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 )
res2=stat_lcDmc( class, f, alpha0, pdf_info=res\$pdf_info )

```

[Package lazy.stat version 0.1.3 Index]