scispace - formally typeset
Search or ask a question
Topic

Cumulative distribution function

About: Cumulative distribution function is a research topic. Over the lifetime, 6049 publications have been published within this topic receiving 145696 citations. The topic is also known as: CDF & distribution function.


Papers
More filters
ReportDOI
01 Nov 2002
TL;DR: The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol’ variance decomposition, and fast probability integration.
Abstract: The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol’ variance decomposition, and fast probability integration. Desirable features of Monte Carlo analysis in conjunction with Latin hypercube sampling are described in discussions of the following topics: (i) properties of random, stratified and Latin hypercube sampling, (ii) comparisons of random and Latin hypercube sampling, (iii) operations involving Latin hypercube sampling (i.e. correlation control, reweighting of samples to incorporate changed distributions, replicated sampling to test reproducibility of results), (iv) uncertainty analysis (i.e. cumulative distribution functions, complementary cumulative distribution functions, box plots), (v) sensitivity analysis (i.e. scatterplots, regression analysis, correlation analysis, rank transformations, searches for nonrandom patterns), and (vi) analyses involving stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty. Published by Elsevier Science Ltd.

644 citations

Journal ArticleDOI
TL;DR: In this article, the authors introduced a class of distortion operators, ga(t) = D[44-(u + a), where D is the standard normal cumulative distribution for any loss (or asset) variable X with a probability distribution Sx(x) = 1Fx (x), and ga [Sx(X)] defines a distorted probability distribution whose mean value yields a risk-adjusted premium (or an asset price) The distortion operator ga can be applied to both assets and liabilities, with opposite signs in the parameter a based on CAPM, the author establishes
Abstract: This article introduces a class of distortion operators, ga(t) = D[44-(u) + a], where D is the standard normal cumulative distribution For any loss (or asset) variable X with a probability distribution Sx(x) = 1Fx(x), ga [Sx(x)] defines a distorted probability distribution whose mean value yields a risk-adjusted premium (or an asset price) The distortion operator ga can be applied to both assets and liabilities, with opposite signs in the parameter a Based on CAPM, the author establishes that the parameter ca should correspond to the systematic risk of X For a normal (L,aU2) distribution, the distorted distribution is also normal with '= u + aa and a5' = a For a lognormal distribution, the distorted dis

618 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is (possibly) nonrandomized, but there is a binary-instrument available for the researcher.
Abstract: This article considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is (possibly) nonrandomized, but there is a binaryinstrument available for the researcher. Such a scenario is common in observational studies and in randomized experiments with imperfect compliance. One possible approach to this problem is to compare the counterfactual cumulative distribution functions of the outcome with and without the treatment. This article shows how to estimate these distributions using instrumental variable methods and a simple bootstrap procedure is proposed to test distributional hypotheses, such as equality of distributions, first-order and second-order stochastic dominance. These tests and estimators are applied to the study of the effects of veteran status on the distribution of civilian earnings. The results show a negative effect of military service during the Vietnam era that appears to be concentrated on the lower tail of ...

614 citations

Posted Content
TL;DR: The third-degree stochastic dominance condition was introduced in this article, where the authors show that the set of probability distributions that can be ordered by means of second-degree Stieltjes dominance is, in general, larger than that which can be order by first-degree SDE.
Abstract: Here F(x) and G(x) are less-than cumulative probability distributionis where x is a continuous or discrete random variable representing the outcome of a prospect. The closed interval [a, b] is the sample space of both prospects. The integral shown in Rule 2 and those shown throughout the paper are Stieltjes integrals. Recall that the Stieltjes integral fb f(x)dg(x) exists if one of the functions f and g is continuous and the other has finite variation in [a, b]. Let D1, D2, and D3 be three sets of utility functions ?(x). D1 is the set containing all utility functions with 4(x) and +1(x) continuous, and 41(x) >0 for all xE[a, b]. D2 is the set with ?(x), ?1(x), ?2(x) continuous, and q$j(x)>0, 02(x)?O for all xC[a, b]. D3 is the set with ?(x), ?1(x), ?2(X), ?3(X) continuous, and +1(x) > 04 2(x) O O for all xC[a, b]. Here +1(x) denotes the ith derivative of +(x). Hadar and Russell proved that Rule 1 is valid for all ,CD1 and Rutle 2 is valid for all ED2. The authors point out that the set of probability distributions that can be ordered by means of second-degree stochastic dominance is, in general, larger than that which can be ordered by means of first-degree stochastic dominance. Note that in Rule 2, they assume that +(x) is not only an increasing function of x but also exhibits weak global risk aversion, a condition guaranteed by requiring the second derivative of ?(x) to be nonpositive. In this paper, a condition which will be called third-degree stochastic dominance is considered. It is based on the following assumption about the form of the utility function ?(x). From a normative point of view, one expects the risk premium associated with an uncertain prospect to become smaller the greater is the individual's wealth. The plausibility and implications of this assumption h'ave been explored by John Pratt, as well as others. The risk premium of an uncertain prospect is that amount by which the certainty equivalent of the prospect differs from its expected value. In mathematical terms, given the prospect F(x) with expected value A, the corresponding risk premium -t is obtained by solving the following equation. rb

537 citations

Journal ArticleDOI
TL;DR: In this article, the problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments was studied.
Abstract: Several authors have constructed nonparametric Bayes estimators for a cumulative distribution function based on (possibly right-censored) data. The prior distributions have, for example, been Dirichlet processes or, more generally, processes neutral to the right. The present article studies the related problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments. A particular class of prior processes, termed beta processes, is introduced and is shown to constitute a conjugate class. To arrive at these, a nonparametric time-discrete framework for survival data, which has some independent interest, is studied first. An important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated, for example, time-inhomogeneous Markov chains. We find posterior distributions and derive Bayes estimators in such models and also present a semiparametric Bayesian analysis of the Cox regression model. The Bayes estimators are easy to interpret and easy to compute. In the limiting case of a vague prior the Bayes solution for a cumulative hazard is the Nelson-Aalen estimator and the Bayes solution for a survival probability is the Kaplan-Meier estimator.

515 citations


Network Information
Related Topics (5)
Estimator
97.3K papers, 2.6M citations
84% related
Optimization problem
96.4K papers, 2.1M citations
79% related
Cluster analysis
146.5K papers, 2.9M citations
77% related
Matrix (mathematics)
105.5K papers, 1.9M citations
77% related
Node (networking)
158.3K papers, 1.7M citations
77% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023135
2022330
2021280
2020353
2019272
2018344