# Statistics

Statistics are functions taking as input one or more aesthetics, operating on those values, then outputting to one or more aesthetics. For example, drawing of boxplots typically uses the boxplot statistic (Stat.boxplot) that takes as input the x and y aesthetic, and outputs the middle, and upper and lower hinge, and upper and lower fence aesthetics.

Gadfly.Stat.bandType
Stat.band[(; orientation=:vertical)]

Transform points in the xmin, xmax, ymin and ymax aesthetics into rectangles in the xmin, xmax, ymin and ymax aesthetics. Used by Geom.band.

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Gadfly.Stat.binmeanType
Stat.binmean[(; n=20)]

Transform the the x and y aesthetics into n bins each of which contains the mean within than bin.

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Gadfly.Stat.boxplotType
Stat.boxplot[(; method=:tukey)]

Transform the the x and y aesthetics into the x, middle, lower_hinge, upper_hinge, lower_fence, upper_fence and outliers aesthetics. If method is :tukey then Tukey's rule is used (i.e. fences are 1.5 times the inter-quartile range). Otherwise, method should be a vector of five numbers giving quantiles for lower fence, lower hinge, middle, upper hinge, and upper fence in that order. Used by Geom.boxplot.

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Gadfly.Stat.contourType
Stat.contour[(; levels=15, samples=150)]

Transform the 2D function, matrix, or DataFrame in the z aesthetic into a set of lines in x and y showing the iso-level contours. A function requires that either the x and y or the xmin, xmax, ymin and ymax aesthetics also be defined. The latter are interpolated using samples. A matrix and DataFrame can optionally input x and y aesthetics to specify the coordinates of the rows and columns, respectively. In each case levels sets the number of contours to draw: either a vector of contour levels, an integer that specifies the number of contours to draw, or a function which inputs z and outputs either a vector or an integer. Used by Geom.contour.

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Gadfly.Stat.densityType
Stat.density[(; n=256, bandwidth=-Inf)]

Estimate the density of x at n points, and put the result in x and y. Smoothing is controlled by bandwidth. Used by Geom.density.

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Gadfly.Stat.density2dType
Stat.density2d[(; n=(256,256), bandwidth=(-Inf,-Inf), levels=15)]

Estimate the density of the x and y aesthetics at n points and put the results into the x, y and z aesthetics. Smoothing is controlled by bandwidth. Calls Stat.contour to compute the levels. Used by Geom.density2d.

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Gadfly.Stat.dodgeType
Stat.dodge[(; position=:dodge, axis=:x)]

Transform the points in the x and y aesthetics into set of dodged or stacked points in the x and y aesthetics. position is :dodge or :stack. axis is :x or :y.

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Gadfly.Stat.ellipseType
Stat.ellipse[(; distribution=MvNormal, levels=[0.95], nsegments=51)]

Transform the points in the x and y aesthetics into set of a lines in the x and y aesthetics. distribution specifies a multivariate distribution to use; levels the quantiles for which confidence ellipses are calculated; and nsegments the number of segments with which to draw each ellipse. Used by Geom.ellipse.

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Gadfly.Stat.funcType
Stat.func[(; num_samples=250)]

Transform the functions or expressions in the y, xmin and xmax aesthetics into points in the x, y and group aesthetics.

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Gadfly.Stat.hairType
Stat.hair[(; intercept=0.0, orientation=:vertical)]

Transform points in the x and y aesthetics into lines in the x, y, xend and yend aesthetics. Used by Geom.hair.

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Gadfly.Stat.hexbinType
Stat.hexbin[(; xbincount=50, ybincount=50)]

Bin the points in the x and y aesthetics into hexagons in the x, y, xsize and ysize aesthetics. xbincount and ybincount manually fix the number of bins.

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Gadfly.Stat.histogramType
Stat.histogram[(; bincount=nothing, minbincount=3, maxbincount=150,
position=:stack, orientation=:vertical, density=false, limits=NamedTuple())]

Transform the x aesthetic into the x, y, xmin and xmax aesthetics, optionally grouping by color. Exchange y for x when orientation is :horizontal. bincount specifies the number of bins to use. If set to nothing, an optimization method is used to determine a reasonable value which uses minbincount and maxbincount to set the lower and upper limits. If density is true, normalize the counts by their total. limits is a NamedTuple that sets the limits of the histogram (min= , max= ): min or max or both can be set.

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Gadfly.Stat.histogram2dType
Stat.histogram2d[(; xbincount=nothing, xminbincount=3, xmaxbincount=150,
ybincount=nothing, yminbincount=3, ymaxbincount=150)]

Bin the points in the x and y aesthetics into rectangles in the xmin, ymax, ymin, ymax and color aesthetics. xbincount and ybincount manually fix the number of bins. If set to nothing, an optimization method is used to determine a reasonable value which uses xminbincount, xmaxbincount, yminbincount and ymaxbincount to set the lower and upper limits.

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Gadfly.Stat.qqType
Stat.qq

Transform the x and y aesthetics into quantiles. If each is a numeric vector, their sample quantiles will be compared. If one is a Distribution, then its theoretical quantiles will be compared with the sample quantiles of the other. Optionally group using the color aesthetic. Stat.qq uses function qqbuild from Distributions.jl.

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Gadfly.Stat.quantile_barsType
Stat.quantile_bars[(; quantiles=[0.025, 0.975], bar_width=0.1, n=256, bandwidth=-Inf)]

Transform the point in the x aesthetic into a set of the x, y, xend and yend aesthetics points. These points can then be drawn via Geom.segment. Here, bandwidth works independently from the bandwidth setting for Stat.density.

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Gadfly.Stat.rectbinType
Stat.rectbin

Transform the x and y aesthetics into the xmin, xmax, ymin and ymax aesthetics.

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Gadfly.Stat.smoothType
Stat.smooth[(; method=:loess, smoothing=0.75, levels=[0.95])]

Transform the x and y aesthetics into the x, y, ymin and ymax aesthetics. method can either be:loess or :lm. smoothing controls the degree of smoothing. For :loess, this is the span parameter giving the proportion of data used for each local fit where 0.75 is the default. Larger values use more data (less local context), smaller values use less data (more local context). levels is a vector of quantiles at which confidence bands are calculated (currently for method=:lm only). For confidence bands, use Stat.smooth() with Geom.ribbon.

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Gadfly.Stat.stepType
Stat.step[(; direction=:hv)]

Perform stepwise interpolation between the points in the x and y aesthetics. If direction is :hv a horizontal line extends to the right of each point and a vertical line below it; if :vh then vertical above and horizontal to the left. More concretely, between (x[i], y[i]) and (x[i+1], y[i+1]), either (x[i+1], y[i]) or (x[i], y[i+1]) is inserted, for :hv and :vh, respectively.

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Gadfly.Stat.vectorfieldType
Stat.vectorfield[(; smoothness=1.0, scale=1.0, samples=20)]

Transform the 2D function or matrix in the z aesthetic into a set of lines from x, y to xend, yend showing the gradient vectors. A function requires that either the x and y or the xmin, xmax, ymin and ymax aesthetics also be defined. The latter are interpolated using samples. A matrix can optionally input x and y aesthetics to specify the coordinates of the rows and columns, respectively. In each case, smoothness can vary from 0 to Inf; and scale sets the size of vectors.

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Gadfly.Stat.x_jitterMethod
Stat.x_jitter[(; range=0.8, seed=0x0af5a1f7)]

Add a random number to the x aesthetic, which is typically categorical, to reduce the likelihood that points overlap. The maximum jitter is range times the smallest non-zero difference between two points.

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Gadfly.Stat.xticksMethod
Stat.xticks[(; ticks=:auto, granularity_weight=1/4, simplicity_weight=1/6,
coverage_weight=1/3, niceness_weight=1/4)]

Compute an appealing set of x-ticks that encompass the data by transforming the x, xmin, xmax, xintercept and xend aesthetics into the xtick and xgrid aesthetics. ticks is a vector of desired values, or :auto to indicate they should be computed. the importance of having a reasonable number of ticks is specified with granularity_weight; of including zero with simplicity_weight; of tightly fitting the span of the data with coverage_weight; and of having a nice numbering with niceness_weight.

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Gadfly.Stat.y_jitterMethod
Stat.y_jitter[(; range=0.8, seed=0x0af5a1f7)]

Add a random number to the y aesthetic, which is typically categorical, to reduce the likelihood that points overlap. The maximum jitter is range times the smallest non-zero difference between two points.

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Gadfly.Stat.yticksMethod
Stat.yticks[(; ticks=:auto, granularity_weight=1/4, simplicity_weight=1/6,
coverage_weight=1/3, niceness_weight=1/4)]

Compute an appealing set of y-ticks that encompass the data by transforming the y, ymin, ymax, yintercept, middle, lower_hinge, upper_hinge, lower_fence, upper_fence and yend aesthetics into the ytick and ygrid aesthetics. ticks is a vector of desired values, or :auto to indicate they should be computed. the importance of having a reasonable number of ticks is specified with granularity_weight; of including zero with simplicity_weight; of tightly fitting the span of the data with coverage_weight; and of having a nice numbering with niceness_weight.

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