p.plot {RecordTest}

Probabilities of Record Plots

Description

This function builds a ggplot object to display different functions of the record probabilities at time t, p_t. A graphical tool to study the hypothesis of the classical record model (i.e., of IID continuous RVs).

Usage

p.plot(
  X,
  plot = c("1", "2", "3"),
  record = c(FU = 1, FL = 1, BU = 1, BL = 1),
  point.col = c(FU = "red", FL = "blue", BU = "red", BL = "blue"),
  point.shape = c(FU = 19, FL = 19, BU = 4, BL = 4),
  conf.int = TRUE,
  conf.level = 0.9,
  conf.aes = c("ribbon", "errorbar"),
  conf.col = "grey69",
  smooth = TRUE,
  smooth.formula = y ~ x,
  smooth.method = stats::lm,
  smooth.weight = TRUE,
  smooth.linetype = c(FU = 1, FL = 1, BU = 2, BL = 2),
  ...
)

Arguments

X

A numeric vector, matrix (or data frame).

plot

One of the values "1", "2" or "3" (character or numeric class are both allowed). It determines the type of plot to be displayed (see Details).

record

Logical vector. Vector with four elements indicating if forward upper, forward lower, backward upper and backward lower are going to be shown, respectively. Logical values or 0,1 values are accepted.

point.col, point.shape

Vector with four elements indicating the colour and shape of the points. Every one of the four elements represents forward upper, forward lower, backward upper and backward lower, respectively.

conf.int

Logical. Indicates if the RIs are also shown.

conf.level

(If conf.int == TRUE) Confidence level of the RIs.

conf.aes

(If conf.int == TRUE) A character string indicating the aesthetic to display for the RIs, "ribbon" (grey area) or "errorbar" (vertical lines).

conf.col

Colour used to plot the expected value and (if conf.int == TRUE) RIs.

smooth

(If plot = 1 or 3) Logical. If TRUE, a smoothing in the probabilities is also plotted.

smooth.formula

(smooth = TRUE) formula to use in the smooth function, e.g., y ~ x, y ~ poly(x, 2, raw = TRUE), y ~ log(x).

smooth.method

(If smooth = TRUE) Smoothing method (function) to use, e.g., lm or loess.

smooth.weight

(If smooth = TRUE) Logical. If TRUE (the default) the smoothing is estimated with weights.

smooth.linetype

(If smooth = TRUE) Vector with four elements indicating the line type of the smoothing. Every one of the four elements represents forward upper, forward lower, backward upper and backward lower, respectively.

...

Further arguments to pass through the smooth (see ggplot2::geom_smooth).

Details

Three different types of plots which aim to analyse the hypothesis of the classical record model using the record probabilities are implemented. Estimations of the record probabilities \hat p_t used in the plots are obtained as the proportion of records at time t in M vectors (columns of matrix X) (see p.record).

Type 1 is the plot of the observed values t \hat p_t versus time t (see p.regression.test for its associated test and details). The expected values under the classical record model are 1 for any value t, so that a cloud of points around 1 and with no trend should be expected. The estimated values are plotted, together with binomial reference intervals (RIs). In addition, a smoothing function can be fitted to the cloud of points.

Type 2 is the plot of the estimated record probabilities p_t versus time t. The expected probabilities under the classical record model, p_t=1/t, are also plotted, together with binomial RIs.

Type 3 is the same plot but on a logarithmic scale, so that the expected value is -\log(t). In this case, another smoothing function can be fitted to the cloud of points.

Type 1 plot was proposed by Cebrián, Castillo-Mateo, Asín (2022), while type 2 and 3 appear in Benestad (2003, Figures 8 and 9, 2004, Figure 4).

Value

A ggplot object.

Author(s)

Jorge Castillo-Mateo

References

Benestad RE (2003). “How Often Can We Expect a Record Event?” Climate Research, 25(1), 3-13. doi:10.3354/cr025003.

Benestad RE (2004). “Record-Values, Nonstationarity Tests and Extreme Value Distributions.” Global and Planetary Change, 44(1-4), 11–26. doi:10.1016/j.gloplacha.2004.06.002.

Cebrián AC, Castillo-Mateo J, Asín J (2022). “Record Tests to Detect Non Stationarity in the Tails with an Application to Climate Change.” Stochastic Environmental Research and Risk Assessment, 36(2), 313-330. doi:10.1007/s00477-021-02122-w.

See Also

p.regression.test

Examples

# three plots available
p.plot(ZaragozaSeries, plot = 1)
p.plot(ZaragozaSeries, plot = 2)
p.plot(ZaragozaSeries, plot = 3)

# Posible fits (plot 1):
#fit a line
p.plot(ZaragozaSeries, record = c(1,0,0,0))
# fit a second order polynomial
p.plot(ZaragozaSeries, record = c(1,0,0,0), 
  smooth.formula = y ~ poly(x, degree = 2))
# force the line to pass by E(t*p_t) = 1 when t = 1, i.e., E(t*p_t) = 1 + beta_1 * (t-1)
p.plot(ZaragozaSeries, record = c(1,0,0,0), 
  smooth.formula = y ~ I(x-1) - 1 + offset(rep(1, length(x))))
# force the second order polynomial pass by E(t*p_t) = 1 when t = 1
p.plot(ZaragozaSeries, record = c(1,0,0,0), 
  smooth.formula = y ~ I(x-1) + I(x^2-1) - 1 + offset(rep(1, length(x))))
# fit a loess
p.plot(ZaragozaSeries, record = c(1,0,0,0), 
  smooth.method = stats::loess, span = 0.25)