Testing whether survival function is harmonic new better than used in expectation
type: Item
instance of: scholarly article
title: Testing whether survival function is harmonic new better than used in expectation
zbMATH Open document ID: 0608.62123
author: Nader Ebrahimi
author: Asit P. Basu
published in: Annals of the Institute of Statistical Mathematics
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 3984411
zbMATH Keywords: HNBUE
zbMATH Keywords: harmonic new better than used in expectation
zbMATH Keywords: empirical scaled total time on test
zbMATH Keywords: exact distributions
reviewed by: F. Spizzichino
MaRDI profile type: Publication
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cites work: Q4077379
cites work: Q4158362
cites work: Geometry of the total time on test transform
cites work: On k-order harmonic new better than used in expectation distributions
cites work: Q3658936
cites work: A simple test for new better than used in expectation
cites work: Q4151052
cites work: Tests for Monotone Failure Rate Based on Normalized Spacings
cites work: Q3347121
cites work: A class of tests for exponentiality against increasing failure rate average alternatives
cites work: Testing Whether New is Better than Used
cites work: Tests for the mean residual life
cites work: The hnbue and hnwue classes of life distributions
cites work: Some tests against aging based on the total time on test transform
cites work: A test for new better than used
cites work: Testing for new is better than used in expectation
cites work: Testing for New Better than Used in Expectation with Incomplete Data
cites work: A class of test statistics for testing whether new is better than used
cites work: Q4125587
cites work: Q5602041
cites work: Empirical Bayes estimation of a distribution (survival) function from right censored observations
description: scientific article; zbMATH DE number 3984411