Discordancy tests for two-parameter exponential samples

Lin, Chien‐Tai; Wang, Shih-Chun

doi:10.1007/s00362-014-0597-3

Cited by 7 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…exponential random variables with arbitrary real coefficients and can be expressed in the form of Pr (AZ > 0) where A is any matrix of real values. For example, the tests listed in Barnett and Lewis (1994), Kimber and Stevens (1981), Kimber (1982), Balasooriya and Gadag (1994), Zerbet and Nikulin (2003), Lalitha and Kumar (2012), Lin and Wang (2015), Kumar (2015) and others. Moreover, a basic computer program can be made with an advantage that only a small modification would be required for obtaining the distribution of any test of discordancy for the exponential samples.…”

Section: Discussionmentioning

confidence: 99%

“…This recursion is an immediate consequence of the more general recursion given in Huffer (1988). Details on examples of the recursion and its applications can be found in Huffer andLin (2001), (2006), and Lin and Wang (2015) and the references contained therein.…”

Section: Exact Distribution Of Mlr Test For Exponential Samples: Single-outlier Problemmentioning

confidence: 93%

“…These probabilities can be calculated by using the recursion of Huffer and Lin (2001) as previously discussed. For more details, readers are referred to Lin and Balakrishnan (2009) and Lin and Wang (2015). Once we have the probabilities of the type Pr…”

Section: Sequential Proceduresmentioning

confidence: 99%

“…The tests of discordancy are widely used in the literature for testing outliers in univariate and multivariate samples (Barnett and Lewis 1994;Hadi 1994;Balasooriya and Gadag 1994;Kumar 2013;Fieller 2014). Due to the important role of exponential distribution in the areas of life-testing and reliability (Johnson et al 1994;Meeker and Escobar 1998), many discordancy tests have been investigated in literature for testing single and multiple outliers in the exponential samples (Kabe 1970;Lewis and Fieller 1979;Kimber 1982Kimber , 1988Lin and Wang 2015;Kumar 2015;Kumar and Lin 2017). However, the focus of most of the studies have been on the derivation of the null distribution of the test statistics and to present their critical values for commonly used significance levels (Dumitrescu et al 1994;Zhang 1998; Lin and Balakrishnan 2009).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Exact distributions of tests of outliers for exponential samples

Kumar

2017

Stat Papers

View full text Add to dashboard Cite

In this paper, we propose an algorithm to derive the exact distributions of discordancy tests for exponential samples under the slippage alternative providing that their survival functions involve the linear combinations of independent and identically distributed exponential random variables with arbitrary real coefficients. In addition, we define the various performance measures in terms of conditional probabilities that the observed value of the test statistic exceeds the critical value given that the contaminants have the specific position numbers in the ordered sample. These make possible to calculate various performance measures of discordancy tests for the exponential samples to any desired degree of accuracy. For the purpose of illustration, we derive the distributions of the maximum likelihood ratio tests for testing single and multiple outliers in the exponential samples and then we calculate their performance measures accurately to six decimal places. Moreover, the definitions of the performance criteria are not restricted to the discordancy tests for exponential samples only, they are also equally applicable to the discordancy tests for samples from other distributions. KeywordsExponential distribution • Slippage alternative • Contaminants • Performance measures • Tests of discordancy • Spurious and non-spurious power B Nirpeksh Kumar

show abstract