By scanning a fiber beard and generating a fibrogram, certain cotton fiber length parameters can be obtained rapidly. This is the length measurement method used by the High Volume Instrument (HVITM). The objective of this study is to infer fiber length distribution from beard test data. Part 1 of this study deals with the mathematical functions describing length distributions related to the beard method. Eight cottons with a wide range of fiber length were selected and tested on the Advanced Fiber Information System (AFISTM). The measured fiber length data are used for finding the underlying theoretical length distributions. Fiber length distributions by number and by weight are discussed separately, and in both cases a mix of two Weibull distributions shows a good fit to the data. Kolmogorov-Smirnov goodness-of-fit tests were conducted to confirm the findings. Various length parameters such as Mean Length (ML) and Upper Half Mean Length (UHML) are compared between the original distribution from the experimental data and the fitted distributions. A subsequent paper will discuss the inference of fiber length distributions from the beard testing method.