Topic
Probability density function
About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.
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01 Jan 1990
TL;DR: The probability function is derived axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.
Abstract: Summary We derive axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.
511 citations
TL;DR: In this paper, a nonparametric model of the generalized mass, damping and stiffness matrices is proposed, which does not require identifying the uncertain local parameters and obviates construction of functions that map the domains of uncertain local parameter vectors into the generalized matrix.
499 citations
01 Jan 2006
TL;DR: A new wavelet based approach is described to separate the trend from the fluctuations in a time series, and a deterministic (non-linear regression) model is constructed for the trend using genetic algorithm.
Abstract: Financial time series, in general, exhibit average behaviour at “long” time scales and stochastic behaviour at ‘short” time scales As in statistical physics, the two have to be modelled using different approaches — deterministic for trends and probabilistic for fluctuations about the trend In this talk, we will describe a new wavelet based approach to separate the trend from the fluctuations in a time series A deterministic (non-linear regression) model is then constructed for the trend using genetic algorithm We thereby obtain an explicit analytic model to describe dynamics of the trend Further the model is used to make predictions of the trend We also study statistical and scaling properties of the fluctuations The fluctuations have non-Gaussian probability distribution function and show multi-scaling behaviour Thus, our work results in a comprehensive model of trends and fluctuations of a financial time series
498 citations
TL;DR: The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function and can be considered as another useful 3-parameter generalization of the Weibull distribution.
Abstract: A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.
488 citations
TL;DR: In this paper, the authors define a variable V(t) the probability function of a quantity z, which may assume certain real values with certain probabilistic properties, and call V t the probability of z having exactly the value t.
Abstract: 1. By a variable in the sense of the Theory of Probability we mean a quantity z, which may assume certain real values with certain probahilities. We shall call V(t) the probability function of z if, for every real t, V(t) is equal to the probabiliby that z has a value < t, increased by half the probability that z has exactly the value t.
476 citations