On the asymptotic approximation of inverse moment for non negative random variables

2014 ◽  
Vol 46 (16) ◽  
pp. 7787-7797 ◽  
Author(s):  
Wenzhi Yang ◽  
Shuhe Hu ◽  
Xuejun Wang
2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Aiting Shen

Wu et al. (2009) studied the asymptotic approximation of inverse moments for nonnegative independent random variables. Shen et al. (2011) extended the result of Wu et al. (2009) to the case of -mixing random variables. In the paper, we will further study the asymptotic approximation of inverse moments for nonnegative -mixing random variables, which improves the corresponding results of Wu et al. (2009), Wang et al. (2010), and Shen et al. (2011) under the case of identical distribution.


2014 ◽  
Vol 43 (8) ◽  
pp. 1750-1757 ◽  
Author(s):  
Shuhe Hu ◽  
Xinghui Wang ◽  
Wenzhi Yang ◽  
Xuejun Wang

2009 ◽  
Vol 79 (11) ◽  
pp. 1366-1371 ◽  
Author(s):  
Tiee-Jian Wu ◽  
Xiaoping Shi ◽  
Baiqi Miao

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.


1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.


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