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#' @name Poisson3_1D
#' @title 1-Dimensional NonHomogeneous Poisson example.
#' @docType data
#' @description Point data and count data, together with intensity function and expected counts for
#' a multimodal nonhomogeneous 1-dimensional Poisson process example. Counts are given for two
#' different gridded data interval widths.
#'
#' @aliases lambda3_1D E_nc3a E_nc3b pts3 countdata3a countdata3b
#'
#' @usage data(Poisson3_1D)
#'
#' @format The data contain the following `R` objects:
#' \describe{
#' \item{`lambda3_1D`:}{ A function defining the intensity function of a
#' nonhomogeneous Poisson process. Note that this function is only defined on
#' the interval (0,55).}
#' \item{`E_nc3a`}{ The expected counts of gridded data for the wider bins (10 bins).}
#' \item{`E_nc3b`}{ The expected counts of gridded data for the wider bins (20 bins).}
#' \item{`pts3`}{ The locations of the observed points (a data frame with one column, named `x`).}
#' \item{`countdata3a`}{ A data frame with three columns, containing the count data for the
#' 10-interval case:}
#' \item{`countdata3b`}{ A data frame with three columns, containing the count data for the
#' 20-interval case:}
#' \describe{
#' \item{`x`}{ The grid cell midpoint.}
#' \item{`count`}{ The number of detections in the cell.}
#' \item{`exposure`}{ The width of the cell.}
#' }
#' }
#'
#' @examples
#' \donttest{
#' if (require("ggplot2", quietly = TRUE)) {
#' data(Poisson3_1D)
#' # first the plots for the 10-bin case:
#' p1a <- ggplot(countdata3a) +
#' geom_point(data = countdata3a, aes(x = x, y = count), col = "blue") +
#' ylim(0, max(countdata3a$count, E_nc3a)) +
#' geom_point(
#' data = countdata3a, aes(x = x), y = 0, shape = "+",
#' col = "blue", cex = 4
#' ) +
#' geom_point(
#' data = data.frame(x = countdata3a$x, y = E_nc3a),
#' aes(x = x), y = E_nc3a, shape = "_", cex = 5
#' ) +
#' xlab(expression(bold(s))) +
#' ylab("count")
#' ss <- seq(0, 55, length.out = 200)
#' lambda <- lambda3_1D(ss)
#' p2a <- ggplot() +
#' geom_line(
#' data = data.frame(x = ss, y = lambda), aes(x = x, y = y),
#' col = "blue"
#' ) +
#' ylim(0, max(lambda)) +
#' geom_point(data = pts3, aes(x = x), y = 0.2, shape = "|", cex = 4) +
#' xlab(expression(bold(s))) +
#' ylab(expression(lambda(bold(s))))
#' multiplot(p1a, p2a, cols = 1)
#'
#' # Then the plots for the 20-bin case:
#' p1a <- ggplot(countdata3b) +
#' geom_point(data = countdata3b, aes(x = x, y = count), col = "blue") +
#' ylim(0, max(countdata3b$count, E_nc3b)) +
#' geom_point(
#' data = countdata3b, aes(x = x), y = 0, shape = "+",
#' col = "blue", cex = 4
#' ) +
#' geom_point(
#' data = data.frame(x = countdata3b$x, y = E_nc3b),
#' aes(x = x), y = E_nc3b, shape = "_", cex = 5
#' ) +
#' xlab(expression(bold(s))) +
#' ylab("count")
#' ss <- seq(0, 55, length.out = 200)
#' lambda <- lambda3_1D(ss)
#' p2a <- ggplot() +
#' geom_line(
#' data = data.frame(x = ss, y = lambda), aes(x = x, y = y),
#' col = "blue"
#' ) +
#' ylim(0, max(lambda)) +
#' geom_point(data = pts3, aes(x = x), y = 0.2, shape = "|", cex = 4) +
#' xlab(expression(bold(s))) +
#' ylab(expression(lambda(bold(s))))
#' multiplot(p1a, p2a, cols = 1)
#' }
#' }
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