1. Characterizations of continuous log-symmetric distributions based on properties of order statistics.
- Author
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Ahmadi, Jafar and Balakrishnan, N.
- Subjects
- *
DISTRIBUTION (Probability theory) , *ORDER statistics , *LOGNORMAL distribution , *CONTINUOUS distributions , *GOODNESS-of-fit tests , *T-test (Statistics) - Abstract
The class of log-symmetric distributions is a generalization of log-normal distribution and includes some well-known distributions such as log-normal, log-logistic, log-Laplace, log-Cauchy, log-power-exponential, log-student-t, log-slash, and Birnbaum-Saunders distributions. In this paper, several characterization results are obtained for log-symmetric distributions based on moments of some functions of the parent distribution and also on the basis of some properties of order statistics. Specifically, when X is identical in distribution with a decreasing continuous function $ h(X) $ h (X) , then a relationship is established between upper and lower order statistics which is then utilized to construct characterization results for log-symmetric distributions in terms of functions of order statistics. The established results can be used for constructing a goodness-of-fit test for log-symmetric distributions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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