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Subset Selection of ε- Better Exponential Populations under Heteroscedasticity |
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PP: 377-384 |
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doi:10.18576/jsap/110201
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Author(s) |
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Anju Goyal,
A. N. Gill,
Vishal Maurya,
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Abstract |
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| Suppose we have $k( \geq 2)$independent processes/populations/sources/ treatments
such that the data from $i^{th}$ treatment follow two-parameter exponential distribution with location parameter $\mu_i$ and scale parameter $\theta_i$, denoted $E(\mu_i,\theta_i )$, $i=1,\dots, k$. The location parameters $\mu_1, \dots, \mu_k$ and scale parameters $\theta_1, \dots, \theta_k$ are unknown and possibly unequal. Let $\underline{\delta}=(\mu_1 , \dots ,\mu_k, \theta_1, \dots \theta_k ) \in R^k \times R_+^k =\Omega $ and $\mu_{[k]} =max_{1\leq i \leq k}\mu_{i}$. For a given $\epsilon_1>0$, we define a set of good populations as $G=\{i:\mu_i \geq \mu_{[k]}-\epsilon_1 \}$. In this paper two-stage and one-stage subset selection procedures have been proposed to select a subset, say $S$, of $k$ populations which contains $G$ with a pre-specified probability $ P^*$, i.e.,
$P_{\underline{\delta}}= (G\subseteq S|$under the proposed procedure)$ \geq P^* \forall \underline{\delta} \in \Omega)$.
The related simultaneous confidence intervals for $\mu_{[k]} -\mu_i, i=1,…,k $ and $\mu_{[j]} -\mu_{[i]}, i \neq j=1,…,k,$ have been derived. A subset selection procedure is also proposed which controls the probability of omitting a “good” treatment or selecting a “bad” treatment at $1-P^*$ by considering a set $B=\{i:\mu_i\leq \mu_{[k]}-\epsilon_2 \}$ of bad treatments, where $\epsilon_2>\epsilon_1$.The implementation of proposed procedure is demonstrated through a real life data. |
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