On the calculation and shaping of staircase random variables

Crespo, Luis Bermello; Giesy, Daniel P.; Kenny, Sean P.

doi:10.1201/9781315210469-331

Cited by 1 publication

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“…These features, which are caused by changes in the width of the bins that result from changing Ω, disappear when a fixed number of bins per unit of length, ρ, is used, i.e., n b = ρ(z − z) . Means for seeking a staircase variable that closely approximates a staircase infeasible h are available in [20].…”

Section: Staircase Feasibilitymentioning

confidence: 99%

“…For instance, μ − 1.96 ṁ 2 /N ≤ μ(l) ≤ μ + 1.96 ṁ 2 /N for a 95% confidence interval. Note that the box of moments defined by ( 17)- (20) might not be fully contained in Θ.…”

Section: Staircase Estimationmentioning

confidence: 99%

“…Hence, the effects of sampling error are accounted for by solving for a staircase subject to the inequality constraints ( 14) and ( 17)- (20). Note however that the resulting variable will not account for the manner in which the sampling distribution allocates probability within the chosen box of moments.…”

Section: Staircase Estimationmentioning

confidence: 99%

“…Next we calculate a maximal-entropy SPM whose moment functions are free to take on any value within these interval functions. Hence, each staircase variable comprising the SPM will maximize the entropy while satisfying the spread constraint ( 14), along with the box-ofmoments constraints (17)(18)(19)(20). We will refer to this predictor as a moment-bounded SPM.…”

Section: Examplesmentioning

confidence: 99%

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Random variables with moment-matching staircase density functions

Crespo

Kenny

Giesy

et al. 2018

Applied Mathematical Modelling

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This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal loglikelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

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Section: Staircase Feasibilitymentioning

confidence: 99%

“…For instance, μ − 1.96 ṁ 2 /N ≤ μ(l) ≤ μ + 1.96 ṁ 2 /N for a 95% confidence interval. Note that the box of moments defined by ( 17)- (20) might not be fully contained in Θ.…”

Section: Staircase Estimationmentioning

confidence: 99%

Section: Staircase Estimationmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

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