Sample path analysis and distributions of boundary crossing times
From MaRDI portal
Publication:2406458
DOI10.1007/978-3-319-67059-1zbMath1393.60004OpenAlexW2762885165MaRDI QIDQ2406458
Publication date: 29 September 2017
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-67059-1
CUSUMrenewal processesexact distributionsequential estimationcompound Poisson processesfirst boundary crossing
Sample path properties (60G17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)
Related Items
An optimal purely sequential strategy with asymptotic second-order properties: Applications from statistical inference and data analysis ⋮ Some results on the telegraph process driven by gamma components ⋮ A two-state neuronal model with alternating exponential excitation ⋮ Regulation of a single-server queue with customers who dynamically choose their service durations ⋮ First crossing times of telegraph processes with jumps ⋮ A new formulation of minimum risk fixed-width confidence interval (MRFWCI) estimation problems for a normal mean with illustrations and simulations: Applications to air quality data ⋮ A general theory of three-stage estimation strategy with second-order asymptotics and its applications ⋮ Asymptotic results for the absorption time of telegraph processes with a non-standard barrier at the origin ⋮ Theory of new second-order expansions for the moments of \({100\rho \%}\) accelerated sequential stopping times in normal mean estimation problems when \({0<\rho <1}\) is arbitrary ⋮ On general asymptotically second-order efficient purely sequential fixed-width confidence interval (FWCI) and minimum risk point estimation (MRPE) strategies for a normal mean and optimality ⋮ EDA on the asymptotic normality of the standardized sequential stopping times, Part-I: Parametric models ⋮ Two-stage procedures for the bounded risk point estimation of the parameter and hazard rate in two families of distributions ⋮ Level crossing statistics in a biologically motivated model of a long dynamic protrusion: passage times, random and extreme excursions ⋮ On the exact distributions of the maximum of the asymmetric telegraph process ⋮ Purely sequential point estimation of a function of the mean in an exponential distribution ⋮ Some results on the telegraph process confined by two non-standard boundaries ⋮ Ornstein-Uhlenbeck processes of bounded variation ⋮ On telegraph processes, their first passage times and running extrema ⋮ Two-stage estimation for a normal mean having a known lower bound of variance with final sample size defined via Gini’s mean difference and mean absolute deviation ⋮ Two-stage and sequential procedures for estimation of powers of parameter of a family of distributions ⋮ Certain functionals of squared telegraph processes ⋮ Purely sequential FWCI and MRPE problems for the mean of a normal population by sampling in groups with illustrations using breast cancer data ⋮ Purely sequential estimation problems for the mean of a normal population by sampling in groups under permutations within each group and illustrations ⋮ A general theory of purely sequential minimum risk point estimation (MRPE) of a function of the mean in a normal distribution ⋮ Tandem-width sequential confidence intervals for a Bernoulli proportion ⋮ Two-stage fixed-width and bounded-width confidence interval estimation methodologies for the common correlation in an equi-correlated multivariate normal distribution ⋮ An unusual application of Cramér-Rao inequality to prove the attainable lower bound for a ratio of complicated gamma functions ⋮ Purely sequential minimum risk point estimation (MRPE) for a survival function in an exponential distribution: illustration with remission times for bladder cancer patients ⋮ Second-order asymptotics in a class of purely sequential minimum risk point estimation (MRPE) methodologies ⋮ More for less insurance model: an alternative to (re)insurance ⋮ Minimum risk point estimation for a function of a normal mean under weighted power absolute error loss plus cost: First-order and second-order asymptotics
Uses Software