R/hist.R
In abnormally-distributed/Bayezilla: Bayesian Models With JAGS and Several Utilities for Data Exploration and Model Evaluation.
Defines functions
hist
Documented in
hist
#' Modified Version of hist() with additional functionality
#'
#' @param x a vector of values for which the histogram is desired.
#' @param breaks one of: a vector giving the breakpoints between histogram cells, a function to compute the vector of breakpoints,
#' a single number giving the number of cells for the histogram, or a character string naming an algorithm to compute the number of cells (see ‘Details’), a function to compute the number of cells. Defaults to "dhist".
#' @param freq logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, probability densities, component density, are plotted (so that the histogram has a total area of one). Defaults to FALSE.
#' @param probability an alias for !freq, for S compatibility.
#' @param include.lowest logical; if TRUE, an x[i] equal to the breaks value will be included in the first (or last, for right = FALSE) bar. This will be ignored (with a warning) unless breaks is a vector.
#' @param right logical; if TRUE, the histogram cells are right-closed (left open) intervals.
#' @param density the density of shading lines, in lines per inch. The default value of NULL means that no shading lines are drawn. Non-positive values of density also inhibit the drawing of shading lines.
#' @param angle the slope of shading lines, given as an angle in degrees (counter-clockwise).
#' @param col a colour to be used to fill the bars. The default is "#00ff3cCC".
#' @param border the color of the border around the bars. The default is to use the standard foreground color.
#' @param main these arguments to title have useful defaults here.
#' @param xlim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param ylim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param xlab these arguments to title have useful defaults here.
#' @param ylab these arguments to title have useful defaults here.
#' @param axes logical. If TRUE (default), axes are draw if the plot is drawn.
#' @param rug Should a rug be plotted under the histogram? Defaults to TRUE.
#' @param rug.col The rug color. Defaults to #8d03e7.
#' @param plot logical. If TRUE (default), a histogram is plotted, otherwise a list of breaks and counts is returned. In the latter case, a warning is used if (typically graphical) arguments are specified that only apply to the plot = TRUE case.
#' @param labels logical or character string. Additionally draw labels on top of bars, if not FALSE; see plot.histogram.
#' @param nclass numeric (integer). For S(-PLUS) compatibility only, nclass is equivalent to breaks for a scalar or character argument.
#' @param warn.unused logical. If plot = FALSE and warn.unused = TRUE, a warning will be issued when graphical parameters are passed to hist.default().
#' @param ... further arguments and graphical parameters passed to plot.histogram and thence to title and axis (if plot = TRUE).
#'
#' @return a histogram
#' @export
#'
#' @examples
#' x <- rgamma(1000, 2, .25)
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist")
#' hist(x, breaks = "fd")
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist", main = "'dhist' breaks method")
#' hist(x, breaks = "fd", main = "'Freedman-Diaconis' breaks method")
#' hist(x, breaks = "scott", main = "'Scott' breaks method")
#' hist(x, breaks = "sturges", main = "'Sturges' breaks method")
#'
#'
#' @description
#' The definition of histogram differs by source (with country-specific biases).
#' R's default with equi-spaced breaks (also the default) is to plot the counts in the cells defined by breaks.
#' Thus the height of a rectangle is proportional to the number of points falling into the cell, as is the area
#' provided the breaks are equally-spaced. The modified hist() function included in the Bayezilla package however
#' utilizes non-equal sized breaks. More details are given below.
#' If right = TRUE (default), the histogram cells are intervals of the form (a, b], i.e.,
#' they include their right-hand endpoint,
#' but not their left one, with the exception of the first cell when include.lowest is TRUE.
#' For right = FALSE, the intervals are of the form [a, b), and include.lowest means ‘include highest’.
#' A numerical tolerance of 1e-7 times the median bin size (for more than four bins, otherwise the median is substituted)
#' is applied when counting entries on the edges of bins. This is not included in the reported breaks nor in the calculation
#' of density. \cr
#' \cr
#' Breaks Algorithms: \cr
#' \cr
#' The default breaks algorithm is "dhist", which implements the varying binwidth algorithm of Lorraine Denby.
#' This algorithm has some notable
#' advantages from a statistical point of view. Regions of high density have not only taller bins (as is usual)
#' but more narrow bins as well. Regions of lower denisty have not only shorter, but wider bins. This makes the
#' probability density much more
#' immediately obvious, and captures interesting features of heavy tails and skew with greater efficacy. Algorithms
#' that yield The former oversmooths in regions of high density, and is poor at identifying sharp peaks and multimodality.
#' By contrast, the latter variety oversmooths in regions of low density and can mask outliers and the
#' heavy tails of more leptokurtotic distributions. For more information, see Denby & Mallows (2009).
#' Other options include "scott", "sturges" and "fd" / "Freedman-Diaconis". Case is ignored and partial matching is used.
#' Alternatively, a function can be supplied which will compute the
#' intended number of breaks or the actual breakpoints as a function of x.
#' \cr
#' An example of output: \cr
#' \cr
#' \if{html}{\figure{breaks.png}{}}
#' \if{latex}{\figure{breaks.png}{}}
#' \cr
#' @references Denby, L., & Mallows, C. (2009). Variations on the Histogram. Journal of Computational and Graphical Statistics, 18(1), 21–31. doi:10.1198/jcgs.2009.0002
#'
hist <- function(x, breaks = "dhist", freq = FALSE, probability = !freq,
include.lowest = TRUE, right = TRUE, density = NULL, angle = 45,
col = "#00ff3cCC", border = NULL, main = NULL,
xlim = range(breaks), ylim = NULL, xlab = xname, ylab, axes = TRUE,
plot = TRUE, labels = FALSE, nclass = NULL, warn.unused = TRUE, rug = TRUE,
rug.col = "#8d03e7",
...) { UseMethod("hist") }
#' Modified Version of hist() with additional functionality
#'
#' @param x a vector of values for which the histogram is desired.
#' @param breaks one of: a vector giving the breakpoints between histogram cells, a function to compute the vector of breakpoints,
#' a single number giving the number of cells for the histogram, or a character string naming an algorithm to compute the number of cells (see ‘Details’), a function to compute the number of cells. Defaults to "dhist".
#' @param freq logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, probability densities, component density, are plotted (so that the histogram has a total area of one). Defaults to FALSE.
#' @param probability an alias for !freq, for S compatibility.
#' @param include.lowest logical; if TRUE, an x[i] equal to the breaks value will be included in the first (or last, for right = FALSE) bar. This will be ignored (with a warning) unless breaks is a vector.
#' @param right logical; if TRUE, the histogram cells are right-closed (left open) intervals.
#' @param density the density of shading lines, in lines per inch. The default value of NULL means that no shading lines are drawn. Non-positive values of density also inhibit the drawing of shading lines.
#' @param angle the slope of shading lines, given as an angle in degrees (counter-clockwise).
#' @param col a colour to be used to fill the bars. The default is "#00ff3cCC".
#' @param border the color of the border around the bars. The default is to use the standard foreground color.
#' @param main these arguments to title have useful defaults here.
#' @param xlim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param ylim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param xlab these arguments to title have useful defaults here.
#' @param ylab these arguments to title have useful defaults here.
#' @param axes logical. If TRUE (default), axes are draw if the plot is drawn.
#' @param rug Should a rug be plotted under the histogram? Defaults to TRUE.
#' @param rug.col The rug color. Defaults to #8d03e7.
#' @param plot logical. If TRUE (default), a histogram is plotted, otherwise a list of breaks and counts is returned. In the latter case, a warning is used if (typically graphical) arguments are specified that only apply to the plot = TRUE case.
#' @param labels logical or character string. Additionally draw labels on top of bars, if not FALSE; see plot.histogram.
#' @param nclass numeric (integer). For S(-PLUS) compatibility only, nclass is equivalent to breaks for a scalar or character argument.
#' @param warn.unused logical. If plot = FALSE and warn.unused = TRUE, a warning will be issued when graphical parameters are passed to hist.default().
#' @param ... further arguments and graphical parameters passed to plot.histogram and thence to title and axis (if plot = TRUE).
#'
#' @return a histogram
#'
#' @examples
#' x <- rgamma(1000, 2, .25)
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist")
#' hist(x, breaks = "fd")
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist", main = "'dhist' breaks method")
#' hist(x, breaks = "fd", main = "'Freedman-Diaconis' breaks method")
#' hist(x, breaks = "scott", main = "'Scott' breaks method")
#' hist(x, breaks = "sturges", main = "'Sturges' breaks method")
#'
#' @details
#' The definition of histogram differs by source (with country-specific biases).
#' R's default with equi-spaced breaks (also the default) is to plot the counts in the cells defined by breaks.
#' Thus the height of a rectangle is proportional to the number of points falling into the cell, as is the area
#' provided the breaks are equally-spaced. The modified hist() function included in the Bayezilla package however
#' utilizes non-equal sized breaks. More details are given below.
#' If right = TRUE (default), the histogram cells are intervals of the form (a, b], i.e.,
#' they include their right-hand endpoint,
#' but not their left one, with the exception of the first cell when include.lowest is TRUE.
#' For right = FALSE, the intervals are of the form [a, b), and include.lowest means ‘include highest’.
#' A numerical tolerance of 1e-7 times the median bin size (for more than four bins, otherwise the median is substituted)
#' is applied when counting entries on the edges of bins. This is not included in the reported breaks nor in the calculation
#' of density. \cr
#' \cr
#' Breaks Algorithms: \cr
#' \cr
#' The default breaks algorithm is "dhist", which implements the varying binwidth algorithm of Lorraine Denby.
#' This algorithm has some notable
#' advantages from a statistical point of view. Regions of high density have not only taller bins (as is usual)
#' but more narrow bins as well. Regions of lower denisty have not only shorter, but wider bins. This makes the
#' probability density much more
#' immediately obvious, and captures interesting features of heavy tails and skew with greater efficacy. Algorithms
#' that yield The former oversmooths in regions of high density, and is poor at identifying sharp peaks and multimodality.
#' By contrast, the latter variety oversmooths in regions of low density and can mask outliers and the
#' heavy tails of more leptokurtotic distributions. For more information, see Denby & Mallows (2009).
#' Other options include "scott", "sturges" and "fd" / "Freedman-Diaconis". Case is ignored and partial matching is used.
#' Alternatively, a function can be supplied which will compute the
#' intended number of breaks or the actual breakpoints as a function of x.
#' \cr
#' An example of output: \cr
#' \cr
#' \if{html}{\figure{breaks.png}{}}
#' \if{latex}{\figure{breaks.png}{}}
#' \cr
#' \cr
#' @references Denby, L., & Mallows, C. (2009). Variations on the Histogram. Journal of Computational and Graphical Statistics, 18(1), 21–31. doi:10.1198/jcgs.2009.0002
#' @export
#'
hist.default <- function (x, breaks = "dhist", freq = FALSE, probability = !freq,
include.lowest = TRUE, right = TRUE, density = NULL, angle = 45,
col = "#00ff3cCC", border = NULL, main = NULL,
xlim = range(breaks), ylim = NULL, xlab = xname, ylab, axes = TRUE,
plot = TRUE, labels = FALSE, nclass = NULL, warn.unused = TRUE, rug = TRUE,
rug.col = "#8d03e7",
...)
{
if (!is.numeric(x))
stop("'x' must be numeric")
xname <- paste(deparse(substitute(x), 500), collapse = "\n")
n <- length(x <- x[is.finite(x)])
n <- as.integer(n)
if (is.na(n))
stop("invalid length(x)")
use.br <- !missing(breaks)
if (use.br) {
if (!missing(nclass))
warning("'nclass' not used when 'breaks' is specified")
}
else if (!is.null(nclass) && length(nclass) == 1L)
breaks <- nclass
use.br <- use.br && (nB <- length(breaks)) > 1L
if (use.br)
breaks <- sort(breaks)
else {
if (!include.lowest) {
include.lowest <- TRUE
warning("'include.lowest' ignored as 'breaks' is not a vector")
}
if (is.character(breaks)) {
breaks <- match.arg(tolower(breaks), c("sturges", "dhist",
"fd", "freedman-diaconis", "scott"))
breaks <- switch(breaks, sturges = nclass.Sturges(x),
`freedman-diaconis` = , dhist = nclass.dhist(x), fd = nclass.FD(x), scott = nclass.scott(x),
stop("unknown 'breaks' algorithm"))
}
else if (is.function(breaks)) {
breaks <- breaks(x)
}
if (length(breaks) == 1) {
if (!is.numeric(breaks) || !is.finite(breaks) ||
breaks < 1L)
stop("invalid number of 'breaks'")
if (breaks > 1e+06) {
warning(gettextf("'breaks = %g' is too large and set to 1e6",
breaks), domain = NA)
breaks <- 1000000L
}
breaks <- pretty(range(x), n = breaks, min.n = 1)
nB <- length(breaks)
if (nB <= 1)
stop(gettextf("hist.default: pretty() error, breaks=%s",
format(breaks)), domain = NA)
}
else {
if (!is.numeric(breaks) || length(breaks) <= 1)
stop(gettextf("Invalid breakpoints produced by 'breaks(x)': %s",
format(breaks)), domain = NA)
breaks <- sort(breaks)
nB <- length(breaks)
use.br <- TRUE
}
}
nB <- as.integer(nB)
if (is.na(nB))
stop("invalid length(breaks)")
h <- diff(breaks)
equidist <- !use.br || diff(range(h)) < 1e-07 * max(c(mean(h), median(h)))
if (!use.br && any(h <= 0))
stop("'breaks' are not strictly increasing")
freq1 <- freq
if (is.null(freq)) {
freq1 <- if (!missing(probability))
!as.logical(probability)
else equidist
}
else if (!missing(probability) && any(probability == freq))
stop("'probability' is an alias for '!freq', however they differ.")
diddle <- 1e-07 * if (nB > 5)
stats::median(h)
else if (nB <= 3)
diff(range(x))
else min(h[h > 0])
fuzz <- if (right)
c(if (include.lowest) -diddle else diddle, rep.int(diddle,
nB - 1L))
else c(rep.int(-diddle, nB - 1L), if (include.lowest) diddle else -diddle)
fuzzybreaks <- breaks + fuzz
counts <- .Call(graphics:::C_BinCount, x, fuzzybreaks, right, include.lowest)
if (any(counts < 0L))
stop("negative 'counts'. Internal Error.", domain = NA)
if (sum(counts) < n)
stop("some 'x' not counted; maybe 'breaks' do not span range of 'x'")
dens <- counts/(n * h)
mids <- 0.5 * (breaks[-1L] + breaks[-nB])
r <- structure(list(breaks = breaks, counts = counts, density = dens,
mids = mids, xname = xname, equidist = equidist), class = "histogram")
if (plot) {
plot(r, freq = freq1, col = col, border = border, angle = angle,
density = density, main = main, xlim = xlim, ylim = ylim,
xlab = xlab, ylab = ylab, axes = axes, labels = labels,
...)
invisible(r)
if (isTRUE(rug)){
rug(x, ticksize = 0.015, side = 1, lwd = 0.5, col = rug.col,
quiet = getOption("warn") < 0, ...)
}
}
else {
if (warn.unused) {
nf <- names(formals())
nf <- nf[is.na(match(nf, c("x", "breaks", "nclass",
"plot", "include.lowest", "right")))]
missE <- lapply(nf, function(n) substitute(missing(.),
list(. = as.name(n))))
not.miss <- !sapply(missE, eval, envir = environment())
if (any(not.miss))
warning(sprintf(ngettext(sum(not.miss), "argument %s is not made use of",
"arguments %s are not made use of"), paste(sQuote(nf[not.miss]),
collapse = ", ")), domain = NA)
}
r
}
}
#' Density-based adaptive width histogram bins
#'
#' @description This algorithm has some notable
#' advantages from a statistical point of view. Regions of high density have not only taller bins (as is usual)
#' but more narrow bins as well. Regions of lower denisty have not only shorter, but wider bins. This makes the
#' probability density much more
#' immediately obvious, and captures interesting features of heavy tails and skew with greater efficacy. Algorithms
#' that yield The former oversmooths in regions of high density, and is poor at identifying sharp peaks and multimodality.
#' By contrast, the latter variety oversmooths in regions of low density and can mask outliers and the
#' heavy tails of more leptokurtotic distributions. Alternatively, a function can be supplied which will compute the
#' intended number of breaks or the actual breakpoints as a function of x. For more information, see Denby & Mallows (2009).
#' The original code was authored by Lorraine Denby, but some minor improvements have been made here.
#' @author Lorraine Denby, Brandon Vaughan
#' @seealso
#' \url{http://pubs.research.avayalabs.com/pdfs/ALR-2007-003-paper.pdf}
#' @references L. Denby and C. Mallows. Variations on the histogram. Journal
#' of Computational and Graphical Statistics, 18 (1):21-31, 2009.
#' URL \url{http://pubs.amstat.org/doi/abs/10.1198/jcgs.2009.0002.}
#' @param b slope. See paper for details. Defaults to 1.5.
#' @param nbins number of bins. See Denby & Mallows (2009).
#' @param min.bins the minimum number of bins. Optional.
#' @param rx range of data, if not taken from data.
#' @return A function that takes a single parameter, a numeric x specifying
#' the data for which breaks are needed, and returns a vector of breaks.
#' @export
#' @examples
#' nclass.dhist()
#'
nclass.dhist = function(x, b = 1.5, rx = range(x), min.bins = NULL){
n.bins <-function(x, min.bins = NULL){
binsfunc = function(b){
bincounts = b^2
bincounts = bincounts/sum(b)
bincounts = 1 - b
bincounts = floor(weighted.mean(b, bincounts))
return(bincounts)
}
hdi = Bayezilla::cred_interval(x, method = "HDI", cred.level = 0.80)
if(hdi[1] == hdi[2]){
num = hdi[1]
newx = x[which(x != num)]
hdi = Bayezilla::cred_interval(newx, method = "HDI", cred.level = 0.80)
}
ecd = ecdf(x)
l = ecd(hdi[1])
u = ecd(hdi[2])
x<-x[!is.na(x)]
n<-length(x)
Q<-quantile(x, c(l, u))
X<-range(x)
result<- ceiling(n^(1/3)*(X[2]-X[1])/(2*(Q[2]-Q[1])))
if (is.null(min.bins)){
fd = nclass.FD(x)
sturge = nclass.Sturges(x)
scott = nclass.scott(x)
result <- binsfunc(b = c(fd, sturge, scott, result))
names(result)<-NULL
result
} else if (!is.null(min.bins)){
result <- c(min.bins, result)
if(is.nan(result)) {
result <- min.bins
}
names(result)<-NULL
result
}
}
hdi = Bayezilla::cred_interval(x, method = "HDI", cred.level = 0.80)
if(hdi[1] == hdi[2]){
num = hdi[1]
newx = x[which(x != num)]
hdi = Bayezilla::cred_interval(newx, method = "HDI", cred.level = 0.80)
}
ecd = ecdf(x)
l = ecd(hdi[1])
u = ecd(hdi[2])
a = b*diff(quantile(x, c(l , u)))
nbins <- n.bins(x, min.bins = min.bins)
x <- sort(x)
if(a == 0)
a <- diff(range(x))/100000000
if(a != Inf) {
n <- length(x)
h <- (rx[2] + a - rx[1])/nbins
ybr <- rx[1] + h * (0:nbins)
yupper <- x + (a * (1:n))/n
# upper and low Fer corners in the ecdf
ylower <- yupper - a/n
cmtx <- cbind(
cut(yupper, breaks = ybr),
cut(yupper, breaks = ybr, left.include = T),
cut(ylower, breaks = ybr),
cut(ylower, breaks = ybr, left.include = T)
)
cmtx[1, 3] <- cmtx[1, 4] <- 1
# to replace NAs when default r is used
cmtx[n, 1] <- cmtx[n, 2] <- nbins
checksum <- rowSums(cmtx) %% 4
# will be 2 for obs. that straddle two bins
straddlers <- (1:n)[checksum == 2]
# to allow for zero counts
if(length(straddlers) > 0) {
counts <- table(c(1:nbins, cmtx[- straddlers, 1]))
} else {
counts <- table(c(1:nbins, cmtx[, 1]))
}
counts <- counts - 1
if(length(straddlers) > 0) {
for(i in straddlers) {
binno <- cmtx[i, 1]
theta <- ((yupper[i] - ybr[binno]) * n)/a
counts[binno - 1] <- counts[binno - 1] + (1 - theta)
counts[binno] <- counts[binno] + theta
}
}
xbr <- ybr
xbr[-1] <- ybr[-1] - (a * cumsum(counts))/n
} else {
bin.size <- length(x)/nbins
cut.pt <- c(
min(x) - abs(min(x))/1000,
approx(seq(length(x)),
x,
(1:(nbins - 1)) * bin.size, rule = 2)$y,
max(x)
)
aa <- hist(x, breaks = cut.pt, plot = F, probability = T)
xbr <- unique(aa$breaks)
}
unique(xbr)
}
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Defines functions hist
Documented in hist
#' Modified Version of hist() with additional functionality
#'
#' @param x a vector of values for which the histogram is desired.
#' @param breaks one of: a vector giving the breakpoints between histogram cells, a function to compute the vector of breakpoints,
#' a single number giving the number of cells for the histogram, or a character string naming an algorithm to compute the number of cells (see ‘Details’), a function to compute the number of cells. Defaults to "dhist".
#' @param freq logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, probability densities, component density, are plotted (so that the histogram has a total area of one). Defaults to FALSE.
#' @param probability an alias for !freq, for S compatibility.
#' @param include.lowest logical; if TRUE, an x[i] equal to the breaks value will be included in the first (or last, for right = FALSE) bar. This will be ignored (with a warning) unless breaks is a vector.
#' @param right logical; if TRUE, the histogram cells are right-closed (left open) intervals.
#' @param density the density of shading lines, in lines per inch. The default value of NULL means that no shading lines are drawn. Non-positive values of density also inhibit the drawing of shading lines.
#' @param angle the slope of shading lines, given as an angle in degrees (counter-clockwise).
#' @param col a colour to be used to fill the bars. The default is "#00ff3cCC".
#' @param border the color of the border around the bars. The default is to use the standard foreground color.
#' @param main these arguments to title have useful defaults here.
#' @param xlim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param ylim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param xlab these arguments to title have useful defaults here.
#' @param ylab these arguments to title have useful defaults here.
#' @param axes logical. If TRUE (default), axes are draw if the plot is drawn.
#' @param rug Should a rug be plotted under the histogram? Defaults to TRUE.
#' @param rug.col The rug color. Defaults to #8d03e7.
#' @param plot logical. If TRUE (default), a histogram is plotted, otherwise a list of breaks and counts is returned. In the latter case, a warning is used if (typically graphical) arguments are specified that only apply to the plot = TRUE case.
#' @param labels logical or character string. Additionally draw labels on top of bars, if not FALSE; see plot.histogram.
#' @param nclass numeric (integer). For S(-PLUS) compatibility only, nclass is equivalent to breaks for a scalar or character argument.
#' @param warn.unused logical. If plot = FALSE and warn.unused = TRUE, a warning will be issued when graphical parameters are passed to hist.default().
#' @param ... further arguments and graphical parameters passed to plot.histogram and thence to title and axis (if plot = TRUE).
#'
#' @return a histogram
#' @export
#'
#' @examples
#' x <- rgamma(1000, 2, .25)
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist")
#' hist(x, breaks = "fd")
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist", main = "'dhist' breaks method")
#' hist(x, breaks = "fd", main = "'Freedman-Diaconis' breaks method")
#' hist(x, breaks = "scott", main = "'Scott' breaks method")
#' hist(x, breaks = "sturges", main = "'Sturges' breaks method")
#'
#'
#' @description
#' The definition of histogram differs by source (with country-specific biases).
#' R's default with equi-spaced breaks (also the default) is to plot the counts in the cells defined by breaks.
#' Thus the height of a rectangle is proportional to the number of points falling into the cell, as is the area
#' provided the breaks are equally-spaced. The modified hist() function included in the Bayezilla package however
#' utilizes non-equal sized breaks. More details are given below.
#' If right = TRUE (default), the histogram cells are intervals of the form (a, b], i.e.,
#' they include their right-hand endpoint,
#' but not their left one, with the exception of the first cell when include.lowest is TRUE.
#' For right = FALSE, the intervals are of the form [a, b), and include.lowest means ‘include highest’.
#' A numerical tolerance of 1e-7 times the median bin size (for more than four bins, otherwise the median is substituted)
#' is applied when counting entries on the edges of bins. This is not included in the reported breaks nor in the calculation
#' of density. \cr
#' \cr
#' Breaks Algorithms: \cr
#' \cr
#' The default breaks algorithm is "dhist", which implements the varying binwidth algorithm of Lorraine Denby.
#' This algorithm has some notable
#' advantages from a statistical point of view. Regions of high density have not only taller bins (as is usual)
#' but more narrow bins as well. Regions of lower denisty have not only shorter, but wider bins. This makes the
#' probability density much more
#' immediately obvious, and captures interesting features of heavy tails and skew with greater efficacy. Algorithms
#' that yield The former oversmooths in regions of high density, and is poor at identifying sharp peaks and multimodality.
#' By contrast, the latter variety oversmooths in regions of low density and can mask outliers and the
#' heavy tails of more leptokurtotic distributions. For more information, see Denby & Mallows (2009).
#' Other options include "scott", "sturges" and "fd" / "Freedman-Diaconis". Case is ignored and partial matching is used.
#' Alternatively, a function can be supplied which will compute the
#' intended number of breaks or the actual breakpoints as a function of x.
#' \cr
#' An example of output: \cr
#' \cr
#' \if{html}{\figure{breaks.png}{}}
#' \if{latex}{\figure{breaks.png}{}}
#' \cr
#' @references Denby, L., & Mallows, C. (2009). Variations on the Histogram. Journal of Computational and Graphical Statistics, 18(1), 21–31. doi:10.1198/jcgs.2009.0002
#'
hist <- function(x, breaks = "dhist", freq = FALSE, probability = !freq,
include.lowest = TRUE, right = TRUE, density = NULL, angle = 45,
col = "#00ff3cCC", border = NULL, main = NULL,
xlim = range(breaks), ylim = NULL, xlab = xname, ylab, axes = TRUE,
plot = TRUE, labels = FALSE, nclass = NULL, warn.unused = TRUE, rug = TRUE,
rug.col = "#8d03e7",
...) { UseMethod("hist") }
#' Modified Version of hist() with additional functionality
#'
#' @param x a vector of values for which the histogram is desired.
#' @param breaks one of: a vector giving the breakpoints between histogram cells, a function to compute the vector of breakpoints,
#' a single number giving the number of cells for the histogram, or a character string naming an algorithm to compute the number of cells (see ‘Details’), a function to compute the number of cells. Defaults to "dhist".
#' @param freq logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, probability densities, component density, are plotted (so that the histogram has a total area of one). Defaults to FALSE.
#' @param probability an alias for !freq, for S compatibility.
#' @param include.lowest logical; if TRUE, an x[i] equal to the breaks value will be included in the first (or last, for right = FALSE) bar. This will be ignored (with a warning) unless breaks is a vector.
#' @param right logical; if TRUE, the histogram cells are right-closed (left open) intervals.
#' @param density the density of shading lines, in lines per inch. The default value of NULL means that no shading lines are drawn. Non-positive values of density also inhibit the drawing of shading lines.
#' @param angle the slope of shading lines, given as an angle in degrees (counter-clockwise).
#' @param col a colour to be used to fill the bars. The default is "#00ff3cCC".
#' @param border the color of the border around the bars. The default is to use the standard foreground color.
#' @param main these arguments to title have useful defaults here.
#' @param xlim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param ylim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).
#' @param xlab these arguments to title have useful defaults here.
#' @param ylab these arguments to title have useful defaults here.
#' @param axes logical. If TRUE (default), axes are draw if the plot is drawn.
#' @param rug Should a rug be plotted under the histogram? Defaults to TRUE.
#' @param rug.col The rug color. Defaults to #8d03e7.
#' @param plot logical. If TRUE (default), a histogram is plotted, otherwise a list of breaks and counts is returned. In the latter case, a warning is used if (typically graphical) arguments are specified that only apply to the plot = TRUE case.
#' @param labels logical or character string. Additionally draw labels on top of bars, if not FALSE; see plot.histogram.
#' @param nclass numeric (integer). For S(-PLUS) compatibility only, nclass is equivalent to breaks for a scalar or character argument.
#' @param warn.unused logical. If plot = FALSE and warn.unused = TRUE, a warning will be issued when graphical parameters are passed to hist.default().
#' @param ... further arguments and graphical parameters passed to plot.histogram and thence to title and axis (if plot = TRUE).
#'
#' @return a histogram
#'
#' @examples
#' x <- rgamma(1000, 2, .25)
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist")
#' hist(x, breaks = "fd")
#' par(mfrow = c(2, 2))
#' hist(x, breaks = "dhist", main = "'dhist' breaks method")
#' hist(x, breaks = "fd", main = "'Freedman-Diaconis' breaks method")
#' hist(x, breaks = "scott", main = "'Scott' breaks method")
#' hist(x, breaks = "sturges", main = "'Sturges' breaks method")
#'
#' @details
#' The definition of histogram differs by source (with country-specific biases).
#' R's default with equi-spaced breaks (also the default) is to plot the counts in the cells defined by breaks.
#' Thus the height of a rectangle is proportional to the number of points falling into the cell, as is the area
#' provided the breaks are equally-spaced. The modified hist() function included in the Bayezilla package however
#' utilizes non-equal sized breaks. More details are given below.
#' If right = TRUE (default), the histogram cells are intervals of the form (a, b], i.e.,
#' they include their right-hand endpoint,
#' but not their left one, with the exception of the first cell when include.lowest is TRUE.
#' For right = FALSE, the intervals are of the form [a, b), and include.lowest means ‘include highest’.
#' A numerical tolerance of 1e-7 times the median bin size (for more than four bins, otherwise the median is substituted)
#' is applied when counting entries on the edges of bins. This is not included in the reported breaks nor in the calculation
#' of density. \cr
#' \cr
#' Breaks Algorithms: \cr
#' \cr
#' The default breaks algorithm is "dhist", which implements the varying binwidth algorithm of Lorraine Denby.
#' This algorithm has some notable
#' advantages from a statistical point of view. Regions of high density have not only taller bins (as is usual)
#' but more narrow bins as well. Regions of lower denisty have not only shorter, but wider bins. This makes the
#' probability density much more
#' immediately obvious, and captures interesting features of heavy tails and skew with greater efficacy. Algorithms
#' that yield The former oversmooths in regions of high density, and is poor at identifying sharp peaks and multimodality.
#' By contrast, the latter variety oversmooths in regions of low density and can mask outliers and the
#' heavy tails of more leptokurtotic distributions. For more information, see Denby & Mallows (2009).
#' Other options include "scott", "sturges" and "fd" / "Freedman-Diaconis". Case is ignored and partial matching is used.
#' Alternatively, a function can be supplied which will compute the
#' intended number of breaks or the actual breakpoints as a function of x.
#' \cr
#' An example of output: \cr
#' \cr
#' \if{html}{\figure{breaks.png}{}}
#' \if{latex}{\figure{breaks.png}{}}
#' \cr
#' \cr
#' @references Denby, L., & Mallows, C. (2009). Variations on the Histogram. Journal of Computational and Graphical Statistics, 18(1), 21–31. doi:10.1198/jcgs.2009.0002
#' @export
#'
hist.default <- function (x, breaks = "dhist", freq = FALSE, probability = !freq,
include.lowest = TRUE, right = TRUE, density = NULL, angle = 45,
col = "#00ff3cCC", border = NULL, main = NULL,
xlim = range(breaks), ylim = NULL, xlab = xname, ylab, axes = TRUE,
plot = TRUE, labels = FALSE, nclass = NULL, warn.unused = TRUE, rug = TRUE,
rug.col = "#8d03e7",
...)
{
if (!is.numeric(x))
stop("'x' must be numeric")
xname <- paste(deparse(substitute(x), 500), collapse = "\n")
n <- length(x <- x[is.finite(x)])
n <- as.integer(n)
if (is.na(n))
stop("invalid length(x)")
use.br <- !missing(breaks)
if (use.br) {
if (!missing(nclass))
warning("'nclass' not used when 'breaks' is specified")
}
else if (!is.null(nclass) && length(nclass) == 1L)
breaks <- nclass
use.br <- use.br && (nB <- length(breaks)) > 1L
if (use.br)
breaks <- sort(breaks)
else {
if (!include.lowest) {
include.lowest <- TRUE
warning("'include.lowest' ignored as 'breaks' is not a vector")
}
if (is.character(breaks)) {
breaks <- match.arg(tolower(breaks), c("sturges", "dhist",
"fd", "freedman-diaconis", "scott"))
breaks <- switch(breaks, sturges = nclass.Sturges(x),
`freedman-diaconis` = , dhist = nclass.dhist(x), fd = nclass.FD(x), scott = nclass.scott(x),
stop("unknown 'breaks' algorithm"))
}
else if (is.function(breaks)) {
breaks <- breaks(x)
}
if (length(breaks) == 1) {
if (!is.numeric(breaks) || !is.finite(breaks) ||
breaks < 1L)
stop("invalid number of 'breaks'")
if (breaks > 1e+06) {
warning(gettextf("'breaks = %g' is too large and set to 1e6",
breaks), domain = NA)
breaks <- 1000000L
}
breaks <- pretty(range(x), n = breaks, min.n = 1)
nB <- length(breaks)
if (nB <= 1)
stop(gettextf("hist.default: pretty() error, breaks=%s",
format(breaks)), domain = NA)
}
else {
if (!is.numeric(breaks) || length(breaks) <= 1)
stop(gettextf("Invalid breakpoints produced by 'breaks(x)': %s",
format(breaks)), domain = NA)
breaks <- sort(breaks)
nB <- length(breaks)
use.br <- TRUE
}
}
nB <- as.integer(nB)
if (is.na(nB))
stop("invalid length(breaks)")
h <- diff(breaks)
equidist <- !use.br || diff(range(h)) < 1e-07 * max(c(mean(h), median(h)))
if (!use.br && any(h <= 0))
stop("'breaks' are not strictly increasing")
freq1 <- freq
if (is.null(freq)) {
freq1 <- if (!missing(probability))
!as.logical(probability)
else equidist
}
else if (!missing(probability) && any(probability == freq))
stop("'probability' is an alias for '!freq', however they differ.")
diddle <- 1e-07 * if (nB > 5)
stats::median(h)
else if (nB <= 3)
diff(range(x))
else min(h[h > 0])
fuzz <- if (right)
c(if (include.lowest) -diddle else diddle, rep.int(diddle,
nB - 1L))
else c(rep.int(-diddle, nB - 1L), if (include.lowest) diddle else -diddle)
fuzzybreaks <- breaks + fuzz
counts <- .Call(graphics:::C_BinCount, x, fuzzybreaks, right, include.lowest)
if (any(counts < 0L))
stop("negative 'counts'. Internal Error.", domain = NA)
if (sum(counts) < n)
stop("some 'x' not counted; maybe 'breaks' do not span range of 'x'")
dens <- counts/(n * h)
mids <- 0.5 * (breaks[-1L] + breaks[-nB])
r <- structure(list(breaks = breaks, counts = counts, density = dens,
mids = mids, xname = xname, equidist = equidist), class = "histogram")
if (plot) {
plot(r, freq = freq1, col = col, border = border, angle = angle,
density = density, main = main, xlim = xlim, ylim = ylim,
xlab = xlab, ylab = ylab, axes = axes, labels = labels,
...)
invisible(r)
if (isTRUE(rug)){
rug(x, ticksize = 0.015, side = 1, lwd = 0.5, col = rug.col,
quiet = getOption("warn") < 0, ...)
}
}
else {
if (warn.unused) {
nf <- names(formals())
nf <- nf[is.na(match(nf, c("x", "breaks", "nclass",
"plot", "include.lowest", "right")))]
missE <- lapply(nf, function(n) substitute(missing(.),
list(. = as.name(n))))
not.miss <- !sapply(missE, eval, envir = environment())
if (any(not.miss))
warning(sprintf(ngettext(sum(not.miss), "argument %s is not made use of",
"arguments %s are not made use of"), paste(sQuote(nf[not.miss]),
collapse = ", ")), domain = NA)
}
r
}
}
#' Density-based adaptive width histogram bins
#'
#' @description This algorithm has some notable
#' advantages from a statistical point of view. Regions of high density have not only taller bins (as is usual)
#' but more narrow bins as well. Regions of lower denisty have not only shorter, but wider bins. This makes the
#' probability density much more
#' immediately obvious, and captures interesting features of heavy tails and skew with greater efficacy. Algorithms
#' that yield The former oversmooths in regions of high density, and is poor at identifying sharp peaks and multimodality.
#' By contrast, the latter variety oversmooths in regions of low density and can mask outliers and the
#' heavy tails of more leptokurtotic distributions. Alternatively, a function can be supplied which will compute the
#' intended number of breaks or the actual breakpoints as a function of x. For more information, see Denby & Mallows (2009).
#' The original code was authored by Lorraine Denby, but some minor improvements have been made here.
#' @author Lorraine Denby, Brandon Vaughan
#' @seealso
#' \url{http://pubs.research.avayalabs.com/pdfs/ALR-2007-003-paper.pdf}
#' @references L. Denby and C. Mallows. Variations on the histogram. Journal
#' of Computational and Graphical Statistics, 18 (1):21-31, 2009.
#' URL \url{http://pubs.amstat.org/doi/abs/10.1198/jcgs.2009.0002.}
#' @param b slope. See paper for details. Defaults to 1.5.
#' @param nbins number of bins. See Denby & Mallows (2009).
#' @param min.bins the minimum number of bins. Optional.
#' @param rx range of data, if not taken from data.
#' @return A function that takes a single parameter, a numeric x specifying
#' the data for which breaks are needed, and returns a vector of breaks.
#' @export
#' @examples
#' nclass.dhist()
#'
nclass.dhist = function(x, b = 1.5, rx = range(x), min.bins = NULL){
n.bins <-function(x, min.bins = NULL){
binsfunc = function(b){
bincounts = b^2
bincounts = bincounts/sum(b)
bincounts = 1 - b
bincounts = floor(weighted.mean(b, bincounts))
return(bincounts)
}
hdi = Bayezilla::cred_interval(x, method = "HDI", cred.level = 0.80)
if(hdi[1] == hdi[2]){
num = hdi[1]
newx = x[which(x != num)]
hdi = Bayezilla::cred_interval(newx, method = "HDI", cred.level = 0.80)
}
ecd = ecdf(x)
l = ecd(hdi[1])
u = ecd(hdi[2])
x<-x[!is.na(x)]
n<-length(x)
Q<-quantile(x, c(l, u))
X<-range(x)
result<- ceiling(n^(1/3)*(X[2]-X[1])/(2*(Q[2]-Q[1])))
if (is.null(min.bins)){
fd = nclass.FD(x)
sturge = nclass.Sturges(x)
scott = nclass.scott(x)
result <- binsfunc(b = c(fd, sturge, scott, result))
names(result)<-NULL
result
} else if (!is.null(min.bins)){
result <- c(min.bins, result)
if(is.nan(result)) {
result <- min.bins
}
names(result)<-NULL
result
}
}
hdi = Bayezilla::cred_interval(x, method = "HDI", cred.level = 0.80)
if(hdi[1] == hdi[2]){
num = hdi[1]
newx = x[which(x != num)]
hdi = Bayezilla::cred_interval(newx, method = "HDI", cred.level = 0.80)
}
ecd = ecdf(x)
l = ecd(hdi[1])
u = ecd(hdi[2])
a = b*diff(quantile(x, c(l , u)))
nbins <- n.bins(x, min.bins = min.bins)
x <- sort(x)
if(a == 0)
a <- diff(range(x))/100000000
if(a != Inf) {
n <- length(x)
h <- (rx[2] + a - rx[1])/nbins
ybr <- rx[1] + h * (0:nbins)
yupper <- x + (a * (1:n))/n
# upper and low Fer corners in the ecdf
ylower <- yupper - a/n
cmtx <- cbind(
cut(yupper, breaks = ybr),
cut(yupper, breaks = ybr, left.include = T),
cut(ylower, breaks = ybr),
cut(ylower, breaks = ybr, left.include = T)
)
cmtx[1, 3] <- cmtx[1, 4] <- 1
# to replace NAs when default r is used
cmtx[n, 1] <- cmtx[n, 2] <- nbins
checksum <- rowSums(cmtx) %% 4
# will be 2 for obs. that straddle two bins
straddlers <- (1:n)[checksum == 2]
# to allow for zero counts
if(length(straddlers) > 0) {
counts <- table(c(1:nbins, cmtx[- straddlers, 1]))
} else {
counts <- table(c(1:nbins, cmtx[, 1]))
}
counts <- counts - 1
if(length(straddlers) > 0) {
for(i in straddlers) {
binno <- cmtx[i, 1]
theta <- ((yupper[i] - ybr[binno]) * n)/a
counts[binno - 1] <- counts[binno - 1] + (1 - theta)
counts[binno] <- counts[binno] + theta
}
}
xbr <- ybr
xbr[-1] <- ybr[-1] - (a * cumsum(counts))/n
} else {
bin.size <- length(x)/nbins
cut.pt <- c(
min(x) - abs(min(x))/1000,
approx(seq(length(x)),
x,
(1:(nbins - 1)) * bin.size, rule = 2)$y,
max(x)
)
aa <- hist(x, breaks = cut.pt, plot = F, probability = T)
xbr <- unique(aa$breaks)
}
unique(xbr)
}
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