Sum of the $N-K$ largest out of $N$ normal random variables with different variables
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Given $N$ independent normal random variables, $X_1,X_2,ldots,X_N$, the ordered sequence is denoted as $X_{(1)}, X_{(2)}, ldots,X_{(N)}$ where $X_{(1)}ge X_{(2)}ge cdotsge X_{(N)}$.
Let $X_isim N(mu_i,sigma^2_i)$, if $sigma_i=sigma_j$ for all $ineq j$, then we can have the exact distribution of $sum_{i=1}^{N-K}X_{(i)}$ as mentioned in following paper "On the exact distribution of the sum of the largest n − k out of n normal random variables with differing mean values".
I would like to know if there is any result for identical means and different variances, i.e., Suppose $mu_i=mu_j$ for all $ineq j$ and $sigma_1gesigma_2gecdotsgesigma_N$, what is the distribution of $sum_{i=1}^{N-K}X_{(i)}$?
probability probability-distributions
asked Nov 21 at 5:38
Wu Ting-Yi
184
add a comment |
up vote
0
down vote
favorite
Given $N$ independent normal random variables, $X_1,X_2,ldots,X_N$, the ordered sequence is denoted as $X_{(1)}, X_{(2)}, ldots,X_{(N)}$ where $X_{(1)}ge X_{(2)}ge cdotsge X_{(N)}$.
Let $X_isim N(mu_i,sigma^2_i)$, if $sigma_i=sigma_j$ for all $ineq j$, then we can have the exact distribution of $sum_{i=1}^{N-K}X_{(i)}$ as mentioned in following paper "On the exact distribution of the sum of the largest n − k out of n normal random variables with differing mean values".
I would like to know if there is any result for identical means and different variances, i.e., Suppose $mu_i=mu_j$ for all $ineq j$ and $sigma_1gesigma_2gecdotsgesigma_N$, what is the distribution of $sum_{i=1}^{N-K}X_{(i)}$?
probability probability-distributions
asked Nov 21 at 5:38
Wu Ting-Yi
184
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given $N$ independent normal random variables, $X_1,X_2,ldots,X_N$, the ordered sequence is denoted as $X_{(1)}, X_{(2)}, ldots,X_{(N)}$ where $X_{(1)}ge X_{(2)}ge cdotsge X_{(N)}$.
Let $X_isim N(mu_i,sigma^2_i)$, if $sigma_i=sigma_j$ for all $ineq j$, then we can have the exact distribution of $sum_{i=1}^{N-K}X_{(i)}$ as mentioned in following paper "On the exact distribution of the sum of the largest n − k out of n normal random variables with differing mean values".
I would like to know if there is any result for identical means and different variances, i.e., Suppose $mu_i=mu_j$ for all $ineq j$ and $sigma_1gesigma_2gecdotsgesigma_N$, what is the distribution of $sum_{i=1}^{N-K}X_{(i)}$?
probability probability-distributions
asked Nov 21 at 5:38
Wu Ting-Yi
184
Given $N$ independent normal random variables, $X_1,X_2,ldots,X_N$, the ordered sequence is denoted as $X_{(1)}, X_{(2)}, ldots,X_{(N)}$ where $X_{(1)}ge X_{(2)}ge cdotsge X_{(N)}$.
Let $X_isim N(mu_i,sigma^2_i)$, if $sigma_i=sigma_j$ for all $ineq j$, then we can have the exact distribution of $sum_{i=1}^{N-K}X_{(i)}$ as mentioned in following paper "On the exact distribution of the sum of the largest n − k out of n normal random variables with differing mean values".
I would like to know if there is any result for identical means and different variances, i.e., Suppose $mu_i=mu_j$ for all $ineq j$ and $sigma_1gesigma_2gecdotsgesigma_N$, what is the distribution of $sum_{i=1}^{N-K}X_{(i)}$?
probability probability-distributions
probability probability-distributions
asked Nov 21 at 5:38
Wu Ting-Yi
184
asked Nov 21 at 5:38
Wu Ting-Yi
184
asked Nov 21 at 5:38
Wu Ting-Yi
184
asked Nov 21 at 5:38
Wu Ting-Yi
184
asked Nov 21 at 5:38
Wu Ting-Yi
184
184
add a comment |
add a comment |
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