Probability Distribution Functions

NCL V5.1.0 is required to use the univariate PDF function, pdfx. This version was released March 4, 2009.

NCL V5.1.1 is required to use the bivariate (joint) PDF function, pdfxy. This version has not been released.

The probability (frequency of occurrence) distribution of a variable, X: the (pdfx) returns probabilities associated with each of its possible values. Given two variables X and Y, the bivariate joint probability distribution indicates the probability of occurrence defined in terms of both X and Y.

Generally, the larger the array(s) the smoother the derived PDF. Bin sizes of less-than [greater-than] the default number of 25 bins will result in smoother [rougher] plots.

pdf_1.ncl: This example illustrates PDFs from three arrays representing variables with three different distributions. The default of 25 bins was used.

pdf_2.ncl: This illustrates using a user specified number of bins. Here, 40 bins are specified. This results in a more ragged view of the distribution. Use of the returned bin_center attributes from three PDFs to place all on a common x-axis is illustrated. (Minor changes would be required if the number of bins used had been different.) The gsnXYBarChart and gsnXYBarChartOutlineOnly illustrate using a bar style plot.

pdf_3.ncl: Illustrate a simple bivariate PDF using two variables having normal distributions.

pdf_4.ncl: Similar to Example 3 but use different bin numbers. Given a fixed number of values, the fewer bins used, the smoother the resulting PDF.

pdf_5.ncl: The bivariate distributions of variables from variables with different univariate distributions will yield different patterns. Here, the univariate distributions of Example 1 are used to create bivariate PDFs.

Some tuning of plots may be necessary to focus on regions of interest. Here, the "Gamma/Chi" distributions are highly skewed. There are large areas where the joint probabilites are near or at zero. NCL coordinate subscripting is used to select regions of interest.

pdf_6.ncl: Variables that may not be continuous [probabilities=0.0] may be best viewed via use of "raster" plots. These clearly show the bin and data resolution.

Note that using gsn_csm_contour results in the raster bins at the edges being reduced to half width. The use of plt_pdfxy located in the shea_util expands the contour area and allows the edge raster bins to be fully viewed.