The beta distribution has two shape parameters: For example, the following statements fit a Weibull distribution function with and maximum likelihood estimates for and c:. By default, maximum likelihood estimates are computed for and. There does not appear to be a standard term for the quantity on the horizontal axis, which I have labeled “proportion of data. The parameter must be less than the minimum data value. A problem of scale If one of the variables has a range that is an order of magnitude greater than the range of another variable, the comparative histogram can lose its effectiveness. By default, maximum likelihood estimates are computed for and.

The default value for is 0. Note that the maximum likelihood estimate of is calculated iteratively using the Newton-Raphson approximation. The following statements create a cdf plot for each of the three variables:. By default, the procedure produces a plot for the normal distribution. The cdf is an increasing step function that has a vertical jump of at each value of equal to an observed value. In addition, the gamma distribution has a shape parameter and a scale parameter. The cdf is an increasing step function that has a vertical jump of at each value of x equal to an observed value.

If you do not specify values for andthe procedure calculates maximum likelihood estimates. The default values for and are 0 and 1, respectively. There does not appear to be a standard term for the quantity on the horizontal axis, which I have labeled “proportion of data.

## The UNIVARIATE Procedure

Note that the maximum likelihood estimate of is calculated iteratively using the Newton-Raphson approximation. One technique is to display a panel of histograms, which are known as comparative histograms.

In addition, the Weibull distribution has a shape parameter and a scale parameter. The default value is the sample mean. For example, the following statements fit a lognormal distribution function with and maximum likelihood estimates for and: Although the spread plot is not a well-known plit, it appears prominently in the output of several popular SAS procedures.

Options can be any of the following:. If you also center the data so that each variable has zero mean, then the result called a spread plot. For example, the following statements fit a Weibull distribution function with and sass likelihood estimates for and c:. By default, the sample mean and sample standard deviation are calculated for and.

For example, the following statements fit an exponential distribution with and a maximum likelihood estimate for:. The equation of the fitted cdf is. The parameter must be less than or equal to the minimum data value.

Options can be any of the following: However, the quantile plot requires more skill to interpret. The parameter must be less than the minimum data value. By default, the procedure produces a plot for the normal distribution.

### SAS and R: Example Plot an empirical cumulative distribution function from scratch

The equation of the fitted olot is. If you specify more than one variable, the options apply equally to each variable. Chambers and Cleveland each use the simpler fractional rank given by r i —0. The Normal variable clearly has two moderate tails, whereas the Uniform variable appears to be a bounded distribution. See the section Dictionary of Common Options for detailed descriptions of options common to all plot statements. The default value for is 0. The variable in the top histogram has a range that is 10 times the range of the variable in the lower histogram.

By default, maximum likelihood estimates are computed for and.

### CDFPLOT Statement :: Base SAS(R) Procedures Guide: Statistical Procedures, Third Edition

I have used this approach to compare salaries between two categories of workers. The distributions available are the beta, exponential, gamma, lognormal, normal, and three-parameter Weibull. By default, a maximum likelihood estimate is computed for.

univafiate In addition, the lognormal distribution has a shape parameter and a scale parameter. For example, the following statements fit a lognormal distribution function with and maximum likelihood estimates for and:.

See the section Dictionary of Common Options for detailed descriptions of options common to all plot statements. New heat maps in the REG procedure. For example, the following statements fit a gamma distribution function with and maximum likelihood estimates for and: The beta distribution has two shape parameters: In addition, the generalized Pareto distribution has a shape parameter and a scale parameter.

However, the plot is far from perfect. The distributions available are listed in Table cddf. To sqs this, consider the following comparative histogram of three widely varying quantities: