- Intervals for the Poisson Parameter and the Substitution Approach

2012 ◽  
pp. 146-155
Keyword(s):  
Poisson Parameter

Table of Neyman-Shortest Unbiased Confidence Intervals for the Poisson Parameter

Biometrika ◽  
1961 ◽  
Vol 48 (1/2) ◽  
pp. 191
Author(s):  
Colin R. Blyth ◽  
David W. Hutchinson
Keyword(s):  
Confidence Intervals ◽  
Poisson Parameter

scholarly journals Tracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylor’s Abnormal Fluctuation Scaling

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Gen Sakoda ◽  
Hideki Takayasu ◽  
Misako Takayasu
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
State Space Model ◽  
Estimation Method ◽  
Stationary Time Series ◽  
Series Data ◽  
Large Fluctuations ◽  
Taylor’S Law ◽  
Fluctuation Scaling ◽  
Poisson Parameter

We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor’s law. By introducing the effect of Taylor’s fluctuation scaling into the State Space Model with the Particle Filter, the underlying Poisson parameter’s time evolution is estimated correctly from given non-stationary time series data with abnormally large fluctuations. We also developed a discontinuity detection method which enables tracking the Poisson parameter even for time series including sudden discontinuous jumps. As an example of application of this new general method, we analyzed Point-of-Sales data in convenience stores to estimate change of probability of purchase of commodities under fluctuating number of potential customers. The effectiveness of our method for Poisson time series with non-stationarity, large discontinuities and Taylor’s fluctuation scaling is verified by artificial and actual time series.

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