duos_stat: Statistics for 'duos'
In reykp/biRd: What the Package Does in One 'Title Case' Line

Description Usage Arguments Details Value Examples

Calculates a variety of statistics from the duos density estimate.

1	duos_stat(duos_output, stat = "m", p = NA, burnin = NA)

`duos_output`	The list returned by `duos` containing the density estimate results.
`stat`	A value indicating choice of statistic (see details).
`p`	A list of quantiles if quantiles are requested (see details).
`burnin`	The desired burnin to discard from the results. If no value is entered, the default is half the number of iterations.
`print`	By default, the posterior mean values and their credible intervals are printed. Change to FALSE if no printing is desired.

The form of the density is below:

f(x) =

(π_1) / (γ_1) , 0 ≤ x < γ_1

(π_2) / (γ_2-γ_1) , γ_1 ≤ x < γ_2

(π_3) / (γ_3-γ_2) , γ_2 ≤ x < γ_3

... , ... ≤ x < ...

(π_k) / (γ_k-γ_{k-1}) , γ_{k-1} ≤ x < γ_k

(π_{k+1}) / (1-γ_k) , γ_k ≤ x < 1

where γ_1 < γ_2 < ... < γ_k is in (0,1) and π_1 + π_2 + ... + π_{k+1} = 1

E[X] = ∑_{i=1}^{k+1} ((γ_i+γ_{i-1}) * π_i) / 2

Var[X] = ∑_{i=1}^{k+1} ((γ_i^3-γ_{i-1}^3) / 3) * π_i / (γ_i-γ_{i-1}) - (E[x])^2

The inverse CDF is specified below:

F^{-1}(x) =

x * (γ_1) / (π_1) , 0 ≤ x < π_1

(x - π_1) * (γ_2 - γ_1) / (π_2) + γ_1 , π_1 ≤ x < π_1 + π_2

(x - π_1 + π_2) * (γ_3-γ_2) / (π_3) + γ_2 , π_1 + π_2 ≤ x < π_1 + π_2 + π_3

... , ... ≤ x < ...

(x - ∑_{i=1}^{k-1} π_i) * (γ_k - γ_{k-1}) / (π_k) + γ_{k-1} , ∑_{i=1}^{k-1} π_i ≤ x < ∑_{i=1}^{k} π_i

(x - ∑_{i=1}^{k} π_i) * (1 - γ_{k}) / (π_{k+1}) + γ_{k} , ∑_{i=1}^{k} π_i ≤ x < 1

Options for stat

Several of the standard statistics are available through the function duos_stat.

"mean" or "m": The E[x] is calculated as in the details section for each iteration, and the average of this result is returned as the mean.
"var" or "v": The Var[x] is calculated as in the details section for each iteration, and the average of this result is returned as the variance.
"quant" or "q": Returns the quantiles specified in 'p' using the inverse CDF described in the details section.

Options for p

Default is NA if quantiles are not the desired statistics. If 'quant' is specified for stat, p is a single value or vector of values between 0 and 1.

duos_stat the statistic of choice and the credible intervals associated with it.

If 'mean' or 'm' is specified for stat:

`mean`	The E[X] from the details is calculated at each iteration and the mean of these is returned.
`cri`	The credible intervals for E[X] calculated using the 0.025th and 0.975th quantiles.

If 'var' or 'v' is specified for stat:

`variance`	The Var[X] from the details is calculated at each iteration and the mean of these is returned.
`cri`	The credible intervals for Var[X] calculated using the 0.025th and 0.975th quantiles.

If 'quant' or 'q' is specified for stat:

`quantiles`	The quantiles specified in 'p' is calculated using the inverse CDF in the details at each iteration and the mean of these is returned.
`cri`	The credible intervals for the quantiles calculated using the 0.025th and 0.975th quantiles.

duos_pdf returns a list of the PDF results from duos.

`"mean", "var", or "quantiles"`	Contains the mean, the variance, or a vector of the quantile values from `duos_stat`.
`cri`	Contains the credible intervals for the requested statistics.
`mat`	Contains a matrix of the posterior simulations for the requested statistic.

## --------------------------------------------------------------------------------
## Beta Distribution
## --------------------------------------------------------------------------------

# First run 'duos' on data sampled from a Beta(2, 6) distribution with 100 data points.
y <- rbeta(100, 2, 6)
duos_beta <- duos(y = y, k = 5, MH_N = 20000)

# Get an estimate of the mean and its credible intervals
beta_mean <- duos_stat(duos_beta, stat = "mean")

#Look at a histogram of the posterior simulations of the mean
hist(beta_mean$mat)

# Get an estimate of the variance and its credible intervals
beta_var <- duos_stat(duos_beta, stat = "var")

## --------------------------------------------------------------------------------
## Normal Distribution
## --------------------------------------------------------------------------------

# First run 'duos' on data sampled from a Normal(0, 1) distribution with 200 data points.
y <- rnorm(200, 0, 1)
duos_norm <- duos(y = y, k = 7, MH_N = 20000)

# Get an estimate of the mean and credible intervals
mean_norm <- duos_stat(duos_norm, stat = "m")

#Get an estimate of the quantiles and their credible intervals
quant_norm <- duos_stat(duos_norm, stat = "q", p = c(0.1, 0.5, 0.9))