lcDmc {lazy.stat}

R Documentation

Estimates the Density of the Weighed Linear Combination of a Dirichlet Variables by Simulation.

Description

Estimates the Density of the Weighed Linear Combination of a Dirichlet Variables by Simulation.

Usage

lcDmc(
  class,
  f,
  table = NULL,
  alpha0 = 0.5,
  omitmiss = 1,
  nsample = 1000,
  smooth = 0,
  bandwid = 3,
  maxiter = 2,
  density = 2,
  ndensity = 201,
  epsz = 1e-09,
  ...,
  hdr_prob = 0.95,
  print = 0,
  plot = 0,
  outmcmc = 0,
  simple = 0
)

stat_lcDmc(class, f, alpha0, hdr_prob = 0, pdf_info)

Arguments

class	A vector containing the numeric values of scored multinomial
f	A vector containing the frequency associated with class The set (class,f) consists of the frequency distribution: (midpoints,freq)
table	The output of native table function. This has the priority over (class, f).
alpha0	prior constant for Dirichlet
omitmiss	= 1 to remove the classes with f=0 from (class,f)
nsample	# of Dirichlet random numbers to simulate distribution of mu.
smooth	= 1 to smooth the density by mative smooth = 2 to smooth the density by smoothra
bandwid	= length of the running average smooth
maxiter	= # of repetition for smooth
density	= 1 to use simple tabulation = 2 to use native density function
ndensity	# of points to be used to density estimation by native density. or 0 to skip.
epsz	= the value which defines almost zero.
...	additional parameters to native density function.
hdr_prob	= probability value for hdr: 0 <= hdr_prob < 1 When hpd_prob is given "hpd" function of "TeachingDemos" package is used.
print	= 1 to print the result
plot	= 1 to plot the density When plot=1, "hpd" function of "TeachingDemos" package is used.
outmcmc	= 1 to output mcmc result of mu
simple	= 1 to produce simple output

Details

Let (class, f) be the observed frequency distribution of the scored multinomial R.V.
The likelihood of the multinomial parameter vector p is:
sum_{k=1}^{ncat} f[k]*log(p[k])
Given the Dirichlet prior of p with parameter vector alpha0,
the posterior distribution of p is the Dirichlet with alpha=f+alpha0.
The posterior mean of the scored multinomial distribution is defined as:
mu = sum_{k=1}^{ncat} class[k]*p[k]
and this function simulates the distribution of mu by sampling from the posterior Dirichlet distribution.

When hpd_prob is given or plot=1,
"hpd" function of "TeachingDemos" package is used.

Value

When simple = 1:
A list of sample, param, dom
where
param is the alpha parameter of the post means (freq+prior),
class is the categorie values
nobs is the # of observations: sum(f)
nsample # of mcmc samples

pdf_info a list consisting of:
dtable a matrix consisting of the estimated density (ndensity x 3)
where the density in column 2 is normalized to unit sum.
locz1, locnz, locz2, minval, maxval

When simple = 0:
A list consisting of above and more.

When outmcmc = 1:
A list consisting of above and
sample is the vector of length nsample consisting of mu's,

Examples

# Increase nsample when in real use.
class=1:3
f=c(1,2,1)
alpha0=0.5
res=lcDmc( class, f, alpha0=alpha0, nsample=1000, density=2, ndensity=201
           , smooth=0, print=1, plot=0, simple=1, hdr_prob=0 )
res2=stat_lcDmc( class, f, alpha0, pdf_info=res$pdf_info, hdr_prob=0 )

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