Operator-based intensity functions for the nonhomogeneous Poisson process

2016 ◽  
Vol 25 (2) ◽  
pp. 79-98 ◽  
Author(s):  
S. K. Bar-Lev ◽  
D. Bshouty ◽  
F. A. van der Duyn Schouten
Keyword(s):  
Poisson Process ◽  
Nonhomogeneous Poisson Process ◽  
Intensity Functions

The Exponential Power-Law Process for the Nonhomogeneous Poisson Process and Bathtub Data

2020 ◽  
Vol 27 (04) ◽  
pp. 2050011
Author(s):  
Shaul K. Bar-Lev ◽  
Frank A. van der Duyn Schouten
Keyword(s):  
Poisson Process ◽  
Power Law ◽  
Likelihood Estimation ◽  
Intensity Function ◽  
Nonhomogeneous Poisson Process ◽  
Base Function ◽  
Power Law Process ◽  
Failure Data ◽  
Exponential Power ◽  
Intensity Functions

Recently, Bar-Lev, Bshouty and Van der Duyn Schouten [Math. Methods Stat. 25 (2016) 79–980] developed a systematic method, called operator-based intensity function, for constructing huge classes of nonmonotonic intensity functions (convex or concave) for the nonhomogeneous Poisson process, all of which are suitable for modeling bathtub data. Each class is parametrized by several parameters (as scale and shape parameters) in addition to the operator index parameter [Formula: see text]. For the sake of demonstration only, we focus in this paper on a special subclass called the exponential power law process (EXPLP[Formula: see text]) whose base function is the intensity function of the power-law process. We describe various properties of such a subclass and use one of its special case, namely EXPLP[Formula: see text] intensity function, to analyze failure data which lack monotonicity. Maximum likelihood estimation of the parameters involved and relevant functions thereof is discussed with respect various aspects as existence, uniqueness, asymptotic behavior and statistical inference facets. Using two real datasets from the literature we provide evidence that the EXPLP[Formula: see text] intensity function is well suited to analyze data which exhibit a bathtub behavior.

scholarly journals Bayesian modeling and prediction of accrual in multi-regional clinical trials

2014 ◽  
Vol 26 (2) ◽  
pp. 752-765 ◽  
Author(s):  
Yi Deng ◽  
Xiaoxi Zhang ◽  
Qi Long
Keyword(s):  
Clinical Trials ◽  
Poisson Process ◽  
Process Model ◽  
Nonhomogeneous Poisson Process ◽  
Modeling And Prediction ◽  
Accuracy And Precision ◽  
Start Up ◽  
Accrual Rate ◽  
Model Region ◽  
Over Time

In multi-regional trials, the underlying overall and region-specific accrual rates often do not hold constant over time and different regions could have different start-up times, which combined with initial jump in accrual within each region often leads to a discontinuous overall accrual rate, and these issues associated with multi-regional trials have not been adequately investigated. In this paper, we clarify the implication of the multi-regional nature on modeling and prediction of accrual in clinical trials and investigate a Bayesian approach for accrual modeling and prediction, which models region-specific accrual using a nonhomogeneous Poisson process and allows the underlying Poisson rate in each region to vary over time. The proposed approach can accommodate staggered start-up times and different initial accrual rates across regions/centers. Our numerical studies show that the proposed method improves accuracy and precision of accrual prediction compared to existing methods including the nonhomogeneous Poisson process model that does not model region-specific accrual.

Optimal Advertizing Policy for Selling a Single Asset

1991 ◽  
Vol 5 (1) ◽  
pp. 89-100 ◽  
Author(s):  
David Assaf ◽  
Benny Levikson
Keyword(s):  
Poisson Process ◽  
Nonhomogeneous Poisson Process ◽  
Independent And Identically Distributed

Suppose we have a single asset that we would like to sell. As time goes by, independent and identically distributed offers with a common known distribution F are given to us. At any given moment, we may either accept the current offer or reject it, thereby losing it forever. The rate at which offers arrive follows a nonhomogeneous Poisson process whose instantaneous intensity is under our control, using advertizing in a manner to be described. Our objective is, roughly, that of maximizing the total discounted expected reward composed of the offer we decide to accept, minus the total advertizing costs.

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.

scholarly journals Separable and semiparametric network-based counting processes applied to the international combat aircraft trades

2021 ◽  
pp. 1-21
Author(s):  
Cornelius Fritz ◽  
Paul W. Thurner ◽  
Göran Kauermann
Keyword(s):  
Poisson Process ◽  
Random Effects ◽  
Network Data ◽  
Counting Processes ◽  
Time Varying ◽  
Political Factors ◽  
Combat Aircraft ◽  
Intensity Functions ◽  
Multivariate Poisson Process

Abstract We propose a novel tie-oriented model for longitudinal event network data. The generating mechanism is assumed to be a multivariate Poisson process that governs the onset and repetition of yearly observed events with two separate intensity functions. We apply the model to a network obtained from the yearly dyadic number of international deliveries of combat aircraft trades between 1950 and 2017. Based on the trade gravity approach, we identify economic and political factors impeding or promoting the number of transfers. Extensive dynamics as well as country heterogeneities require the specification of semiparametric time-varying effects as well as random effects. Our findings reveal strong heterogeneous as well as time-varying effects of endogenous and exogenous covariates on the onset and repetition of aircraft trade events.

Stochastic processes involving random deletion

2001 ◽  
Vol 38 (01) ◽  
pp. 95-107 ◽  
Author(s):  
Mark D. Rothmann ◽  
Hammou El Barmi
Keyword(s):  
Stochastic Processes ◽  
Poisson Process ◽  
Finite Time ◽  
Empirical Distribution ◽  
Nonhomogeneous Poisson Process

We consider a system where units having magnitudes arrive according to a nonhomogeneous Poisson process, remain there for a random period and then depart. Eventually, at any point in time only a portion of those units which have entered the system remain. Of interest are the finite time properties and limiting behaviors of the distribution of magnitudes among the units present in the system and among those which have departed from the system. We will derive limiting results for the empirical distribution of magnitudes among the active (departed) units. These results are also shown to extend to systems having stages or steps through which units must proceed. Examples are given to illustrate these results.

Sign in / Sign up

Export Citation Format

Share Document