The UNIVARIATE Procedure
- Overview
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Getting Started
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Syntax
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Details
Missing Values Rounding Descriptive Statistics Calculating the Mode Calculating Percentiles Tests for Location Confidence Limits for Parameters of the Normal Distribution Robust Estimators Creating Line Printer Plots Creating High-Resolution Graphics Using the CLASS Statement to Create Comparative Plots Positioning Insets Formulas for Fitted Continuous Distributions Goodness-of-Fit Tests Kernel Density Estimates Construction of Quantile-Quantile and Probability Plots Interpretation of Quantile-Quantile and Probability Plots Distributions for Probability and Q-Q Plots Estimating Shape Parameters Using Q-Q Plots Estimating Location and Scale Parameters Using Q-Q Plots Estimating Percentiles Using Q-Q Plots Input Data Sets OUT= Output Data Set in the OUTPUT Statement OUTHISTOGRAM= Output Data Set OUTKERNEL= Output Data Set OUTTABLE= Output Data Set Tables for Summary Statistics ODS Table Names ODS Tables for Fitted Distributions ODS Graphics Computational Resources
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Examples
Computing Descriptive Statistics for Multiple Variables Calculating Modes Identifying Extreme Observations and Extreme Values Creating a Frequency Table Creating Plots for Line Printer Output Analyzing a Data Set With a FREQ Variable Saving Summary Statistics in an OUT= Output Data Set Saving Percentiles in an Output Data Set Computing Confidence Limits for the Mean, Standard Deviation, and Variance Computing Confidence Limits for Quantiles and Percentiles Computing Robust Estimates Testing for Location Performing a Sign Test Using Paired Data Creating a Histogram Creating a One-Way Comparative Histogram Creating a Two-Way Comparative Histogram Adding Insets with Descriptive Statistics Binning a Histogram Adding a Normal Curve to a Histogram Adding Fitted Normal Curves to a Comparative Histogram Fitting a Beta Curve Fitting Lognormal, Weibull, and Gamma Curves Computing Kernel Density Estimates Fitting a Three-Parameter Lognormal Curve Annotating a Folded Normal Curve Creating Lognormal Probability Plots Creating a Histogram to Display Lognormal Fit Creating a Normal Quantile Plot Adding a Distribution Reference Line Interpreting a Normal Quantile Plot Estimating Three Parameters from Lognormal Quantile Plots Estimating Percentiles from Lognormal Quantile Plots Estimating Parameters from Lognormal Quantile Plots Comparing Weibull Quantile Plots Creating a Cumulative Distribution Plot Creating a P-P Plot
- References
Example 4.26 Creating Lognormal Probability Plots
This example is a continuation of the example explored in the section Modeling a Data Distribution.
In the normal probability plot shown in Output 4.6, the nonlinearity of the point pattern indicates a departure from normality in the distribution of Deviation. Because the point pattern is curved with slope increasing from left to right, a theoretical distribution that is skewed to the right, such as a lognormal distribution, should provide a better fit than the normal distribution. See the section Interpretation of Quantile-Quantile and Probability Plots.
You can explore the possibility of a lognormal fit with a lognormal probability plot. When you request such a plot, you must specify the shape parameter 
for the lognormal distribution. This value must be positive, and typical values of range from 0.1 to 1.0. You can specify values for with the SIGMA= secondary option in the LOGNORMAL primary option, or you can specify that is to be estimated from the data.
The following statements illustrate the first approach by creating a series of three lognormal probability plots for the variable Deviation introduced in the section Modeling a Data Distribution:
symbol v=plus height=3.5pct;
title 'Lognormal Probability Plot for Position Deviations';
ods graphics off;
proc univariate data=Aircraft noprint;
probplot Deviation /
lognormal(theta=est zeta=est sigma=0.7 0.9 1.1)
href = 95
lhref = 1
square;
run;
The LOGNORMAL primary option requests plots based on the lognormal family of distributions, and the SIGMA= secondary option requests plots for equal to 0.7, 0.9, and 1.1. These plots are displayed in Output 4.26.1, Output 4.26.2, and Output 4.26.3, respectively. Alternatively, you can specify to be estimated using the sample standard deviation by using the option SIGMA=EST.
The SQUARE option displays the probability plot in a square format, the HREF= option requests a reference line at the 95th percentile, and the LHREF= option specifies the line type for the reference line.
=0.7
=0.9
=1.1
The value 
in Output 4.26.2 most nearly linearizes the point pattern. The 95th percentile of the position deviation distribution seen in Output 4.26.2 is approximately 0.001, because this is the value corresponding to the intersection of the point pattern with the reference line.
Note: After the that produces the most linear fit is found, you can then estimate the threshold parameter 
and the scale parameter 
. See Example 4.31.
The following statements illustrate how you can create a lognormal probability plot for Deviation by using a local maximum likelihood estimate for .
symbol v=plus height=3.5pct;
title 'Lognormal Probability Plot for Position Deviations';
ods graphics off;
proc univariate data=Aircraft noprint;
probplot Deviation / lognormal(theta=est zeta=est sigma=est)
href = 95
square;
run;
The plot is displayed in Output 4.26.4. Note that the maximum likelihood estimate of (in this case, 0.882) does not necessarily produce the most linear point pattern.
A sample program for this example, uniex16.sas, is available in the SAS Sample Library for Base SAS software.