{'fraction_non_alphanumeric': 0.019400352733686066, 'fraction_numerical': 0.0, 'mean_word_length': 5.682352941176471, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The Completeness and Uniqueness of Johnson's System in Skewness–Kurtosis Space

Abstract In empirical research, there exist great difficulties in applying results based on assumption of a normal distribution because often data do not come from a normal distribution. For given data, the Johnson system, originally presented by Johnson, provides a possible distribution by covering every possible combination of skewness and kurtosis completely and uniquely. In this paper, we prove the uniqueness and completeness of the Johnson system in its skewness–kurtosis space.