Topic
Probability mass function
About: Probability mass function is a research topic. Over the lifetime, 2853 publications have been published within this topic receiving 101710 citations. The topic is also known as: pmf.
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TL;DR: In this article, a comprehensive survey of the main alternative models and estimation methods suitable to deal with fractional response variables is presented, and a full testing methodology is proposed to assess the validity of the assumptions required by each alternative estimator.
Abstract: In many economic settings, the variable of interest is often a fraction or a proportion, being defined only on the unit interval. The bounded nature of such variables and, in some cases, the possibility of nontrivial probability mass accumulating at one or both boundaries raise some interesting estimation and inference issues. In this paper we: (i) provide a comprehensive survey of the main alternative models and estimation methods suitable to deal with fractional response variables; (ii) propose a full testing methodology to assess the validity of the assumptions required by each alternative estimator; and (iii) examine the finite sample properties of most of the estimators and tests discussed through an extensive Monte Carlo study. An application concerning corporate capital structure choices is also provided.
386 citations
TL;DR: The impact of “uncertain evidence” can be (formally) represented by Dempster conditioning, in Shafer's framework, in the framework of convex sets of classical probabilities by classical conditionalization.
378 citations
Book•
26 Mar 2004
TL;DR: This chapter discusses Random Variables, Linear Models and Linear Regression, and Statistical Inference, Parameter Estimation, and Model Verification, as well as some important Discrete Distributions.
Abstract: Preface1 IntroductionPart A: Probability and Random Variables2 Basic Probability Concepts3 Random Variables and Probability Distributions4 Expectations And Moments5 Functions of Random Variables6 Some Important Discrete Distributions7 Some Important Continuous DistributionsPart B: Statistical Inference, Parameter Estimation, and Model Verification8 Observed Data and Graphical Representation9 Parameter Estimation10 Model Verification11 Linear Models and Linear RegressionAppendix A: TablesAppendix B: Computer SoftwareAppendix C: Answers to Selected ProblemsSubject Index
370 citations
TL;DR: In this paper, second-order expansion is used to approximate the failure surface and some results of the statistical theory of quadratic forms in normal variates are used to calculate improved estimates of the failure probability.
Abstract: Second-moment methods are widely applied in structural reliability. Recently, so-called first-order reliability methods have been developed that are capable of producing reliable estimates of the failure probability for arbitrary design situations and distributional assumptions for the uncertainity vector. In essence, nonlinear functional relationships or probability distribution transformations are approximated by linear Taylor expansions so that the simple second-moment calculus is retained. Failure probabilities are obtained by evaluating the standard normal integral, which is the probability content of a circular normal distribution in a domain bounded by a hyperplane. In this paper second-order expansions are studied to approximate the failure surface and some results of the statistical theory of quadratic forms in normal variates are used to calculate improved estimates of the failure probability.
358 citations