plot_pdf_theory: 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 (if overlay = TRUE). 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). 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)). If overlay = TRUE, the target distribution is also plotted given either a distribution name (plus up to 4 parameters) or a pdf function fx. If a target distribution is specified, y is scaled and then transformed so that it has the same mean and variance as the target distribution. It returns a ggplot2-package object so the user can modify as necessary. The graph parameters (i.e. title, power_color, target_color, target_lty) are ggplot2-package parameters. It works for valid or invalid power method pdfs.

plot_pdf_theory(c = NULL, method = c("Fleishman", "Polynomial"), mu = 0,
  sigma = 1, title = "Probability Density Function", ylower = NULL,
  yupper = NULL, power_color = "dark blue", overlay = TRUE,
  target_color = "dark green", target_lty = 2, Dist = c("Benini", "Beta",
  "Beta-Normal", "Birnbaum-Saunders", "Chisq", "Dagum", "Exponential",
  "Exp-Geometric", "Exp-Logarithmic", "Exp-Poisson", "F", "Fisk", "Frechet",
  "Gamma", "Gaussian", "Gompertz", "Gumbel", "Kumaraswamy", "Laplace",
  "Lindley", "Logistic", "Loggamma", "Lognormal", "Lomax", "Makeham", "Maxwell",
  "Nakagami", "Paralogistic", "Pareto", "Perks", "Rayleigh", "Rice",
  "Singh-Maddala", "Skewnormal", "t", "Topp-Leone", "Triangular", "Uniform",
  "Weibull"), params = NULL, fx = NULL, lower = NULL, upper = NULL,
  n = 100, 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.
`mu`	the desired mean for the continuous variable (used if `overlay = FALSE`, otherwise variable centered to have the same mean as the target distribution)
`sigma`	the desired standard deviation for the continuous variable (used if `overlay = FALSE`, otherwise variable scaled to have the same standard deviation as the target distribution)
`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)
`overlay`	if TRUE (default), the target distribution is also plotted given either a distribution name (and parameters) or pdf function fx (with bounds = ylower, yupper)
`target_color`	the line color for the target pdf (default = "dark green")
`target_lty`	the line type for the target pdf (default = 2, dashed line)
`Dist`	name of the distribution. The possible values are: "Benini", "Beta", "Beta-Normal", "Birnbaum-Saunders", "Chisq", "Exponential", "Exp-Geometric", "Exp-Logarithmic", "Exp-Poisson", "F", "Fisk", "Frechet", "Gamma", "Gaussian", "Gompertz", "Gumbel", "Kumaraswamy", "Laplace", "Lindley", "Logistic", "Loggamma", "Lognormal", "Lomax", "Makeham", "Maxwell", "Nakagami", "Paralogistic", "Pareto", "Perks", "Rayleigh", "Rice", "Singh-Maddala", "Skewnormal", "t", "Topp-Leone", "Triangular", "Uniform", "Weibull". Please refer to the documentation for each package (either `stats-package`, `VGAM-package`, or `triangle`) for information on appropriate parameter inputs.
`params`	a vector of parameters (up to 4) for the desired distribution (keep NULL if `fx` supplied instead)
`fx`	a pdf input as a function of x only, i.e. fx <- function(x) 0.5*(x-1)^2; must return a scalar (keep NULL if `Dist` supplied instead)
`lower`	the lower support bound for `fx`
`upper`	the upper support bound for `fx`
`n`	the number of random standard normal numbers to use in generating y = p(z) (default = 100)
`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

## Not run: 
# Logistic Distribution

# 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 theoretical pdf overlayed
plot_pdf_theory(c = con1$constants, method = "Polynomial",
         title = "Invalid Logistic PDF", overlay = TRUE,
         Dist = "Logistic", params = c(0, 1))

# 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 valid power method pdf with theoretical pdf overlayed
plot_pdf_theory(c = con2$constants, method = "Polynomial",
         title = "Valid Logistic PDF", overlay = TRUE,
         Dist = "Logistic", params = c(0, 1))

## End(Not run)