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2 results on '"Maochao Xu"'

1. On the convolution of heterogeneous Bernoulli random variables

Author

Narayanaswamy Balakrishnan and Maochao Xu

Subjects
Statistics and Probability, Mathematical optimization, 62G30, General Mathematics, 01 natural sciences, Convolution, Bernoulli's principle, 010104 statistics & probability, 62N05, 0502 economics and business, Applied mathematics, Order (group theory), 62D05, 0101 mathematics, Majorization, likelihood ratio order, Mathematics, 050205 econometrics, 010102 general mathematics, 05 social sciences, Bernoulli, reversed hazard rate order, heterogeneous variable, majorization, Bernoulli process, Statistics, Probability and Uncertainty, 60E15, Random variable
Abstract

In this paper, some ordering properties of convolutions of heterogeneous Bernoulli random variables are discussed. It is shown that, under some suitable conditions, the likelihood ratio order and the reversed hazard rate order hold between convolutions of two heterogeneous Bernoulli sequences. The results established here extend and strengthen the previous results of Pledger and Proschan (1971) and Boland, Singh and Cukic (2002).

Published
2011

2. On the skewness of order statistics in multiple-outlier models

Author

Subhash C. Kochar and Maochao Xu

Subjects
Independent and identically distributed random variables, Statistics and Probability, proportional hazard rate, 62G30, Exponential distribution, decreasing failure rate, Open problem, General Mathematics, skewness, k-out-of-n system, star order, 01 natural sciences, 010104 statistics & probability, 62N05, Probability theory, Statistics, Applied mathematics, exponential distribution, 62D05, 0101 mathematics, Mathematics, right spread order, Order statistic, 010102 general mathematics, Exponential function, Skewness, Outlier, Dispersive order, Statistics, Probability and Uncertainty, 60E15
Abstract

Kochar and Xu (2009) proved that a parallel system with heterogeneous exponential component lifetimes is more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. In this paper we extend this study to the general k-out-of-n systems for the case when there are only two types of component in the system. An open problem proposed in Pǎltǎnea (2008) is partially solved.

Published
2011

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