A new discrete distribution arising in a model of DNA replication

During DNA replication, small fragments of DNA are formed. These have been observed experimentally and the mechanism of their formation modelled mathematically. Using the stochastic model of Cowan and Chiu (1992), (1994), we find the probability distribution of the number of fragments. A new discrete distribution arises. The work has interest as an application of the recent theory on quasirenewal equations in Piau (2000).

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Risk Planning with Discrete Distribution Analysis Applied to Petroleum Spills

International Journal of Risk and Contingency Management ◽

10.4018/ijrcm.2013100105 ◽

2013 ◽

Vol 2 (4) ◽

pp. 61-78 ◽

Cited By ~ 9

Author(s):

Roy L. Nersesian ◽

Kenneth David Strang

Keyword(s):

Probability Distribution ◽

Probability Distributions ◽

Low Cost ◽

Discrete Distribution ◽

Distribution Model ◽

Distribution Analysis ◽

Distribution Models ◽

Discrete Probability ◽

Nonparametric Statistical ◽

Spreadsheet Software

This study discussed the theoretical literature related to developing and probability distributions for estimating uncertainty. A theoretically selected ten-year empirical sample was collected and evaluated for the Albany NY area (N=942). A discrete probability distribution model was developed and applied for part of the sample, to illustrate the likelihood of petroleum spills by industry and day of week. The benefit of this paper for the community of practice was to demonstrate how to select, develop, test and apply a probability distribution to analyze the patterns in disaster events, using inferential parametric and nonparametric statistical techniques. The method, not the model, was intended to be generalized to other researchers and populations. An interesting side benefit from this study was that it revealed significant findings about where and when most of the human-attributed petroleum leaks had occurred in the Albany NY area over the last ten years (ending in 2013). The researchers demonstrated how to develop and apply distribution models in low cost spreadsheet software (Excel).

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Fatigue of Metals as Stochastic Phenomena

Journal of Engineering Materials and Technology ◽

10.1115/1.3443399 ◽

1977 ◽

Vol 99 (1) ◽

pp. 26-28 ◽

Cited By ~ 3

Author(s):

C. Ihara ◽

A. Tsurui

Keyword(s):

Crack Initiation ◽

Stochastic Model ◽

Endurance Limit ◽

Recent Theory ◽

Mean Values ◽

Repeated Stress ◽

Coefficients Of Variation ◽

Cumulative Process ◽

The Mean ◽

Stochastic Phenomena

A stochastic model for the fatigue of metals under repeated stress or strain is proposed. Fatigue lives up to crack initiation are investigated with the aid of a recent theory on a cumulative process and the mean values are plotted versus stress amplitudes. Of interest is the fact that this curve behaves as if the endurance limit existed when the parameters are adequately taken. Except the neighborhood of the endurance limit, the coefficients of variation are also calculated approximately.

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Operational Risk Evaluation of an Ice Feature Impact

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2919842 ◽

1990 ◽

Vol 112 (1) ◽

pp. 96-101

Author(s):

A. B. Dunwoody

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Probability Distribution ◽

Stochastic Model ◽

Risk Evaluation ◽

Joint Probability ◽

Joint Probability Distribution ◽

Offshore Structure ◽

Simple Stochastic Model ◽

General Method

The risk of impact by a particular ice feature in the vicinity of an offshore structure or stationary vessel is of concern during operations. A general method is presented for calculating the risk of an impact in terms of the joint probability distribution of the forecast positions and velocities of the ice feature. A simple stochastic model of the motion of an ice feature is introduced for which the joint probability distribution of ice feature position and velocity can be determined as a function of time. The risk of an impact is presented for this model of the motion of an ice feature. Predictions of the distributions of the time until impact and the drift speed upon impact are also presented and discussed. Predictions are compared against results of a Monte Carlo simulation.

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A stochastic model for predicting the probability distribution of the dissolved-oxygen deficit in streams

Professional Paper ◽

10.3133/pp913 ◽

1976 ◽

Cited By ~ 11

Author(s):

I.I. Esen ◽

R.E. Rathbun

Keyword(s):

Probability Distribution ◽

Stochastic Model ◽

Dissolved Oxygen ◽

Oxygen Deficit

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Equilibrium analysis of a stochastic model of traffic flow

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100037695 ◽

1964 ◽

Vol 60 (2) ◽

pp. 227-236 ◽

Cited By ~ 7

Author(s):

W. J. Gordon ◽

G. F. Newell

Keyword(s):

Stochastic Model ◽

Present Model ◽

Discrete Distribution ◽

Equilibrium Analysis ◽

Linear Integral Equation ◽

Main Body ◽

Highway Traffic ◽

Equilibrium Equations ◽

Asymptotic Results ◽

Linear Integral

AbstractA. J. Miller has proposed a stochastic model for the study of highway traffic in one direction along a two-lane road in which the desired speed of a vehicle is sampled from a continuous probability distribution and queues of vehicles are Poisson distributed on the highway. Miller has derived the equilibrium expression for the relation between the spacial densities of all vehicles and the spacial densities of those which are freely travelling. This relationship takes the form of a non-linear integral equation which is left unsolved. The present model differs from the original only in the assumption of a discrete distribution of desired speeds. Although the derivations of the equilibrium equations are based upon different arguments from those of Miller, these relations transform to the corresponding integral equations in the limit of a continuous speed distribution. The main body of the paper is devoted to a detailed investigation of the case of two speeds and asymptotic results are obtained for three speeds.

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