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Testing whether survival function is harmonic new better than used in expectation. (English) Zbl 0608.62123

The concept of HNBUE (harmonic new better than used in expectation) is defined as follows: \(\int^{+\infty}_{t}\bar F(x)dx<\mu \exp \{-t/\mu \}\) for every \(t>0\), where \(\bar F=1-F\), \(\mu =\int^{+\infty}_{0}\bar F(x)dx<\infty\). This concept extends the concept of NBUE distributions.
The authors obtain two test statistics \(A_ n\) and \(B_ n\) (n being the sample size) for testing \(H_ 0: F(x)\) exponential versus \(H_ 1: F(x)\) HNBUE (and not exponential). These statistics are based on the empirical scaled total time on test (TTT). Under the null hypothesis the exact distributions of \(A_ n\) and \(B_ n\) \((n=2,3,...)\) are obtained.
Furthermore, the asymptotic distributions for \(A_ n\) and \(B_ n\) are obtained and some statistical properties of \(B_ n\) are shown.
Reviewer: F.Spizzichino

MSC:

62N05 Reliability and life testing
62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62E15 Exact distribution theory in statistics
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