plot_sim_pdf_theory {SimMultiCorrData}

Plot Simulated Probability Density Function and Target PDF by Distribution Name or Function for Continuous or Count Variables

Description

This plots the pdf of simulated continuous or count data and overlays the target pdf (if overlay = TRUE), which is specified by distribution name (plus up to 4 parameters) or pdf function fx (plus support bounds). If a continuous target distribution is provided (cont_var = TRUE), the simulated data y is scaled and then transformed (i.e. y = sigma * scale(y) + mu) so that it has the same mean (mu) and variance (sigma^2) as the target distribution. If the variable is Negative Binomial, the parameters must be size and success probability (not mu). The function 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.

Usage

plot_sim_pdf_theory(sim_y, title = "Simulated Probability Density Function",
  ylower = NULL, yupper = NULL, power_color = "dark blue",
  overlay = TRUE, cont_var = 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",
  "Poisson", "Negative_Binomial"), params = NULL, fx = NULL, lower = NULL,
  upper = NULL, 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

sim_y

a vector of simulated data

title

the title for the graph (default = "Simulated 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 simulated variable

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)

cont_var

TRUE (default) for continuous variables, FALSE for count variables

target_color

the line color for the target pdf

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", "Poisson", and "Negative_Binomial". 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

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

calc_theory, ggplot2-package, geom_path, geom_density

Examples

## Not run: 
# Logistic Distribution: mean = 0, variance = 1
seed = 1234

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

# Simulate without the sixth cumulant correction
# (invalid power method pdf)
Logvar1 <- nonnormvar1(method = "Polynomial", means = 0, vars = 1,
                       skews = stcum[3], skurts = stcum[4],
                       fifths = stcum[5], sixths = stcum[6],
                       n = 10000, seed = seed)

# Plot pdfs of simulated variable (invalid) and theoretical distribution
plot_sim_pdf_theory(sim_y = Logvar1$continuous_variable,
                    title = "Invalid Logistic Simulated PDF",
                    overlay = TRUE, Dist = "Logistic", params = c(0, 1))

# Simulate with the sixth cumulant correction
# (valid power method pdf)
Logvar2 <- nonnormvar1(method = "Polynomial", means = 0, vars = 1,
                       skews = stcum[3], skurts = stcum[4],
                       fifths = stcum[5], sixths = stcum[6],
                       Six = seq(1.5, 2, 0.05), n = 10000, seed = seed)

# Plot pdfs of simulated variable (invalid) and theoretical distribution
plot_sim_pdf_theory(sim_y = Logvar2$continuous_variable,
                    title = "Valid Logistic Simulated PDF",
                    overlay = TRUE, Dist = "Logistic", params = c(0, 1))

# Simulate 2 Negative Binomial distributions and correlation 0.3
# using Method 1
NBvars <- rcorrvar(k_nb = 2, size = c(10, 15), prob = c(0.4, 0.3),
                  rho = matrix(c(1, 0.3, 0.3, 1), 2, 2), seed = seed)

# Plot pdfs of 1st simulated variable and theoretical distribution
plot_sim_pdf_theory(sim_y = NBvars$Neg_Bin_variable[, 1], overlay = TRUE,
                    cont_var = FALSE, Dist = "Negative_Binomial",
                    params = c(10, 0.4))


## End(Not run)