Statistical Inference for Bounds of Random Variables

1979 ◽  
Author(s):  
Peter Cooke
Keyword(s):  
Statistical Inference ◽  
Random Variables

scholarly journals Ratio of two random variables

2006 ◽  
Vol 3 (1) ◽  
Author(s):  
Anton Cedilnik ◽  
Katarina Košmelj ◽  
Andrej Blejec
Keyword(s):  
Probability Theory ◽  
Statistical Inference ◽  
Additional Assumption ◽  
Existence Theorems ◽  
Random Variables ◽  
Specific Behaviour ◽  
Standard Probability

To enable correct statistical inference, the knowledge about the existence of moments is crucial. The objective of this paper is to study the existence of the moments for the ratio \(Z = X/Y\) , where \(X\) and \(Y\) are arbitrary random variables with the additional assumption \(P(Y = 0) = 0\). We present three existence theorems showing that specific behaviour of the distribution of \(Y\) in the neighbourhood of zero is essential. Simple consequences of these theorems give evidence to the existence of the moments for particular random variables; some of these results are well known from standard probability theory. However, we obtain them in a simple way.

Statistical inference for bounds of random variables

Biometrika ◽  
1979 ◽  
Vol 66 (2) ◽  
pp. 367-374 ◽  
Author(s):  
PETER COOKE
Keyword(s):  
Statistical Inference ◽  
Random Variables

scholarly journals Mutiny on the Boundary: Methods for Bounded Quantitative Variables

2019 ◽  
Author(s):  
Michael Smithson ◽  
Yiyun Shou
Keyword(s):  
Statistical Inference ◽  
Random Variables ◽  
Psychological Research ◽  
Research Assessment ◽  
Bounded Variables ◽  
Assessment And Testing ◽  
Boundary Methods

Many quantitative variables in psychological research, assessment, and testing have bounds, but boundedness often is ignored by researchers. Ignoring bounds can result in miss-estimation, miss-specified models, and improper statistical inference. This tutorial introduces concepts and models for analyzing quantitative random variables that have one or more bounds. These variables fall into two groups: Those where the bounds are “absolute”, and “limited” variables whose bounds are “censored” or “truncated”. This tutorial explains which techniques are suited to dealing with specific types of bounded variables and how to deal with boundary cases, and provides a guide to resources for using these techniques effectively.

Statistical Inference for the Bounds of Random Variables

1991 ◽  
pp. 239-283
Author(s):  
Anatoly A. Zhigljavsky ◽  
J. Pintér
Keyword(s):  
Statistical Inference ◽  
Random Variables

Exchangeability, Representation Theorems, and Subjectivity

2011 ◽  
pp. 39-57 ◽  
Author(s):  
Dale J. Poirier
Keyword(s):  
Statistical Inference ◽  
Joint Distribution ◽  
Likelihood Function ◽  
Random Variables ◽  
Parametric Models ◽  
Bayesian Econometrics ◽  
Representation Theorems ◽  
Bernoulli Random Variables ◽  
Observable Data

This article is concerned with the foundation of statistical inference in the representation theorems. It shows how different assumptions about the joint distribution of the observable data lead to different parametric models defined by prior and likelihood function. Parametric models arise as an implication of the assumptions about observables. The article presents many extensions and offers description of the subjectivist attitude that underlies much of Bayesian econometrics. This subjectivist interpretation is close to probability. This article discusses exchangeability as the foundation for Bayesian econometrics. It serves as the basis for further extensions to incorporate heterogeneity and dependency across observations. It also discusses representation theorems involving random variables more complicated than Bernoulli random variables. They are not true properties of reality but are useful for making inferences regarding future observables.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

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.

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