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# Some Distributions Relevant in Life Testing When an Outlier May Be Present

S. K. Sinha
Sankhyā: The Indian Journal of Statistics, Series B (1960-2002)
Vol. 37, No. 1 (Feb., 1975), pp. 100-105
Stable URL: http://www.jstor.org/stable/25051938
Page Count: 6
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## Abstract

Kale and Sinha (1971) considered a situation in which the random variables $(X_{1},X_{2},\ldots ,X_{n})$ are such that (n-1) of them are independent and identically distributed as $f(x,\sigma)=\frac{1}{\sigma}{\rm exp}\left(-{\textstyle\frac{x}{\sigma}}\right)$, x > 0, σ > 0, and with probability ${\textstyle\frac{1}{n}}$ any one of them could be distributed as f(x, σ/α), 0 < α ≤ 1. In this paper distributions of $s^{\prime}=\underset 1\to{\overset n\to{\Sigma}}x_{i}$ and $s_{m}^{\prime}=\underset 1\to{\overset m\to{\Sigma}}x_{(i)}+(n-m)x_{(m)}$, m ≤ n, for Kale and Sinha's model have been obtained and their properties and applications for estimating the mean life and reliability function have been studied.

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