plot_pdf_ext {SimMultiCorrData}

Plot Theoretical Power Method Probability Density Function and Target PDF of External Data for Continuous Variables

Description

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.

Usage

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)

Arguments

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

Value

A ggplot2-package object.

References

Please see the references for plot_cdf.

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

See Also

find_constants, calc_theory, ggplot2-package, geom_path, geom_density

Examples

## 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)