Abstract
Letx i(1)≤x i(2)≤…≤x i(ri) be the right-censored samples of sizesn i from theith exponential distributions\(\sigma _i^{ - 1} exp\{ - (x - \mu _i )\sigma _i^{ - 1} \} ,i = 1,2\) where μi and σi are the unknown location and scale parameters respectively. This paper deals with the posteriori distribution of the difference between the two location parameters, namely μ2-μ1, which may be represented in the form\(\mu _2 - \mu _1 \mathop = \limits^\mathcal{D} x_{2(1)} - x_{1(1)} + F_1 \sin \theta - F_2 \cos \theta \) where\(\mathop = \limits^\mathcal{D} \) stands for equal in distribution,F i stands for the central F-variable with [2,2(r i−1)] degrees of freedom and\(\tan \theta = \frac{{n_2 s_{x1} }}{{n_1 s_{x2} }}, s_{x1} = (r_1 - 1)^{ - 1} \left\{ {\sum\limits_{j = 1}^{r_i - 1} {(n_i - j)(x_{i(j + 1)} - x_{i(j)} )} } \right\}\)
The paper also derives the distribution of the statisticV=F 1 sin σ−F 2 cos σ and tables of critical values of theV-statistic are provided for the 5% level of significance and selected degrees of freedom.
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Research was supported by NSERC (Canada) under grant 8398-01.
Research supported by NSERC grant# A3088.
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Nassrallah, B., Ehsanes Saleh, A.K.M. Comparison of location parameters of two exponential distributions when scale parameters are different and unknown. Statistical Papers 35, 57–69 (1994). https://doi.org/10.1007/BF02926400
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DOI: https://doi.org/10.1007/BF02926400