In addition to providing an abundance of fiber measurements, the advance fiber information system (AFIS) also provides comprehensive information on the frequency distribution of mean fiber length by weight (FLw), mean fiber length by number (FLn), maturity, and fineness. Efforts were made to find practical and effective applications of the distribution data provided. FLw was the measurement selected to be analyzed by the distribution statistical parameters of cross entropy. Microsoft Excel 2000 macros (Microsoft Corporation, 1999) were used to remove trivial information and organize the FLw distribution data of each sample, which contained 40 length classes.

Cross entropy is a method to measure how good one distribution approximates another distribution, with a value of 0 being a perfect match. Scientific quandary with this procedure surrounds the proposition of what shall serve as the ideal cotton fiber length distribution to be compared with all other samples. No published material exists identifying the optimal length distribution. Questions arise as should the distribution be artificially fabricated, what genotype, how many samples or environments shall be appropriate. In the current study, two genotypes grown in a single environment and one genotype grown in two environments were examined as possible cross entropy check candidates.

To have a valid comparison of distributions from different samples, all FLw distributions were standardized with a mean of 0 and a variance of 1. However, AFIS does not record the length of the 9,000 fiber observations needed to standardize the distribution for each sample. AFIS does provide the percentage of fibers for each of the defined forty length classes. Therefore, a SAS program (SAS, 2004) was created to generate random numbers corresponding to the frequency and range of each length class. The 9,000 fiber observations randomly generated were then uniformly divided into 40 new length classes. The 40 new length classes for each sample were then used to standardize the distribution. Cross entropy values according to Shore and Johnson (1980) were then calculated using a C++ program (Hequet, 2004).