Book ChapterDOI
Some Auxiliary Results — Monotonicity Properties of Probability Distributions
Shanti S. Gupta,Deng-Yuan Huang +1 more
- pp 1-28
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TLDR
In this paper, the authors studied the monotonicity properties of distributions in order to obtain inequalities useful in statistical inference, and showed that some of these properties are well known and have proved to be very useful.Abstract:
It is very important to study the monotonicity properties of distributions in order to obtain inequalities useful in statistical inference. Some monotonicity properties of distributions are well known and have proved to be very useful. During the last decade, more concepts have been introduced and used by several authors in multiple decision problems.read more
References
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Book
Testing statistical hypotheses
TL;DR: The general decision problem, the Probability Background, Uniformly Most Powerful Tests, Unbiasedness, Theory and First Applications, and UNbiasedness: Applications to Normal Distributions, Invariance, Linear Hypotheses as discussed by the authors.
Book ChapterDOI
Some Concepts of Dependence
TL;DR: In this article, the authors give three successively stronger definitions of positive dependence, and investigate their consequences, explore the strength of each definition through a number of examples, and give some statistical applications.
Journal ArticleDOI
Association of Random Variables, with Applications
TL;DR: In this paper, it was shown that a random variable can be associated with another random variable if the test functions are either (a) binary or (b) bounded and continuous.
Journal ArticleDOI
The one-sided barrier problem for Gaussian noise
TL;DR: In this paper, the authors considered the probability that a stationary Gaussian process with mean zero and covariance function r(τ) be nonnegative throughout a given interval of duration T. Several strict upper and lower bounds for P were given, along with some comparison theorems that relate P's for different covariance functions.