1(alp, sc, upper)
alp |
point estimate for shape parameter alpha. |
sc |
point estimate for scale parameter s. |
upper |
non-negative upper quantile |
numeric
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
pmwright1(runif(1), runif(1,0,10),Inf ) pmwright1(runif(1), runif(1,0,10), 0.5 )
pmwright1(runif(1), runif(1,0,10),Inf ) pmwright1(runif(1), runif(1,0,10), 0.5 )
Calculates a left-tail probability.
pmwright2(alp, sc, upper)
pmwright2(alp, sc, upper)
alp |
point estimate for shape parameter alpha. |
sc |
point estimate for scale parameter s. |
upper |
upper quantile |
numeric
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
pmwright2(runif(1), runif(1,0,10), Inf ) pmwright2(runif(1), runif(1,0,10), 0.5 )
pmwright2(runif(1), runif(1,0,10), Inf ) pmwright2(runif(1), runif(1,0,10), 0.5 )
This provides point estimates for the shape and scale parameters.
point_est1(x)
point_est1(x)
x |
numeric vector. |
numeric vector
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
x <- rmwright1(1000, 0.7, 0.4) point_est1(x)
x <- rmwright1(1000, 0.7, 0.4) point_est1(x)
This provides point estimates for the shape and scale parameters.
point_est2(x)
point_est2(x)
x |
numeric vector. |
numeric vector
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
x <- rmwright2(1000, 0.7, 0.4) point_est2(x)
x <- rmwright2(1000, 0.7, 0.4) point_est2(x)
Generates random numbers.
rmwright1(n, nu, sc)
rmwright1(n, nu, sc)
n |
sample size. |
nu |
a number between 0 and 1. |
sc |
a non-negative scale value. |
a vector of one-sided M-Wright distributed random numbers
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoy (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
mwright_1sided <- rmwright1(1000, 0.7, 0.4) hist(mwright_1sided, br=30)
mwright_1sided <- rmwright1(1000, 0.7, 0.4) hist(mwright_1sided, br=30)
Generates random numbers.
rmwright2(n, nu, sc)
rmwright2(n, nu, sc)
n |
sample size. |
nu |
a number between 0 and 1. |
sc |
a non-negative scale value. |
a vector of two-sided M-Wright distributed random numbers.
Cahoy and Minkabo (2017). Inference for three-parameter M-Wright distributions with applications. Model Assisted Statistics and Applications, 12(2), 115-125. https://doi.org/10.3233/MAS-170388
Cahoy (2012). Moment estimators for the two-parameter M-Wright distribution. Computational Statistics, 27(3), 487-497. https://doi.org/10.1007/s00180-011-0269-x
Cahoy (2012). Estimation and simulation for the M-Wright function. Communications in Statistics-Theory and Methods, 41(8), 1466-1477. https://doi.org/10.1080/03610926.2010.543299
Cahoyd (2011). On the parameterization of the M-Wright function. Far East Journal of Theoretical Statistics, 34(2), 155-164. http://www.pphmj.com/abstract/5767.htm
Mainardi, Mura, and Pagnini (2010). The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. Int. J. Differ. Equ., Volume 2010. https://doi.org/10.1155/2010/104505
mwright_2sided <- rmwright2(1000, 0.7, 0.4) hist(mwright_2sided, br=30)
mwright_2sided <- rmwright2(1000, 0.7, 0.4) hist(mwright_2sided, br=30)