Exact bahadur efficiencies of tests for superadditivity of the mean function of a non-homogeneous poisson process

Metrika ◽  
1990 ◽  
Vol 37 (1) ◽  
pp. 129-143
Author(s):  
T. Ramallingam
Keyword(s):  
Poisson Process ◽  
Homogeneous Poisson Process ◽  
The Mean ◽  
Mean Function ◽  
Non Homogeneous Poisson Process

scholarly journals PENDUGAAN KOMPONEN PERIODIK FUNGSI INTENSITAS BERBENTUK FUNGSI PERIODIK KALI TREN LINEAR SUATU PROSES POISSON NON-HOMOGEN

2013 ◽  
Vol 12 (1) ◽  
pp. 49
Author(s):  
W. ISMAYULIA ◽  
I W. MANGKU ◽  
S. SISWANDI
Keyword(s):  
Poisson Process ◽  
Mean Square Error ◽  
Linear Trend ◽  
Periodic Component ◽  
Mean Square ◽  
Homogeneous Poisson Process ◽  
Single Realization ◽  
The Mean ◽  
Bias Variance ◽  
Non Homogeneous Poisson Process

In this manuscript, estimation of the periodic component of intensity having form periodic function multiplied by the linear trend of a non homogeneous Poisson process is discussed. The estimator is constructed using a single realization of the Poisson process observed in the interval  0,𝑛 . It is assumed that the period of the periodic component is known. The convergence of the Mean Square Error (MSE) of the estimator has been proved. In addition, asymptotic approximations to the bias, variance, and Mean Square Error (MSE) of the estimator have been proved. An asymptotic optimal bandwidth is also given.

Weak limit results for the extremes of a class of shot noise processes

1995 ◽  
Vol 32 (03) ◽  
pp. 707-726 ◽  
Author(s):  
Patrick Homble ◽  
William P. McCormick
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Impulse Response Function ◽  
Weak Limit ◽  
Intensity Function ◽  
Important Class ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Non Homogeneous Poisson Process ◽  
Over Time

Shot noise processes form an important class of stochastic processes modeling phenomena which occur as shocks to a system and with effects that diminish over time. In this paper we present extreme value results for two cases — a homogeneous Poisson process of shocks and a non-homogeneous Poisson process with periodic intensity function. Shocks occur with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This work continues work of Hsing and Teugels (1989) and Doney and O'Brien (1991) to the case of random amplitudes.

An optimal parking problem

1982 ◽  
Vol 19 (4) ◽  
pp. 803-814 ◽  
Author(s):  
Mitsushi Tamari
Keyword(s):  
Poisson Process ◽  
Decision Maker ◽  
Optimal Stopping ◽  
Renewal Process ◽  
A Priori ◽  
Expected Loss ◽  
Homogeneous Poisson Process ◽  
Optimal Stopping Rule ◽  
Non Homogeneous Poisson Process ◽  
Parking Place

The decision-maker drives a car along a straight highway towards his destination and looks for a parking place. When he finds a parking place, he can either park there and walk the distance to his destination or continue driving. Parking places are assumed to occur in accordance with a Poisson process along the highway. The decision-maker does not know the distance Y to his destination exactly in advance. Only an a priori distribution is assumed for Y and cases of typically important distribution are examined. When we take as loss the distance the decision-maker must walk and wish to minimize the expected loss, the optimal stopping rule and the minimum expected loss are obtained. In Section 3 a generalization to the cases of a non-homogeneous Poisson process and a renewal process is considered.

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