On the Wald's Sequential Probability Ratio Test for Lévy Processes

Buonaguidi, Bruno; Muliere, Pietro

doi:10.1080/07474946.2013.803799

Cited by 4 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bayraktar and Sezer (2009) and Dayanik (2010)). Problems of sequential testing for such a process were faced in Buonaguidi and Muliere (2013a) and Buonaguidi and Muliere (2013b). These facts make our results valid in those situations where the Poisson process is inappropriate, namely, when the events occur in clusters and are characterized by overdispersion.…”

Section: Introductionmentioning

confidence: 71%

On the Disorder Problem for a Negative Binomial Process

Buonaguidi¹,

Muliere²

2015

J. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

We study the Bayesian disorder problem for a negative binomial process. The aim is to determine a stopping time which is as close as possible to the random and unknown moment at which a sequentially observed negative binomial process changes the value of its characterizing parameter p ∈ (0, 1). The solution to this problem is explicitly derived through the reduction of the original optimal stopping problem to an integrodifferential free-boundary problem. A careful analysis of the free-boundary equation and of the probabilistic nature of the boundary point allows us to specify when the smooth fit principle holds and when it breaks down in favour of the continuous fit principle.

show abstract

Section: Introductionmentioning

confidence: 71%

On the Disorder Problem for a Negative Binomial Process

Buonaguidi¹,

Muliere²

2015

J. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Our study is motivated by the application of the negative binomial process and the related negative binomial distribution in several fields, such as distribution theory (Anscombe (1950), Barndorff-Nielsen and Yeo (1969), Vaillant (1991), Zhou and Carin (2013)), agriculture and pest management (Mukhopadhyay (2014) and Mukhopadhyay and de Silva (2005)), cosmology (Carruthers and Minh (1983)), entomology (Nedelman (1983) and Wilson and Room (1983)), and hydrology (Kozubowski and Podgórski (2009)). Problems of sequential testing for such a process were faced in Buonaguidi and Muliere (2013a) and Buonaguidi and Muliere (2013b).…”

Section: Introductionmentioning

confidence: 99%

On the Disorder Problem for a Negative Binomial Process

Buonaguidi

Muliere

2015

Journal of Applied Probability

Self Cite

View full text Add to dashboard Cite

We study the Bayesian disorder problem for a negative binomial process. The aim is to determine a stopping time which is as close as possible to the random and unknown moment at which a sequentially observed negative binomial process changes the value of its characterizing parameter p ∈ (0, 1). The solution to this problem is explicitly derived through the reduction of the original optimal stopping problem to an integro-differential free-boundary problem. A careful analysis of the free-boundary equation and of the probabilistic nature of the boundary point allows us to specify when the smooth fit principle holds and when it breaks down in favour of the continuous fit principle.

show abstract

Sequential negative binomial problems and statistical ecology: A selected review with new directions

Mukhopadhyay

Banerjee

2015

Statistical Methodology

View full text Add to dashboard Cite

On the Wald's Sequential Probability Ratio Test for Lévy Processes

Cited by 4 publications

References 22 publications

On the Disorder Problem for a Negative Binomial Process

On the Disorder Problem for a Negative Binomial Process

On the Disorder Problem for a Negative Binomial Process

Sequential negative binomial problems and statistical ecology: A selected review with new directions

Contact Info

Product

Resources

About