Exact Statistical Distribution of the Body Mass Index (BMI): Analysis and Experimental Confirmation

Body Mass Index (BMI), defined as the ratio of individual mass (in kilograms) to square associated height meters), is one most widely discussed and utilized risk factors in medicine public health, given increasing obesity worldwide its relation metabolic disease. Statistically, BMI a composite random variable, since human weight (converted mass) are themselves variables. Much effort over years has gone into attempts model or approximate distribution function. This paper derives mathematically exact probability density function (PDF), well bivariate PDF for height. Taken together, shown be correlated lognormal variables whose marginal distributions each form. The mean variance distribution, together with linear correlation coefficient two distributions, provide 5 nonadjustable parameters population that uniquely determine corresponding which also theoretical analysis tested experimentally by gender against large anthropometric data base, found predict near perfection profile empirical and, great accuracy, statistics including mean, variance, skewness, kurtosis, correlation. Beyond solving longstanding statistical problem, significance these findings that, knowledge functions diverse populations, medical health professionals can then make better informed inferences regarding policies reduce obesity.