{'fraction_non_alphanumeric': 0.021844660194174758, 'fraction_numerical': 0.0, 'mean_word_length': 5.762295081967213, '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}}
Trend-transformed independent vectors: construction and stochastic comparison results

A new class of random vectors is introduced, where the components are obtained through trend-transforms of independent random variables. Such a vector is called trend-transformed independent vector. The new class includes many models from the previous literature, such as sequential and intermediate order statistics, or the vectors formed by the first arrival times in classical counting processes such as trend renewal/extended Pólya/non-homogeneous pure-birth processes. This allows to treat all these different models in a unified way. New multivariate stochastic comparison results are obtained between trend-transformed independent vectors with different parameters, which are shown to enlarge previous results from the literature.