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.

Time spent below a random threshold by a Poisson driven sequence of observations

2003 ◽  
Vol 40 (03) ◽  
pp. 807-814 ◽  
Author(s):  
S. N. U. A. Kirmani ◽  
Jacek Wesołowski
Keyword(s):  
Poisson Process ◽  
Asymptotic Distribution ◽  
Random Variables ◽  
Nonhomogeneous Poisson Process ◽  
System Level ◽  
Homogeneous Poisson Process ◽  
Random Threshold ◽  
The Mean ◽  
Current Value ◽  
Independent And Identically Distributed

The mean and the variance of the time S(t) spent by a system below a random threshold until t are obtained when the system level is modelled by the current value of a sequence of independent and identically distributed random variables appearing at the epochs of a nonhomogeneous Poisson process. In the case of the homogeneous Poisson process, the asymptotic distribution of S(t)/t as t → ∞ is derived.

Time spent below a random threshold by a Poisson driven sequence of observations

2003 ◽  
Vol 40 (3) ◽  
pp. 807-814 ◽  
Author(s):  
S. N. U. A. Kirmani ◽  
Jacek Wesołowski
Keyword(s):  
Poisson Process ◽  
Asymptotic Distribution ◽  
Random Variables ◽  
Nonhomogeneous Poisson Process ◽  
System Level ◽  
Homogeneous Poisson Process ◽  
Random Threshold ◽  
The Mean ◽  
Current Value ◽  
Independent And Identically Distributed

The mean and the variance of the time S(t) spent by a system below a random threshold until t are obtained when the system level is modelled by the current value of a sequence of independent and identically distributed random variables appearing at the epochs of a nonhomogeneous Poisson process. In the case of the homogeneous Poisson process, the asymptotic distribution of S(t)/t as t → ∞ is derived.

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.

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

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.

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.

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