The SEVERITY Procedure

ODS Graphics

Statistical procedures use ODS Graphics to create graphs as part of their output. ODS Graphics is described in detail in Chapter 21, Statistical Graphics Using ODS (SAS/STAT User's Guide).

Before you create graphs, ODS Graphics must be enabled (for example, with the ODS GRAPHICS ON statement). For more information about enabling and disabling ODS Graphics, see the section "Enabling and Disabling ODS Graphics" in that chapter.

The overall appearance of graphs is controlled by ODS styles. Styles and other aspects of using ODS Graphics are discussed in the section "A Primer on ODS Statistical Graphics" in that chapter.

This section describes the use of ODS for creating graphics with the SEVERITY procedure.

ODS Graph Names

PROC SEVERITY assigns a name to each graph it creates by using ODS. You can use these names to selectively reference the graphs. The names are listed in Table 23.6.

Table 23.6 ODS Graphics Produced by PROC SEVERITY
ODS Graph Name	Plot Description	PLOTS= Option
CDFPlot	Comparative CDF Plot	CDF
CDFDistPlot	CDF Plot per Distribution	CDFPERDIST
PDFPlot	Comparative PDF Plot	PDF
PDFDistPlot	PDF Plot per Distribution	PDFPERDIST
PPPlot	P-P Plot of CDF and EDF	PP

Comparative CDF Plot

The comparative CDF plot helps you visually compare the cumulative distribution function (CDF) estimates of all the candidate distribution models and the empirical distribution function (EDF) estimate. The plot does not contain CDF estimates for models whose parameter estimation process does not converge. The horizontal axis represents the values of the response variable. The vertical axis represents the values of the CDF or EDF estimates.

If truncation is specified, then conditional CDF estimates are plotted. Otherwise, unconditional CDF estimates are plotted. The conditional estimates are computed using the method described in the section Truncation and Conditional CDF Estimates.

If left-truncation is specified and the MARKTRUNCATED option is specified, then the left-truncated observations are marked in the plot. If right-censoring is specified, left-censoring is not specified, and the MARKCENSORED option is specified, then the right-censored observations are marked in the plot.

If regressor variables are specified, then the plotted CDF estimates are from a mixture distribution. See the section CDF and PDF Estimates with Regression Effects for details.

CDF Plot per Distribution

The CDF plot per distribution shows the CDF estimates of each candidate distribution model unless that model’s parameter estimation process does not converge. The plot also contains estimates of the EDF. The horizontal axis represents the values of the response variable. The vertical axis represents the values of the CDF or EDF estimates.

If truncation is specified, then conditional CDF estimates are plotted. Otherwise unconditional CDF estimates are plotted. The conditional estimates are computed using the method described in the section Truncation and Conditional CDF Estimates.

If regressor variables are specified, then the plotted CDF estimates are from a mixture distribution. See the section CDF and PDF Estimates with Regression Effects for details.

Comparative PDF Plot

The comparative PDF plot helps you visually compare the probability density function (PDF) estimates of all the candidate distribution models. The plot does not contain PDF estimates for models whose parameter estimation process does not converge. The horizontal axis represents the values of the response variable. The vertical axis represents the values of the PDF estimates.

If the HISTOGRAM option is specified, then the plot also contains the histogram of response variable values. If the KERNEL option is specified, then the plot also contains the kernel density estimate for the response variable values.

If regressor variables are specified, then the plotted PDF estimates are from a mixture distribution. See the section CDF and PDF Estimates with Regression Effects for details.

PDF Plot per Distribution

The PDF plot per distribution shows the PDF estimates of each candidate distribution model unless that model’s parameter estimation process does not converge. The horizontal axis represents the values of the response variable. The vertical axis represents the values of the PDF estimates.

If regressor variables are specified, then the plotted PDF estimates are from a mixture distribution. See the section CDF and PDF Estimates with Regression Effects for details.

P-P Plot of CDF and EDF

The P-P plot of CDF and EDF is the probability-probability plot that compares the CDF estimates of a distribution with the EDF estimates. A plot is not prepared for models whose parameter estimation process does not converge. The horizontal axis represents the CDF estimates of a candidate distribution and the vertical axis represents the EDF estimates.

This plot can be interpreted as displaying the data that are used for computing the EDF-based statistics of fit for the given candidate distribution. As described in the section EDF-Based Statistics, these statistics are computed by comparing the EDF, denoted by $\text{[math]}$ , and the CDF, denoted by $\text{[math]}$ , at each of the response variable values $\text{[math]}$ . Using the probability inverse transform $\text{[math]}$ , this is equivalent to comparing the EDF of the $\text{[math]}$ , denoted by $\text{[math]}$ , and the CDF of $\text{[math]}$ , denoted by $\text{[math]}$ (D’Agostino and Stephens 1986, Ch. 4). Given that the CDF of $\text{[math]}$ is a uniform distribution ( $\text{[math]}$ ), the EDF-based statistics can be computed by comparing the EDF estimate of $\text{[math]}$ with the estimate of $\text{[math]}$ . The horizontal axis of the plot represents the estimated CDF $\text{[math]}$ . The vertical axis represents the estimated EDF of $\text{[math]}$ , $\text{[math]}$ . The plot contains a scatter plot of ( $\text{[math]}$ , $\text{[math]}$ ) points and a reference line $\text{[math]}$ that represents the expected uniform distribution of $\text{[math]}$ . Points scattered closer to the reference line indicate a better fit than the points scattered away from the reference line.

If truncation is specified, then the EDF estimates are conditional as described in the section EDF Estimates and Truncation. So, conditional estimates of CDF are displayed, which are computed using the method described in the section Truncation and Conditional CDF Estimates.

If regressor variables are specified, then the displayed CDF estimates, both unconditional and conditional, are from a mixture distribution. See the section CDF and PDF Estimates with Regression Effects for details.