plot_pdf_ext: Plot Theoretical Power Method Probability Density Function...
In SimMultiCorrData: Simulation of Correlated Data with Multiple Variable Types

Description Usage Arguments Value References See Also Examples

This plots the theoretical power method probability density function:

f_p(Z)(p(z)) = f_p(Z)(p(z), f_Z(z)/p'(z)),

as given in Headrick & Kowalchuk (2007, doi: 10.1080/10629360600605065), and target pdf. It is a parametric plot with sigma * y + mu, where y = p(z), on the x-axis and f_Z(z)/p'(z) on the y-axis, where z is vector of n random standard normal numbers (generated with a seed set by user; length equal to length of external data vector). sigma is the standard deviation and mu is the mean of the external data set. Given a vector of polynomial transformation constants, the function generates sigma * y + mu and calculates the theoretical probabilities using f_p(Z)(p(z), f_Z(z)/p'(z)). The target distribution is also plotted given a vector of external data. This external data is required. The y values are centered and scaled to have the same mean and standard deviation as the external data. If the user wants to only plot the power method pdf, plot_pdf_theory should be used instead with overlay = FALSE. It returns a ggplot2-package object so the user can modify as necessary. The graph parameters (i.e. title, power_color, target_color, nbins) are ggplot2-package parameters. It works for valid or invalid power method pdfs.

plot_pdf_ext(c = NULL, method = c("Fleishman", "Polynomial"),
  title = "Probability Density Function", ylower = NULL, yupper = NULL,
  power_color = "dark blue", ext_y = NULL, target_color = "dark green",
  target_lty = 2, seed = 1234, legend.position = c(0.975, 0.9),
  legend.justification = c(1, 1), legend.text.size = 10,
  title.text.size = 15, axis.text.size = 10, axis.title.size = 13)

`c`	a vector of constants c0, c1, c2, c3 (if `method` = "Fleishman") or c0, c1, c2, c3, c4, c5 (if `method` = "Polynomial"), like that returned by `find_constants`
`method`	the method used to generate the continuous variable y = p(z). "Fleishman" uses Fleishman's third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.
`title`	the title for the graph (default = "Probability Density Function")
`ylower`	the lower y value to use in the plot (default = NULL, uses minimum simulated y value)
`yupper`	the upper y value (default = NULL, uses maximum simulated y value)
`power_color`	the line color for the power method pdf (default = "dark blue")
`ext_y`	a vector of external data (required)
`target_color`	the histogram color for the target pdf (default = "dark green")
`target_lty`	the line type for the target pdf (default = 2, dashed line)
`seed`	the seed value for random number generation (default = 1234)
`legend.position`	the position of the legend
`legend.justification`	the justification of the legend
`legend.text.size`	the size of the legend labels
`title.text.size`	the size of the plot title
`axis.text.size`	the size of the axes text (tick labels)
`axis.title.size`	the size of the axes titles

A ggplot2-package object.

Please see the references for plot_cdf.

Wickham H. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2009.

find_constants, calc_theory, ggplot2-package, geom_path, geom_density

## Not run: 
# Logistic Distribution

seed = 1234

# Simulate "external" data set
set.seed(seed)
ext_y <- rlogis(10000)

# Find standardized cumulants
stcum <- calc_theory(Dist = "Logistic", params = c(0, 1))

# Find constants without the sixth cumulant correction
# (invalid power method pdf)
con1 <- find_constants(method = "Polynomial", skews = stcum[3],
                      skurts = stcum[4], fifths = stcum[5],
                      sixths = stcum[6])

# Plot invalid power method pdf with external data
plot_pdf_ext(c = con1$constants, method = "Polynomial",
             title = "Invalid Logistic PDF", ext_y = ext_y,
             seed = seed)

# Find constants with the sixth cumulant correction
# (valid power method pdf)
con2 <- find_constants(method = "Polynomial", skews = stcum[3],
                      skurts = stcum[4], fifths = stcum[5],
                      sixths = stcum[6], Six = seq(1.5, 2, 0.05))

# Plot invalid power method pdf with external data
plot_pdf_ext(c = con2$constants, method = "Polynomial",
             title = "Valid Logistic PDF", ext_y = ext_y,
             seed = seed)

## End(Not run)