stanf_msnburr {neodistr}

Stan function of MSNBurr Distribution

Description

Stan code of MSNBurr distribution for custom distribution in stan

Usage

stanf_msnburr(vectorize = TRUE, rng = TRUE)

Arguments

vectorize

logical; if TRUE, Vectorize Stan code of MSNBurr distribution are given The default value of this parameter is TRUE

rng

logical; if TRUE, Stan code of quantile and random number generation of MSNBurr distribution are given The default value of this parameter is TRUE

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 cumulatif 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 ditribution 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 DDistributions and their Properties. Disertation. Institut Teknologi Sepuluh Nopember.

Examples

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))