Exponential Distribution and the Poisson Process

2013 ◽  
pp. 206-224
Author(s):  
Mor Harchol-Balter
Keyword(s):  
Poisson Process ◽  
Exponential Distribution

scholarly journals A filtered renewal process as a model for a river flow

2005 ◽  
Vol 2005 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Renewal Process ◽  
River Flow ◽  
Realistic Model ◽  
Delaware River ◽  
The Usa ◽  
The One ◽  
Peak Value

Various models, based on a filtered Poisson process, are used for the flow of a river. The aim is to forecast the next peak value of the flow, given that another peak was observed not too long ago. The most realistic model is the one when the time between the successive peaks doesnothave an exponential distribution, as is often assumed. An application to the Delaware River, in the USA, is presented.

scholarly journals Probability distributions of COVID-19 tweet posted trends use a nonhomogeneous Poisson process

2020 ◽  
Vol 1 (4) ◽  
pp. 229-238
Author(s):  
Devi Munandar ◽  
Sudradjat Supian ◽  
Subiyanto Subiyanto
Keyword(s):  
Social Media ◽  
Poisson Process ◽  
Exponential Distribution ◽  
Probability Distributions ◽  
Nonhomogeneous Poisson Process ◽  
Time Interval ◽  
Initial State ◽  
Time Intervals ◽  
Time Parameters ◽  
Parameter Values

The influence of social media in disseminating information, especially during the COVID-19 pandemic, can be observed with time interval, so that the probability of number of tweets discussed by netizens on social media can be observed. The nonhomogeneous Poisson process (NHPP) is a Poisson process dependent on time parameters and the exponential distribution having unequal parameter values and, independently of each other. The probability of no occurrence an event in the initial state is one and the probability of an event in initial state is zero. Using of non-homogeneous Poisson in this paper aims to predict and count the number of tweet posts with the keyword coronavirus, COVID-19 with set time intervals every day. Posting of tweets from one time each day to the next do not affect each other and the number of tweets is not the same. The dataset used in this study is crawling of COVID-19 tweets three times a day with duration of 20 minutes each crawled for 13 days or 39 time intervals. The result of this study obtained predictions and calculated for the probability of the number of tweets for the tendency of netizens to post on the situation of the COVID-19 pandemic.

A generalized bivariate exponential distribution

1967 ◽  
Vol 4 (2) ◽  
pp. 291-302 ◽  
Author(s):  
Albert W. Marshall ◽  
Ingram Olkin
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Residual Life ◽  
Waiting Times ◽  
Practical Importance ◽  
Moment Generating Function ◽  
Bivariate Exponential Distribution ◽  
Bivariate Exponential ◽  
Shock Models ◽  
Bivariate Poisson Process

In a previous paper (Marshall and Olkin (1966)) the authors have derived a multivariate exponential distribution from points of view designed to indicate the applicability of the distribution. Two of these derivations are based on “shock models” and one is based on the requirement that residual life is independent of age.The practical importance of the univariate exponential distribution is partially due to the fact that it governs waiting times in a Poisson process. In this paper, the distribution of joint waiting times in a bivariate Poisson process is investigated. There are several ways to define “joint waiting time”. Some of these lead to the bivariate exponential distribution previously obtained by the authors, but others lead to a generalization of it. This generalized bivariate exponential distribution is also derived from shock models. The moment generating function and other properties of the distribution are investigated.

A characterization of the gamma distribution by the negative binomial distribution

1980 ◽  
Vol 17 (04) ◽  
pp. 1138-1144 ◽  
Author(s):  
Jan Engel ◽  
Mynt Zijlstra
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Gamma Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Random Variable ◽  
One To One

It is proved that for a Poisson process there exists a one-to-one relation between the distribution of the random variable N(Y) and the distribution of the non-negative random variable Y. This relation is used to characterize the gamma distribution by the negative binomial distribution. Furthermore it is applied to obtain some characterizations of the exponential distribution.

Local Design Pressures During Ship Ram Events Modeling the Occurrence and Intensity of High Pressure Zones

2017 ◽  
Author(s):  
Freeman Ralph ◽  
Ian Jordaan
Keyword(s):  
High Pressure ◽  
Poisson Process ◽  
Exponential Distribution ◽  
Design Parameters ◽  
Total Force ◽  
Local Pressure ◽  
Vessel Size ◽  
Event Modeling ◽  
Ice Regime ◽  
Local Pressures

During ship ice interaction events (i.e. rams with multi-year ice), the occurrence of local pressures vary in time and space. A link between local pressures and global forces is the sum of the local forces from n High Pressure Zones (HPZs) across the interaction face equals the total force transmitted into the structure. In this paper, a model for HPZ density, and force during ship ram events is presented. The occurrence and intensity of HPZs on panel areas were simulated using a Poisson process and an exponential distribution for HPZ force. The model is extended to consider HPZ occurrence in time through a ramming event, modeling HPZ rate. Such a model allows the designer to determine baseline ‘parent’ local pressure design parameters based on vessel size and expected operational speed. The faster a ship operates through an ice regime, the greater the HPZ rate. Larger and faster ships will penetrate further, having longer interaction durations and hence a greater number of HPZs forming (unless, for example, the ship passes through a ridge). Rates too will vary along the vessel being greater on the bow and least from mid-body to stern. For design, we are interested in the maximum local pressure on a single panel area through the ram duration. The results are compared with previous local pressure models for design.

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