{'fraction_non_alphanumeric': 0.02664576802507837, 'fraction_numerical': 0.009404388714733543, 'mean_word_length': 4.93953488372093, '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}}
ROBUSTNESS PROPERTIES OF A SEQUENTIAL CONFIDENCE INTERVAL FOR THE COMMON LOCATION PARAMETER OF A NUMBER OF EXPONENTIAL POPULATIONS

The robustness of a sequential confidence interval for the common location parameter of a number k of exponential populations, with possibly different scale parameters, is studied. Asymptotic theory is considered where the underlying exponential distributions are contaminated in a so-called gross errors model with contamination probabilities ε1, …, ε k and where simultaneously d → 0, where d is the length of the confidence interval, and ε1(d) → 0,…, ε k (d) → 0 where the contamination probabilities are taken to be functions of d. In the case k = 1, considered first, the procedure considered reduces to the procedure of Mukhopadyay (1974) and asymptotic results are derived for the coverage probability and the sample size, for contamination to the right and to the left. The relationship with the influence functions of the estimators used is pointed out. The theoretical results for general k are derived using many of the results for the case k = 1. Results of Monte Carlo studies indicate agreement between the asymptotic theory and the actual behavior of the procedures and throw light on rates of ε(d) → 0 not covered by the theory.