Explanation and exact formula of Zipfs law evaluated from rank-share combinatorics

Abstract

This work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. It presents a formula for rank-share distribution and illustrates that Zipfs law, is descended from expected values of various ranks in the new distribution. All conclusions, formulas and charts presented here were tested against publicly available statistical data in different areas. The correlation coefficient between the calculated values and statistical numbers provided by Bureau of Labor Statistics was 0.99899. Monte-Carlo simulations were performed as additional evidence.