Random Number Generation from Right‐Skewed, Symmetric, and Left‐Skewed Distributions

Voit, Eberhard O.; Schwacke, Lorelei H.

doi:10.1111/0272-4332.00006

Cited by 11 publications

(5 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When combined with the rescale survival-constraint method, it produced results indistinguishable from those derived with the beta distribution or matrix selection. Other distributions that have received little attention but that stochastic matrix modelers should explore include the S distribution, which is based on differential equations and is well suited to probabilities (Voit and Schwake 2000), and the beta binomial, which is appropriate for distributions based on probabilities derived from counts (Griffiths 1973, Tamura and Young 1987, Kahn and Raftery 1996. The beta binomial may be especially useful and appropriate for stochastic matrix models because it can separate demographic variability from estimates of environmental stochasticity (Kendall 1998).…”

Section: Effects Of Stochastic Methods and Survival Constraintsmentioning

confidence: 99%

The Effect of Stochastic Technique on Estimates of Population Viability From Transition Matrix Models

Kaye

Pyke

2003

Ecology

View full text Add to dashboard Cite

Population viability analysis is an important tool for conservation biologists, and matrix models that incorporate stochasticity are commonly used for this purpose. However, stochastic simulations may require assumptions about the distribution of matrix parameters, and modelers often select a statistical distribution that seems reasonable without sufficient data to test its fit. We used data from long‐term (5–10 year) studies with 27 populations of five perennial plant species to compare seven methods of incorporating environmental stochasticity. We estimated stochastic population growth rate (a measure of viability) using a matrix‐selection method, in which whole observed matrices were selected at random at each time step of the model. In addition, we drew matrix elements (transition probabilities) at random using various statistical distributions: beta, truncated‐gamma, truncated‐normal, triangular, uniform, or discontinuous/observed. Recruitment rates were held constant at their observed mean values. Two methods of constraining stage‐specific survival to ≤100% were also compared. Different methods of incorporating stochasticity and constraining matrix column sums interacted in their effects and resulted in different estimates of stochastic growth rate (differing by up to 16%). Modelers should be aware that when constraining stage‐specific survival to 100%, different methods may introduce different levels of bias in transition element means, and when this happens, different distributions for generating random transition elements may result in different viability estimates. There was no species effect on the results and the growth rates derived from all methods were highly correlated with one another. We conclude that the absolute value of population viability estimates is sensitive to model assumptions, but the relative ranking of populations (and management treatments) is robust. Furthermore, these results are applicable to a range of perennial plants and possibly other life histories. Corresponding Editor: A. R. Solow.

show abstract

Section: Effects Of Stochastic Methods and Survival Constraintsmentioning

confidence: 99%

The Effect of Stochastic Technique on Estimates of Population Viability From Transition Matrix Models

Kaye

Pyke

2003

Ecology

View full text Add to dashboard Cite

show abstract

“…The probability of a risk occurring is often described by a random number simulation [41]. Randomness determines the uncertainty, the unpredictability, in the process of generation [42].…”

Section: Combined Risk Impact Ratementioning

confidence: 99%

Buffer Sizing in Critical Chain Project Management by Brittle Risk Entropy

Peng

2022

Buildings

View full text Add to dashboard Cite

In order to solve the problems such as project duration delay caused by unreasonable buffer zone setting, a critical chain buffer zone setting method is proposed based on fragility theory. Firstly, we propose that the construction process is brittle and the brittleness of the construction process was analyzed. Secondly, this paper introduces a risk-integrated impact rate to describe the uncertainty of the construction process and establishes a brittle risk entropy function. Then, it presents entropy models and modification models of project buffers and feeding buffers based on the original Root Square Error Method. Finally, an engineering project was selected as an example, and the simulation was carried out using the Monte Carlo simulation software Crystal Ball, and the resulting method was compared with three buffer zone calculation methods. The results show that the method can effectively reduce the construction period and is effective and practical when compared to the other three buffer calculation methods. The results of the study provide a new way of thinking about buffer settings based on existing critical chain project management methods.

show abstract

“…Indeed, the two kinetic orders were used as a shape classi�cation system for continuous as well as discrete distribution functions [731][732][733]. e same distribution was subsequently used in survival analysis and risk assessment [28,625,[734][735][736][737][738], and as a tool for random number generation and quantile analysis [739,740], as well as for inference [741,742]. e efficiency and �exibility of random number generation permitted the use of S-distributions for traditional and hierarchical Monte-Carlo simulations [424,743,744].…”

Section: Recastingmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

Self Cite

149

154

View full text Add to dashboard Cite

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. is paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. e paper is intended as a guide for investigators entering the fascinating �eld of biological systems analysis and as a resource for practitioners and experts. PreambleBiochemical systems theory (BST) is a mathematical and computational framework for analyzing and simulating systems. It was originally developed for biochemical pathways but by now has become much more widely applied to systems throughout biology and beyond. BST is called "canonical, " which means that model construction, diagnosis, and analysis follow stringent rules, which will be discussed throughout this paper. e key ingredient of BST is the power-law representation of all processes in a system.BST has been the focus of a number of books [1-6], including some in Chinese and Japanese [7][8][9]. e most detailed modern text dedicated speci�cally to BST is [3]. Moreover, since its inception, numerous reviews have portrayed the evolving state of the art in BST. Most of these reviews summarized methodological advances for the analysis of biochemical pathway systems . Others compared BST models with alternative modeling frameworks [32,[51][52][53][54][55][56][57][58][59][60][61][62][63]; some of these comparisons will be discussed later. Yet other reviews focused on specialty areas, such as customized methods for optimizing BST models (e.g., [64][65][66][67]) or estimating their parameters (e.g., [68][69][70][71][72]), strategies for discovering design and operating principles in natural system (e.g., [73][74][75][76][77][78]), and even the use of BST models in statistics [79][80][81]. A historical account of the �rst twenty years of BST was presented in [82].Supporting the methodological developments in the �eld, several soware packages were developed for different aspects of BST analysis. e earliest was ESSYNS [83][84][85], which supported all standard steady-state analyses and also contained a numerical solver that, at the time, was many times faster than any off-the-shelf soware [86,87]; see also [88]. Utilizing advances in computing and an extension of the solver from ESSYNS, Ferreira created the very user-friendly package PLAS, which is openly available and still very widely used [89] (see also [3]). Yamada and colleagues developed soware to translate E-cell models into BST models in PLAS format [90]. Okamoto's group created the soware BestKit, which permits the graphical design and translation of models, along with their analysis [91][92][93]. Vera and colleagues developed the soware tool PLMaddon for analyzing BST models within SBML [94]; see also [95]. It expands the Matlab SBToolbox with speci�c functionalities for power-law repr...

show abstract

Random Number Generation from Right‐Skewed, Symmetric, and Left‐Skewed Distributions

Cited by 11 publications

References 23 publications

The Effect of Stochastic Technique on Estimates of Population Viability From Transition Matrix Models

The Effect of Stochastic Technique on Estimates of Population Viability From Transition Matrix Models

Buffer Sizing in Critical Chain Project Management by Brittle Risk Entropy

Biochemical Systems Theory: A Review

Contact Info

Product

Resources

About