ISM Research Memorandum
Statistical properties of the human height distribution: Re-examination of the transition from the log-normal distribution to the normal distribution
Iwata, Takaki (The Institute of Statistical Mathematics);
Yamazaki, Yoshihiro (Department of Physics, Waseda University);
Kuninaka, Horito (Faculty of Education, Mie University)
human height, normal distribution, log-normal distribution, model comparison, maximum likelihood method, skewness, mixture distribution
This study investigates the validity of the transition of the human height distribution from the log-normal distribution to the normal distribution during puberty, as found in an earlier study [Kuninaka et al.: J. Phys. Soc. Jpn. 78 (2009) 125001]. Our data analysis reveals that, in early puberty, the variation in height increases as children grow. Thus, the classification of a height dataset by age at this stage leads us to analyze a mixture of distributions with larger means and greater variations. This mixture distribution has a positive skewness and is consequently closer to the log-normal distribution than to the normal distribution. The opposite case occurs in late puberty, and this scenario mimics the transition during puberty. In conclusion, the transition is just apparent and is not real.