Time‐between‐events monitoring using nonhomogeneous Poisson process with power law intensity

2021 ◽  
Author(s):  
Sajid Ali
Keyword(s):  
Poisson Process ◽  
Power Law ◽  
Nonhomogeneous Poisson Process

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.

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
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