duos_pdf: Estimate of PDF from 'duos'
In reykp/BEDr: What the Package Does in One 'Title Case' Line

Description Usage Arguments Details Value Examples

Calculates a posterior estimate of the PDF based on the output from duos for an individual or vector of values.

1	duos_pdf(x, duos_output, burnin = NA, scale = FALSE)

`x`	A single value or vector of values at which to calculate the PDF. These values should be entered on the scale of the data (i.e. values can fall outside of 0 and 1 if data does).
`duos_output`	The list returned by `duos` containing the density estimate results.
`burnin`	The desired burnin to discard from the results. If no value is entered, the default is half the number of iterations.
`scale`	This value TRUE/FALSE indicates whether to return scaled or unscaled results IF the original data does not fall between 0 and 1. The default is FALSE (i.e. returns results on the original data scale).

The function duos_pdf returns the posterior mean PDF. The PDF is calculated based on the following equation at each iteration:

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

duos_pdf returns a list of the PDF results from duos.

`pdf`	A vector of the posterior mean PDF at each value in `x`.
`cri`	A matrix with 2 columns and a row for each value in `x`. It contains the 95% credible interval for the PDF at each point in `x`.
`mat`	A matrix containing the PDF values for `x` at EACH iteration after the burnin is discarded. There is a column for each value in `x`.
`x`	A vector containing the values at which to estimate the PDF.

## --------------------------------------------------------------------------------
## Uniform Distribution
## --------------------------------------------------------------------------------

# First run \code{duos} on data sampled from a Unif(0,1) distribution with 70 data points.
y <- runif(70)
duos_unif <- duos(y = y, k = 4, MH_N = 20000)

# Estimate the PDF at a vector of values
pdf_unif <- duos_pdf(x = c(.1, .5, .65, .98), duos_unif)

# Examine the PDF at \code{x}
pdf_unif$pdf

# Examine the credible intervals of the PDF at \code{x}
pdf_unif$cri

## --------------------------------------------------------------------------------
## Gamma Distribution
## --------------------------------------------------------------------------------

# First run \code{duos} on data sampled from a Gamma(2,2) distribution with 90 data points.
y <- rgamma(90, 2, 2)
duos_gamma <- duos(y = y, MH_N = 20000)

# Estimate the PDF at a vector of values
pdf_gamma <- duos_pdf(x = c(0.4, 1, 2, 3), duos_gamma)

# Examine the PDF at \code{x}
pdf_gamma$pdf

# Examine the credible intervals of the PDF at \code{x}
pdf_gamma$cri

#Plot a histogram of distribution of the posterior draws for the PDF estimate at 1
hist(pdf_gamma$mat[,2])