Type:	Package
Title:	Neo-Normal Distribution
Version:	0.1.2
Maintainer:	Achmad Syahrul Choir <madsyair@stis.ac.id>
Description:	Calculating the density, cumulative distribution, quantile, and random number of neo-normal distribution. It also interfaces with the 'brms' package, allowing the use of the neo-normal distribution as a custom family. This integration enables the application of various 'brms' formulas for neo-normal regression. Modified to be Stable as Normal from Burr (MSNBurr), Modified to be Stable as Normal from Burr-IIa (MSNBurr-IIa), Generalized of MSNBurr (GMSNBurr), Jones-Faddy Skew-t, Fernandez-Osiewalski-Steel Skew Exponential Power, and Jones Skew Exponential Power distributions are supported. References: Choir, A. S. (2020).Unpublished Dissertation, Iriawan, N. (2000).Unpublished Dissertation, Rigby, R. A., Stasinopoulos, M. D., Heller, G. Z., & Bastiani, F. D. (2019) <doi:10.1201/9780429298547>.
License:	GPL-3
Depends:	R (≥ 3.6.0),shinythemes,plotly,brms
Imports:	rstan , stats,Rmpfr,ggplot2,shiny
Suggests:	spelling, kableExtra, knitr, rmarkdown, testthat, bayesplot, loo
URL:	https://github.com/madsyair/neodistr
BugReports:	https://github.com/madsyair/neodistr/issues
Encoding:	UTF-8
NeedsCompilation:	no
Packaged:	2025-07-12 03:18:23 UTC; madsyair
RoxygenNote:	7.3.2
VignetteBuilder:	knitr, rmarkdown
Language:	en-US
Author:	Achmad Syahrul Choir [aut, cre], Anisa Faoziah [aut], Nur Iriawan [aut], Almira Utami [ctb], Meischa Zahra Nur Adhelia [ctb]
Repository:	CRAN
Date/Publication:	2025-07-12 07:10:02 UTC

Neo-normal model using brms

Description

Neo-normal model using brms

Usage

bnrm(
  formula,
  data,
  family = msnburr(),
  prior = NULL,
  data2 = NULL,
  sample_prior = "no",
  knots = NULL,
  drop_unused_levels = TRUE,
  stanvars = NULL,
  fit = NA,
  save_pars = getOption("brms.save_pars", NULL),
  init = NULL,
  chains = 4,
  iter = 2000,
  warmup = floor(iter/2),
  thin = 1,
  cores = getOption("mc.cores", 1),
  threads = getOption("brms.threads", NULL),
  opencl = getOption("brms.opencl", NULL),
  normalize = getOption("brms.normalize", TRUE),
  control = list(adapt_delta = 0.9),
  algorithm = getOption("brms.algorithm", "sampling"),
  backend = getOption("brms.backend", "rstan"),
  future = getOption("future", FALSE),
  silent = 1,
  seed = NA,
  save_model = NULL,
  stan_model_args = list(),
  file = NULL,
  file_compress = TRUE,
  file_refit = getOption("brms.file_refit", "never"),
  empty = FALSE,
  rename = TRUE,
  ...
)

Arguments

Details

Fit a neo-normal model that using brm function in brms package.All arguments in this functions follow arguments of brm function, except family

Value

An object of class brmsfit, which contains the posterior draws along with many other useful information about the model. Use methods(class = "brmsfit") for an overview on available methods.

Author(s)

Achmad Syahrul Choir

References

Burkner,P-C (2017). brms: An R Package for Bayesian Multilevel Models Using Stan. Journal of Statistical Software, 80(1), 1-28. doi:10.18637/jss.v080.i01

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember.

Iriawan, N. (2000). Computationally Intensive Approaches to Inference in Neo-Normal Linear Models. Curtin University of Technology.

Examples

## Not run: 
  library(neodistr)
  x<-runif(100)
  e<-rmsnburr(100,0,1,0.8)
  y<-0.5+0.8*x+e
  data<-data.frame(y,x)
  fit <- bnrm(
    y ~ x, data = data,
    family = msnburr())
  summary(fit)
  pp <- posterior_predict(fit)
  ppe <- posterior_epred(fit)
  loo(fit)
  
## End(Not run)

Neo-normal as custom distribution family in brms

Description

Neo-normal as custom distribution family in brms

Usage

brms_custom_family(family = "msnburr", vectorize = TRUE)

Arguments

Value

custom_family is an object of class custom family of brms and stanvars_family is stanvars object (the Stan code of function of neo-normal distributions (lpdf,cdf,lcdf,lccdf,quantile and rng))

Author(s)

Achmad Syahrul Choir

Examples

## Not run: 
  library(brms)
  library(neodistr)
  x<-runif(100)
  e<-rmsnburr(100,0,1,0.8)
  y<-0.5+0.8*x+e
  data<-data.frame(y,x)
  msnburr<-brms_custom_family("msnburr")
  fit <- brm(
    y ~ x, data = data,
    family = msnburr$custom_family, stanvars = msnburr$stanvars_family,
    prior=c(set_prior("cauchy(0,5)",class="alpha"),set_prior("cauchy(0,1)",class="sigma"))
  )
  summary(fit)
  pp <- posterior_predict(fit)
  ppe <- posterior_epred(fit)
  loo(fit)
  
## End(Not run)

Fernandez-Osiewalski-Steel Skew Exponential Power Distribution

Description

To calculate density function, distribution function, quantile function, and build data from random generator function for the Fernandez-Osiewalski-Steel Skew Exponential Power Distribution.

Usage

dfossep(x, mu = 0, sigma = 1, alpha = 2, beta = 2, log = FALSE)

pfossep(
  q,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

qfossep(
  p,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

rfossep(n, mu = 0, sigma = 1, alpha = 2, beta = 2)

Arguments

Details

Fernandez-Osiewalski-Steel Skew Exponential Power Distribution

The Fernandez-Osiewalski-Steel Skew Exponential Power distribution with parameters \mu, \sigma,\alpha, and \beta has density:

f(x |\mu,\sigma,\beta,\alpha) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| v z \right|^\tau \right) \quad \text{if } x < \mu

f(x |\mu,\sigma,\beta,\alpha) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| \frac{v}{z} \right|^\tau \right) \quad \text{if } x \ge \mu

\text{where } -\infty < y < \infty, \ -\infty < \mu < \infty, \ \sigma > 0, \ \alpha > 0, \ \beta > 0

z = \frac{x - \mu}{\sigma}

c = v \tau \left[ (1 + v^2) 2^{\frac{1}{\tau}} \Gamma \left( \frac{1}{\tau} \right) \right]^{-1}

Value

dfossep gives the density , pfossep gives the distribution function, qfossep gives quantiles function, rfossep generates random numbers.

Author(s)

Almira Utami

References

Fernandez, C., Osiewalski, J., & Steel, M. F. (1995) Modeling and inference with v-spherical distributions. Journal of the American Statistical Association, 90(432), pp 1331-1340.

Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press

Examples

dfossep(4, mu=0, sigma=1, alpha=2, beta=2)
pfossep(4, mu=0, sigma=1, alpha=2, beta=2)
qfossep(0.4, mu=0, sigma=1, alpha=2, beta=2)
rfossep(4, mu=0, sigma=1, alpha=2, beta=2)

GMSNBurr distribution

Description

To calculate density function, distribution function, quantile function, and build data from random generator function for the GMSNBurr Distribution.

Usage

dgmsnburr(x, mu = 0, sigma = 1, alpha = 1, beta = 1, log = FALSE)

pgmsnburr(
  q,
  mu = 0,
  sigma = 1,
  alpha = 1,
  beta = 1,
  lower.tail = TRUE,
  log.p = FALSE
)

qgmsnburr(
  p,
  mu = 0,
  sigma = 1,
  alpha = 1,
  beta = 1,
  lower.tail = TRUE,
  log.p = FALSE
)

rgmsnburr(n, mu = 0, sigma = 1, alpha = 1, beta = 1)

Arguments

Details

GMSNBurr Distribution

The GMSNBurr distribution with parameters \mu, \sigma,\alpha, and \beta has density:

f(x |\mu,\sigma,\alpha,\beta) = {\frac{\omega}{{B(\alpha,\beta)}\sigma}}{{\left(\frac{\beta}{\alpha}\right)}^\beta} {{\exp{\left(-\beta \omega {\left(\frac{x-\mu}{\sigma}\right)}\right)} {{\left(1+{\frac{\beta}{\alpha}} {\exp{\left(-\omega {\left(\frac{x-\mu}{\sigma}\right)}\right)}}\right)}^{-(\alpha+\beta)}}}}

where -\infty<x<\infty, -\infty<\mu<\infty, \sigma>0, \alpha>0, \beta>0 and \omega = {\frac{B(\alpha,\beta)}{\sqrt{2\pi}}}{{\left(1+{\frac{\beta}{\alpha}}\right)}^{\alpha+\beta}}{\left(\frac{\beta}{\alpha}\right)}^{-\beta}

Value

dgmsnburr gives the density , pgmasnburr gives the distribution function, qgmsnburr gives quantiles function, rgmsnburr generates random numbers.

Author(s)

Achmad Syahrul Choir

References

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember.

Iriawan, N. (2000). Computationally Intensive Approaches to Inference in Neo-Normal Linear Models. Curtin University of Technology.

Examples

library("neodistr")
dgmsnburr(0, mu=0, sigma=1, alpha=1,beta=1)
pgmsnburr(4, mu=0, sigma=1, alpha=1, beta=1)
qgmsnburr(0.4, mu=0, sigma=1, alpha=1, beta=1)
r=rgmsnburr(10000, mu=0, sigma=1, alpha=1, beta=1)
head(r)
hist(r, xlab = 'GMSNBurr random number', ylab = 'Frequency', 
main = 'Distribution of GMSNBurr Random Number ')

Jones Faddy's Skew-t Distribution

Description

To calculate density function, distribution function, quantile function, and build data from random generator function for the Jones-Faddy's Skew-t Distribution.

Usage

djfst(x, mu = 0, sigma = 1, alpha = 2, beta = 2, log = FALSE)

pjfst(
  q,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

qjfst(
  p,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

rjfst(n, mu = 0, sigma = 1, alpha = 2, beta = 2)

Arguments

Details

Jones-Faddy's Skew-t Distribution

The Jones-Faddy's Skew-t distribution with parameters \mu, \sigma,\alpha, and \beta has density:

f(x |\mu,\sigma,\beta,\alpha)= \frac{c}{\sigma} {\left[{1+\frac{z}{\sqrt{\alpha+\beta+z^2}}}\right]}^{\alpha+\frac{1}{2}} {\left[{1-\frac{z}{\sqrt{\alpha+\beta+z^2}}}\right]}^{\beta+\frac{1}{2}}

where -\infty<x<\infty, -\infty<\mu<\infty, \sigma>0, \alpha>0, \beta>0, z =\frac{x-\mu}{\sigma} , c = {\left[2^{\left(\alpha+\beta-1\right)} {\left(\alpha+\beta\right)^{\frac{1}{2}}} B(a,b)\right]}^{-1} ,

Value

djfst gives the density , pjfst gives the distribution function, qjfst gives quantiles function, rjfst generates random numbers.

Author(s)

Anisa' Faoziah

References

Jones, M.C. and Faddy, M. J. (2003) A skew extension of the t distribution, with applications. Journal of the Royal Statistical Society, Series B, 65, pp 159-174

Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press

Examples

djfst(4, mu=0, sigma=1, alpha=2, beta=2)
pjfst(4, mu=0, sigma=1, alpha=2, beta=2)
qjfst(0.4, mu=0, sigma=1, alpha=2, beta=2)
r=rjfst(10000, mu=0, sigma=1, alpha=2, beta=2)
head(r)
hist(r, xlab = 'jfst random number', ylab = 'Frequency', 
main = 'Distribution of jfst Random Number ')

Jones Skew Exponential Power

Description

To calculate density function, distribution function, quantile function, and build data from random generator function for the Jones Skew Exponential Power

Usage

djsep(x, mu = 0, sigma = 1, alpha = 2, beta = 2, log = FALSE)

pjsep(
  q,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

qjsep(
  p,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

rjsep(n, mu = 0, sigma = 1, alpha = 2, beta = 2)

Arguments

Details

Jones Skew Exponential Power

The Jones Skew Exponential Power with parameters \mu, \sigma,\alpha, and \beta has density:

f(y | \mu, \sigma, \alpha, \beta) = \left\{ \begin{array}{ll} \frac{c}{\sigma} \exp\left(-|z|^{\alpha}\right), & \text{if } y < \mu \\ \frac{c}{\sigma} \exp\left(-|z|^{\beta}\right), & \text{if } y \geq \mu \end{array} \right.

where:

z = \frac{y - \mu}{\sigma},

c = \left[ \Gamma(1 + \beta^{-1}) + \Gamma(1 + \alpha^{-1}) \right]^{-1}.

Value

djsep gives the density , pjsep gives the distribution function, qjsep gives quantiles function, rjsep generates random numbers.

Author(s)

Meischa Zahra Nur Adhelia

References

Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press

Examples

djsep(4, mu=0, sigma=1, alpha=2, beta=2)
pjsep(4, mu=0, sigma=1, alpha=2, beta=2)
qjsep(0.5, mu=0, sigma=1, alpha=2, beta=2)
rjsep(4, mu=0, sigma=1, alpha=2, beta=2)

MSNBurr Distribution

Description

To calculate density function, distribution function, quantile function, and build data from random generator function for the MSNBurr Distribution.

Usage

dmsnburr(x, mu = 0, sigma = 1, alpha = 1, log = FALSE)

pmsnburr(q, mu = 0, sigma = 1, alpha = 1, lower.tail = TRUE, log.p = FALSE)

qmsnburr(p, mu = 0, sigma = 1, alpha = 1, lower.tail = TRUE, log.p = FALSE)

rmsnburr(n, mu = 0, sigma = 1, alpha = 1)

Arguments

Details

MSNBurr Distribution

The MSNBurr distribution with parameters \mu, \sigma,and \alpha has density:

f(x |\mu,\sigma,\alpha)=\frac{\omega}{\sigma}\exp{\left(\omega{\left(\frac{x-\mu}{\sigma}\right)}\right)}{{\left(1+\frac{\exp{\left(\omega{(\frac{x-\mu}{\sigma})}\right)}}{\alpha}\right)}^{-(\alpha+1)}}

where -\infty < x < \infty, -\infty < \mu< \infty, \sigma>0, \alpha>0, \omega = \frac{1}{\sqrt{2\pi}} {\left(1+\frac{1}{\alpha}\right)^{\alpha+1}}

Value

dmsnburr gives the density , pmsnburr gives the distribution function, qmsnburr gives quantiles function, rmsnburr generates random numbers.

Author(s)

Achmad Syahrul Choir and Nur Iriawan

References

Iriawan, N. (2000). Computationally Intensive Approaches to Inference in Neo-Normal Linear Models. Curtin University of Technology.

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember.

Examples

library("neodistr")
dmsnburr(0, mu=0, sigma=1, alpha=0.1)
plot(function(x) dmsnburr(x, alpha=0.1), -20, 3,
main = "Left Skew MSNBurr Density ",ylab="density")
pmsnburr(7, mu=0, sigma=1, alpha=1)
qmsnburr(0.6, mu=0, sigma=1, alpha=1)
r<- rmsnburr(10000, mu=0, sigma=1, alpha=1)
head(r)
hist(r, xlab = 'MSNBurr random number', ylab = 'Frequency', 
main = 'Distribution of MSNBurr Random Number ')

MSNBurr-IIa distribution.

Description

To calculate density function, distribution function, quantile function, and build data from random generator function for the MSNBurr distribution.

Usage

dmsnburr2a(x, mu = 0, sigma = 1, alpha = 1, log = FALSE)

pmsnburr2a(q, mu = 0, sigma = 1, alpha = 1, lower.tail = TRUE, log.p = FALSE)

qmsnburr2a(p, mu = 0, sigma = 1, alpha = 1, lower.tail = TRUE, log.p = FALSE)

rmsnburr2a(n, mu = 0, sigma = 1, alpha = 1)

Arguments

Details

MSNBurr-IIa Distribution

The MSNBurr-IIa distribution with parameters \mu, \sigma, and \alpha has density:

f(x |\mu,\sigma,\alpha)=\frac{\omega}{\sigma}\exp{\left(\omega{\left(\frac{x-\mu}{\sigma}\right)}\right)}{{\left(1+\frac{\exp{\left(\omega{(\frac{x-\mu}{\sigma})}\right)}}{\alpha}\right)}^{-(\alpha+1)}}

where -\infty < x < \infty, -\infty < \mu< \infty, \sigma>0, \alpha>0, \omega = \frac{1}{\sqrt{2\pi}} {\left(1+\frac{1}{\alpha}\right)^{\alpha+1}}

Value

dmsnburr2a gives the density, pmsnburr2a gives the distribution function, qmsnburr2a gives the quantile function and rmsnburr2a generates random numbers.

Author(s)

Achmad Syahrul Choir and Nur Iriawan

References

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember.

Examples

library("neodistr")
dmsnburr2a(7, mu=0, sigma=1, alpha=0.1)
plot(function(x) dmsnburr2a(x, alpha=0.1), -3, 20,
main = "Right Skew MSNBurr-IIa Density ",ylab="density")
p=pmsnburr2a(4, mu=0, sigma=1, alpha=1)
p
q=qmsnburr2a(p, mu=0, sigma=1, alpha=1)
q
qmsnburr2a(0.5, mu=0, sigma=1, alpha=1)
r=rmsnburr2a(10000, mu=0, sigma=1, alpha=0.1)
head(r)
hist(r, xlab = 'MSNBurr random number', ylab = 'Frequency', 
main = 'Distribution of MSNBurr-IIa Random Number ')

Starts shiny application for the neodistr package

Description

Starts shiny application for the neodistr package

Usage

neoshiny()

Value

Starts shiny application for the neodistr package.

Author(s)

Anisa' Faoziah and Achmad Syahrul Choir

Examples

if 	(interactive()) {
	suppressMessages(library(neodistr))	
	neoshiny()
	}

Stan function of Fernandez-Osiewalski-Steel Skew Exponential Power Distribution

Description

Stan code of fossep distribution for custom distribution in stan

Usage

stanf_fossep(vectorize = TRUE)

Arguments

Details

Fernandez-Osiewalski-Steel Skew Exponential Power Distribution has density:

f(y |\mu,\sigma,\alpha,\beta) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| v z \right|^\beta \right) \quad \text{if } y < \mu

f(y |\mu,\sigma,\alpha,\beta) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| \frac{v}{z} \right|^\beta \right) \quad \text{if } y \ge \mu

\text{where } -\infty < y < \infty, \ -\infty < \mu < \infty, \ \sigma > 0, \ \alpha > 0, \ \beta > 0

z = \frac{y - \mu}{\sigma}

c = v \beta \left[ (1 + v^2) 2^{\frac{1}{\beta}} \Gamma \left( \frac{1}{\beta} \right) \right]^{-1}

This function gives stan code of log density, cumulative distribution, log of cumulative distribution, log complementary cumulative distribution of Fernandez-Osiewalski-Steel Skew Exponential Power Distribution

Value

fossep_lpdf gives stan's code of the log of density, fossep_cdf gives stan's code of the distribution function, fossep_lcdf gives stan's code of the log of distribution function and fossep_lccdf gives the stans's code of complement of log distribution function (1-fossep_lcdf)

Author(s)

Almira Utami and Achmad Syahrul Choir

References

Fernandez, C., Osiewalski, J., & Steel, M. F. (1995) Modeling and inference with v-spherical distributions. Journal of the American Statistical Association, 90(432), pp 1331-1340

Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press

Examples

## Not run: 
library (neodistr)
library (rstan)

# inputting data
set.seed(400)
dt <- neodistr::rfossep(100,mu=0, sigma=1, alpha = 2, beta = 2) # random generating fossep data
dataf <- list(
 n = 100,
 y = dt
 )
 
 
#### Vector
## Calling the function of the neonormal distribution that is available in the package.
func_code_vector<-paste(c("functions{",neodistr::stanf_fossep(vectorize=TRUE),"}"),collapse="\n")

# Define Stan Model Code
model_vector <-"
    data{
      int<lower=1> n;
      vector[n] y;
    }
    parameters{
      real mu;
      real <lower=0> sigma;
      real <lower=0> alpha;
      real <lower=0>beta;
    }
    model {
      y ~ fossep(rep_vector(mu,n),sigma, alpha, beta);
      mu ~ cauchy (0,1);
      sigma ~ cauchy (0, 1);
      alpha ~ lognormal(0,2.5);
      beta ~ lognormal(0,2.5);
      
    }
 "
 
 # Merge stan model code and selected neo-normal stan function
fit_code_vector <- paste (c(func_code_vector,model_vector,"\n"), collapse = "\n")

# Create the model using Stan Function
fit2 <- stan(
    model_code = fit_code_vector,  # Stan Program
    data = dataf,                  # named list data
    chains = 2,                    # number of markov chains
    warmup = 5000,                 # total number of warmup iterarions per chain
    iter = 10000,                  # total number of iterations iterarions per chain
    cores = 2,                     # number of cores (could use one per chain)
    control = list(                # control sampel behavior
      adapt_delta = 0.99
    ),
    refresh = 1000                 # progress has shown if refresh >=1, else no progress shown
)

# Showing the estimation result of the parameters that were executed using the Stan file
print(fit2, pars = c("mu", "sigma", "alpha", "beta", "lp__"), probs=c(.025,.5,.975))
 
## End(Not run)

Stan function of GMSNBurr Distribution

Description

Stan code of GMSNBurr distribution for custom distribution in stan

Usage

stanf_gmsnburr(vectorize = TRUE, rng = TRUE)

Arguments

Details

GMSNBurr Distribution has density:

f(y |\mu,\sigma,\alpha,\beta) = {\frac{\omega}{{B(\alpha,\beta)}\sigma}}{{\left(\frac{\beta}{\alpha}\right)}^\beta} {{\exp{\left(-\beta \omega {\left(\frac{y-\mu}{\sigma}\right)}\right)} {{\left(1+{\frac{\beta}{\alpha}} {\exp{\left(-\omega {\left(\frac{y-\mu}{\sigma}\right)}\right)}}\right)}^{-(\alpha+\beta)}}}}

where -\infty<y<\infty, -\infty<\mu<\infty, \sigma>0, \alpha>0, \beta>0 and \omega = {\frac{B(\alpha,\beta)}{\sqrt{2\pi}}}{{\left(1+{\frac{\beta}{\alpha}}\right)}^{\alpha+\beta}}{\left(\frac{\beta}{\alpha}\right)}^{-\beta}

This function gives stan code of log density, cumulative distribution, log of cumulative distribution, log complementary cumulative distribution, quantile, random number of GMSNBurr distribution

Value

msnburr_lpdf gives the stans's code of log of density, msnburr_cdf gives the stans's code of distribution function, gmsnburr_lcdf gives the stans's code of log of distribution function, gmsnburr_lccdf gives the stans's code of complement of log distribution function (1-gmsnburr_lcdf), and gmsnburr_rng the stans's code of generates random numbers.

Author(s)

Achmad Syahrul Choir

References

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember.

Examples

## Not run: 
library(neodistr)
library(rstan)
#inputting data
set.seed(136)
dt <- rgmsnburr(100,0,1,0.5,0.5) # random generating MSNBurr-IIA data 
dataf <- list(
  n = 100,
  y = dt
)
#### not vector  
##Calling the function of the neo-normal distribution that is available in the package.
func_code<-paste(c("functions{",neodistr::stanf_gmsnburr(vectorize=FALSE),"}"),collapse="\n")
#define stan model code
model<-"
  data {
  int<lower=1> n;
  vector[n] y;
  }
  parameters {
  real mu;
  real <lower=0> sigma;
  real <lower=0> alpha;
  real <lower=0> beta; 
  }
  model {
  for(i in 1:n){
  y[i]~gmsnburr(mu,sigma,alpha,beta);
  }
  mu~cauchy(0,1);
  sigma~cauchy(0,2.5);
  alpha~cauchy(0,1);
  beta~cauchy(0,1);
  }
   "
#merge stan model code and selected neo-normal stan function
fit_code<-paste(c(func_code,model,"\n"),collapse="\n") 

# Create the model using stan function
fit1 <- stan(
  model_code = fit_code,  # Stan program
  data = dataf,    # named list of data
  chains = 2,             # number of Markov chains
  #warmup = 5000,          # number of warmup iterations per chain
  iter = 10000,           # total number of iterations per chain
  cores = 2,              # number of cores (could use one per chain)
  control = list(         #control samplers behavior
    adapt_delta=0.9
  )
)

# Showing the estimation results of the parameters that were executed using the Stan file
print(fit1, pars=c("mu", "sigma", "alpha", "beta","lp__"), probs=c(.025,.5,.975))


# Vector
##Calling the function of the neo-normal distribution that is available in the package.
func_code_vector<-paste(c("functions{",neodistr::stanf_gmsnburr(vectorize=TRUE),"}"),collapse="\n")
# define stan model as vector
model_vector<-"
 data {
   int<lower=1> n;
   vector[n] y;
 }
 parameters {
   real mu;
   real <lower=0> sigma;
   real <lower=0> alpha;
   real <lower=0> beta;
 }
 model {
   y~gmsnburr(rep_vector(mu,n),sigma,alpha,beta);
   mu~cauchy(0,1);
   sigma~cauchy(0,2.5);
   alpha~cauchy(0,1);
   beta~cauchy(0,1);
 }
 "
#merge stan model code and selected neo-normal stan function
fit_code_vector<-paste(c(func_code_vector,model_vector,"\n"),collapse="\n")

# Create the model using stan function
fit2 <- stan(
  model_code = fit_code_vector,  # Stan program
  data = dataf,    # named list of data
  chains = 2,             # number of Markov chains
  #warmup = 5000,          # number of warmup iterations per chain
  iter = 10000,           # total number of iterations per chain
  cores = 2,              # number of cores (could use one per chain)
  control = list(         #control samplers behavior
    adapt_delta=0.9
  )
)

# Showing the estimation results of the parameters 
print(fit2, pars=c("mu", "sigma", "alpha","beta",  "lp__"), probs=c(.025,.5,.975))

## End(Not run)

Stan function of Jones and Faddy's Skew-t Distribution

Description

Stan code of JFST distribution for custom distribution in stan

Usage

stanf_jfst(vectorize = TRUE, rng = TRUE)

Arguments

Details

Jones-Faddy’s Skew-t distribution has density:

f(y |\mu,\sigma,\beta,\alpha)= \frac{c}{\sigma} {\left[{1+\frac{z}{\sqrt{\alpha+\beta+z^2}}}\right]}^{\alpha+\frac{1}{2}} {\left[{1-\frac{z}{\sqrt{\alpha+\beta+z^2}}}\right]}^{\beta+\frac{1}{2}}

where -\infty<y<\infty, -\infty<\mu<\infty, \sigma>0, \alpha>0, \beta>0, z =\frac{y-\mu}{\sigma} , c = {\left[2^{\left(\alpha+\beta-1\right)} {\left(\alpha+\beta\right)^{\frac{1}{2}}} B(a,b)\right]}^{-1} ,

This function gives stan code of log density, cumulative distribution, log of cumulative distribution, log complementary cumulative distribution, quantile, random number of Jones-Faddy's Skew-t distribution

Value

jfst_lpdf gives stan's code of the log of density, jfst_cdf gives stan's code of the distribution function, jfst_lcdf gives stan's code of the log of distribution function and jfst_rng gives stan's code of generates random numbers.

Author(s)

Anisa' Faoziah and Achmad Syahrul Choir

References

Jones, M.C. and Faddy, M. J. (2003) A skew extension of the t distribution, with applications. Journal of the Royal Statistical Society, Series B, 65, pp 159-174

Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press

Examples

## Not run: 
library (neodistr)
library (rstan)

# inputting data
set.seed(400)
dt <- neodistr::rjfst(100,mu=0, sigma=1, alpha = 2, beta = 2) # random generating JFST data
dataf <- list(
 n = 100,
 y = dt
 )
 
 
#### not vector
## Calling the function of the neo-normal distribution that is available in the package.
func_code<-paste(c("functions{",neodistr::stanf_jfst(vectorize=FALSE),"}"),collapse="\n")

# Define Stan Model Code
model <-"
    data{
      int<lower=1> n;
      vector[n] y;
    }
    parameters{
      real mu;
      real <lower=0> sigma;
      real <lower=0> alpha;
      real <lower=0> beta;
    }
    model {
      for(i in 1 : n){
      y[i] ~ jfst(mu,sigma, alpha, beta);
      }
      mu ~ cauchy(0,1);
      sigma ~ cauchy(0, 2.5);
      alpha ~ lognormal(0,5);
      beta ~ lognormal(0,5);
      
    }
"

# Merge stan model code and selected neo-normal stan function
fit_code <- paste (c(func_code,model,"\n"), collapse = "\n")

# Create the model using Stan Function
fit1 <- stan(
    model_code = fit_code,  # Stan Program
    data = dataf,           # named list data
    chains = 2,             # number of markov chains
    warmup = 5000,          # total number of warmup iterarions per chain
    iter = 10000,           # total number of iterations iterarions per chain
    cores = 2,              # number of cores (could use one per chain)
    control = list(         # control sampel behavior
      adapt_delta = 0.99
    ),
    refresh = 1000          # progress has shown if refresh >=1, else no progress shown
)

# Showing the estimation result of the parameters that were executed using the Stan file
print(fit1, pars = c("mu", "sigma", "alpha", "beta", "lp__"), probs=c(.025,.5,.975))


#### Vector
## Calling the function of the neonormal distribution that is available in the package.
func_code_vector<-paste(c("functions{",neodistr::stanf_jfst(vectorize=TRUE),"}"),collapse="\n")

# Define Stan Model Code
model_vector <-"
    data{
      int<lower=1> n;
      vector[n] y;
    }
    parameters{
      real mu;
      real <lower=0> sigma;
      real <lower=0> alpha;
      real <lower=0>beta;
    }
    model {
      y ~ jfst(rep_vector(mu,n),sigma, alpha, beta);
      mu ~ cauchy (0,1);
      sigma ~ cauchy (0, 2.5);
      alpha ~ lognormal(0,5);
      beta ~ lognormal(0,5);
      
    }
 "
 
 # Merge stan model code and selected neo-normal stan function
fit_code_vector <- paste (c(func_code_vector,model_vector,"\n"), collapse = "\n")

# Create the model using Stan Function
fit2 <- stan(
    model_code = fit_code_vector,  # Stan Program
    data = dataf,                  # named list data
    chains = 2,                    # number of markov chains
    warmup = 5000,                 # total number of warmup iterarions per chain
    iter = 10000,                  # total number of iterations iterarions per chain
    cores = 2,                     # number of cores (could use one per chain)
    control = list(                # control sampel behavior
      adapt_delta = 0.99
    ),
    refresh = 1000                 # progress has shown if refresh >=1, else no progress shown
)

# Showing the estimation result of the parameters that were executed using the Stan file
print(fit2, pars = c("mu", "sigma", "alpha", "beta", "lp__"), probs=c(.025,.5,.975))
 
## End(Not run)

Stan function of Jones Skew Exponential Power

Description

Stan code of jsep distribution for custom distribution in stan

Usage

stanf_jsep(vectorize = TRUE)

Arguments

Details

The Jones Skew Exponential Power with parameters \mu, \sigma,\alpha, and \beta has density:

f(y | \mu, \sigma, \alpha, \beta) = \left\{ \begin{array}{ll} \frac{c}{\sigma} \exp\left(-|z|^{\alpha}\right), & \text{if } y < \mu \\ \frac{c}{\sigma} \exp\left(-|z|^{\beta}\right), & \text{if } y \geq \mu \end{array} \right.

where:

z = \frac{y - \mu}{\sigma},

c = \left[ \Gamma(1 + \beta^{-1}) + \Gamma(1 + \alpha^{-1}) \right]^{-1}.

Value

jsep_lpdf gives stan's code of the log of density, jsep_cdf gives stan's code of the distribution function, and jsep_lcdf gives stan's code of the log of distribution function

Author(s)

Meischa Zahra Nur Adhelia and Achmad Syahrul Choir

References

Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press

Examples

## Not run: 
library (neodistr)
library (rstan)

# inputting data
set.seed(400)
dt <- neodistr::rjsep(100,mu=0, sigma=1, alpha = 2, beta = 2) # random generating jsep data
dataf <- list(
 n = 100,
 y = dt
 )
 
 
#### not vector
## Calling the function of the neo-normal distribution that is available in the package.
func_code<-paste(c("functions{",neodistr::stanf_jsep(vectorize=TRUE),"}"),collapse="\n")

# Define Stan Model Code
model <-"
    data{
      int<lower=1> n;
      vector[n] y;
    }
    parameters{
      real mu;
      real <lower=0> sigma;
      real <lower=0> alpha;
      real <lower=0> beta;
    }
    model {
      y ~ jsep(rep_vector(mu,n),sigma, alpha, beta);
      mu ~ cauchy(0,1);
      sigma ~ cauchy(0, 2.5);
      alpha ~ lognormal(0,5);
      beta ~ lognormal(0,5);
      
    }
"

# Merge stan model code and selected neo-normal stan function
fit_code <- paste (c(func_code,model,"\n"), collapse = "\n")

# Create the model using Stan Function
fit1 <- stan(
    model_code = fit_code,  # Stan Program
    data = dataf,           # named list data
    chains = 2,             # number of markov chains
    warmup = 5000,          # total number of warmup iterarions per chain
    iter = 10000,           # total number of iterations iterarions per chain
    cores = 2,              # number of cores (could use one per chain)
    control = list(         # control sampel behavior
      adapt_delta = 0.99
    ),
    refresh = 1000          # progress has shown if refresh >=1, else no progress shown
)

# Showing the estimation result of the parameters that were executed using the Stan file
print(fit1, pars = c("mu", "sigma", "alpha", "beta", "lp__"), probs=c(.025,.5,.975))


#### Vector
## Calling the function of the neonormal distribution that is available in the package.
func_code_vector<-paste(c("functions{",neodistr::stanf_jsep(vectorize=TRUE),"}"),collapse="\n")

# Define Stan Model Code
model_vector <-"
    data{
      int<lower=1> n;
      vector[n] y;
    }
    parameters{
      real mu;
      real <lower=0> sigma;
      real <lower=0> alpha;
      real <lower=0>beta;
    }
    model {
      y ~ jsep(rep_vector(mu,n),sigma, alpha, beta);
      mu ~ cauchy (0,1);
      sigma ~ cauchy (0, 2.5);
      alpha ~ lognormal(0,5);
      beta ~ lognormal(0,5);
      
    }
 "
 
 # Merge stan model code and selected neo-normal stan function
fit_code_vector <- paste (c(func_code_vector,model_vector,"\n"), collapse = "\n")

# Create the model using Stan Function
fit2 <- stan(
    model_code = fit_code_vector,  # Stan Program
    data = dataf,                  # named list data
    chains = 2,                    # number of markov chains
    warmup = 5000,                 # total number of warmup iterarions per chain
    iter = 10000,                  # total number of iterations iterarions per chain
    cores = 2,                     # number of cores (could use one per chain)
    control = list(                # control sampel behavior
      adapt_delta = 0.99
    ),
    refresh = 1000                 # progress has shown if refresh >=1, else no progress shown
)

# Showing the estimation result of the parameters that were executed using the Stan file
print(fit2, pars = c("mu", "sigma", "alpha", "beta", "lp__"), probs=c(.025,.5,.975))
 
## End(Not run)

Stan function of MSNBurr Distribution

Description

Stan code of MSNBurr distribution for custom distribution in stan

Usage

stanf_msnburr(vectorize = TRUE, rng = TRUE)

Arguments

Details

MSNBurr Distribution has density:

f(y |\mu,\sigma,\alpha)=\frac{\omega}{\sigma}\exp{\left(-\omega{\left(\frac{y-\mu}{\sigma}\right)}\right)}{{\left(1+\frac{\exp{\left(-\omega{(\frac{y-\mu}{\sigma})}\right)}}{\alpha}\right)}^{-(\alpha+1)}}

where -\infty < y < \infty, -\infty < \mu< \infty, \sigma>0, \alpha>0, \omega = \frac{1}{\sqrt{2\pi}} {\left(1+\frac{1}{\alpha}\right)^{\alpha+1}}

This function gives stan code of log density, cumulative distribution, log of cumulative distribution, log complementary cumulative distribution, quantile, random number of MSNBurr distribution

Value

msnburr_lpdf gives the log of density, msnburr_cdf gives the distribution function, msnburr_lcdf gives the log of distribution function, msnburr_lccdf gives the complement of log distribution function (1-msnburr_lcdf), and msnburr_rng generates random deviates.

Author(s)

Achmad Syahrul Choir and Nur Iriawan

References

Iriawan, N. (2000). Computationally Intensive Approaches to Inference in Neo-Normal Linear Models. Curtin University of Technology. Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember.

Examples

## Not run: 
library (neodistr)
library(rstan)
#inputting data
set.seed(136)
dt <- neodistr::rmsnburr(100,0,1,0.5) # random generating MSNBurr data 
dataf <- list(
  n = 100,
  y = dt
)
#### not vector  
##Calling the function of the neo-normal distribution that is available in the package.
func_code<-paste(c("functions{",neodistr::stanf_msnburr(vectorize=FALSE),"}"),collapse="\n")
#define stan model code
model<-"
 data {
 int<lower=1> n;
 vector[n] y;
 }
 parameters {
 real mu;
 real <lower=0> sigma;
 real <lower=0> alpha;
 
 }
 model {
 for(i in 1:n){
 y[i]~msnburr(mu,sigma,alpha);
 }
 mu~cauchy(0,1);
 sigma~cauchy(0,2.5);
 alpha~cauchy(0,1);
 }
  "
#merge stan model code and selected neo-normal stan function
fit_code<-paste(c(func_code,model,"\n"),collapse="\n") 

# Create the model using stan function
fit1 <- stan(
  model_code = fit_code,  # Stan program
  data = dataf,    # named list of data
  chains = 2,             # number of Markov chains
  #warmup = 5000,          # number of warmup iterations per chain
  iter = 10000,           # total number of iterations per chain
  cores = 2              # number of cores (could use one per chain)
)

# Showing the estimation results of the parameters that were executed using the Stan file
print(fit1, pars=c("mu", "sigma", "alpha", "lp__"), probs=c(.025,.5,.975))


# Vector
##Calling the function of the neo-normal distribution that is available in the package.
func_code_vector<-paste(c("functions{",neodistr::stanf_msnburr(vectorize=TRUE),"}"),collapse="\n")
# define stan model as vector
model_vector<-"
data {
  int<lower=1> n;
  vector[n] y;
}
parameters {
  real mu;
  real <lower=0> sigma;
  real <lower=0> alpha;
}
model {
  y~msnburr(rep_vector(mu,n),sigma,alpha);
  mu~cauchy(0,1);
  sigma~cauchy(0,2.5);
  alpha~cauchy(0,1);
}
"
#merge stan model code and selected neo-normal stan function
fit_code_vector<-paste(c(func_code_vector,model_vector,"\n"),collapse="\n")

# Create the model using stan function
fit2 <- stan(
  model_code = fit_code_vector,  # Stan program
  data = dataf,    # named list of data
  chains = 2,             # number of Markov chains
  #warmup = 5000,          # number of warmup iterations per chain
  iter = 10000,           # total number of iterations per chain
  cores = 2             # number of cores (could use one per chain)
)

# Showing the estimation results of the parameters that were executed using the Stan file
print(fit2, pars=c("mu", "sigma", "alpha",  "lp__"), probs=c(.025,.5,.975))


## End(Not run)

Stan function of MSNBurr-IIa Distribution

Description

Stan code of MSNBurr-IIa distribution for custom distribution in stan

Usage

stanf_msnburr2a(vectorize = TRUE, rng = TRUE)

Arguments

Details

MSNBurr-IIa Distribution has density function:

f(y |\mu,\sigma,\alpha)=\frac{\omega}{\sigma}\exp{\left(\omega{\left(\frac{y-\mu}{\sigma}\right)}\right)}{{\left(1+\frac{\exp{\left(\omega{(\frac{y-\mu}{\sigma})}\right)}}{\alpha}\right)}^{-(\alpha+1)}}

where -\infty < y < \infty, -\infty < \mu< \infty, \sigma>0, \alpha>0, \omega = \frac{1}{\sqrt{2\pi}} {\left(1+\frac{1}{\alpha}\right)^{\alpha+1}} This function gives stan code of log density, cumulative distribution, log of cumulative distribution, log complementary cumulative distribution, quantile, random number of MSNBurr-IIa distribution

Value

msnburr_lpdf gives the log of density, msnburr_cdf gives the distribution function, msnburr_lcdf gives the log of distribution function, msnburr_lccdf gives the complement of log distributionfunction (1-msnburr_lcdf), and msnburr_rng generates random deviates.

Author(s)

Achmad Syahrul Choir and Nur Iriawan

References

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember.

Examples

## Not run: 
library (neodistr)
library(rstan)
#inputting data
set.seed(136)
dt <- neodistr::rmsnburr2a(100,0,1,0.5) # random generating MSNBurr-IIA data 
dataf <- list(
  n = 100,
  y = dt
)
#### not vector  
##Calling the function of the neo-normal distribution that is available in the package.
func_code<-paste(c("functions{",neodistr::stanf_msnburr2a(vectorize=FALSE),"}"),collapse="\n")
#define stan model code
model<-"
 data {
 int<lower=1> n;
 vector[n] y;
 }
 parameters {
 real mu;
 real <lower=0> sigma;
 real <lower=0> alpha;
 
 }
 model {
 for(i in 1:n){
 y[i]~msnburr2a(mu,sigma,alpha);
 }
 mu~cauchy(0,1);
 sigma~cauchy(0,2.5);
 alpha~cauchy(0,1);
 }
  "
#merge stan model code and selected neo-normal stan function
fit_code<-paste(c(func_code,model,"\n"),collapse="\n") 

# Create the model using stan function
fit1 <- stan(
  model_code = fit_code,  # Stan program
  data = dataf,    # named list of data
  chains = 2,             # number of Markov chains
  #warmup = 5000,          # number of warmup iterations per chain
  iter = 10000,           # total number of iterations per chain
  cores = 2              # number of cores (could use one per chain)
)

# Showing the estimation results of the parameters that were executed using the Stan file
print(fit1, pars=c("mu", "sigma", "alpha", "lp__"), probs=c(.025,.5,.975))


# Vector
##Calling the function of the neo-normal distribution that is available in the package.
func_code_vector<-paste(c("functions{",neodistr::stanf_msnburr2a(vectorize=TRUE),"}"),collapse="\n")
# define stan model as vector
model_vector<-"
data {
  int<lower=1> n;
  vector[n] y;
}
parameters {
  real mu;
  real <lower=0> sigma;
  real  alpha;
}
model {
  y~msnburr2a(rep_vector(mu,n),sigma,alpha);
  mu~cauchy(0,1);
  sigma~cauchy(0,2.5);
  alpha~cauchy(0,1);
}
"
#merge stan model code and selected neo-normal stan function
fit_code_vector<-paste(c(func_code_vector,model_vector,"\n"),collapse="\n")

# Create the model using stan function
fit2 <- stan(
  model_code = fit_code_vector,  # Stan program
  data = dataf,    # named list of data
  chains = 2,             # number of Markov chains
  #warmup = 5000,          # number of warmup iterations per chain
  iter = 10000,           # total number of iterations per chain
  cores = 2              # number of cores (could use one per chain)
)

# Showing the estimation results of the parameters that were executed using the Stan file
print(fit2, pars=c("mu", "sigma", "alpha",  "lp__"), probs=c(.025,.5,.975))


## End(Not run)

Summaries of Neo-normal Distribution

Description

To display a summary of calculations for a specific neo-normal distribution, including the mean,median, mode, variance, skewness, and excess.kurtosis.

Usage

summary_dist(family = "msnburr", par = c(mu = 0, sigma = 1, alpha = 1))

Arguments

Value

media, mean, mode, variance, skewness, and excess kurtosis of neo-normal distributions

Author(s)

Achmad Syahrul Choir

References

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. Institut Teknologi Sepuluh Nopember. Jones, M.C. and Faddy, M. J. (2003) A skew extension of the t distribution, with applications. Journal of the Royal Statistical Society, Series B, 65, pp 159-174 Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2020) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press Fernandez, C., Osiewalski, J., & Steel, M. F. (1995) Modeling and inference with v-spherical distributions. Journal of the American Statistical Association, 90(432), pp 1331-1340

Examples

summary_dist (family="msnburr2a", par=c(mu=0,sigma=1,alpha=4))