Understanding empirical cdf graphs
main topic 

The empirical cdf (cumulative distribution function) plot below is for a sample with the following values: 0.5, 1.0, 2.1, 2.1, and 7.3.

Minitab first plots each value against the percentage of values in the sample that are less than or equal to it (circled in above illustration). Identical values are plotted only once. The points are then connected with a stepped line (blue). In the plot above:

·    The smallest of the five values in the sample is 0.5. Thus, 20% of the values are less than or equal to 0.5.

·    The next smallest value is 1.0; 40% percent of the sample values are less than or equal to 1.0.

·    The value 2.1 occurs twice; 80% of the sample values are less than or equal to 2.1.

·    The largest value is 7.3; 100% of the sample values are less than or equal to 7.3.

Minitab also displays parameter estimates (or historical parameters, if you provide them) and the fitted cdf (cumulative distribution function; red line in above illustration). For the normal distribution, the mean and standard deviation are estimated from the data. For the lognormal distribution, the mean and standard deviation of the log of the data serve as the location and scale estimates, respectively. For other distributions, Minitab reports maximum likelihood estimates.