Poisson Sequence Research Articles

On the estimation of intensities in a stochastic process generated by a stochastic intensity sequence

A stationary doubly stochastic Poisson sequence is considered. Asymptotic properties of the best linear estimates of the intensities are investigated.

On the estimation of intensities in a stochastic process generated by a stochastic intensity sequence

A stationary doubly stochastic Poisson sequence is considered. Asymptotic properties of the best linear estimates of the intensities are investigated.

The statistical model of the fading of shortwave radio signals that are obliquely reflected from the ionosphere

Fast fadings of a shortwave signal are simulated by a Poisson sequence of pulses. The laws governing the distribution of the amplitudes and lengths of the pulses are determined from experiments. The autocorrelation function and the distribution function of the signal levels are calculated, and a comparison is made with experiments.

Erlang’s Formulas in the Theory of Mass Service

A stationary Poisson sequence of calls of intensity $\lambda $ enters a service system with n lines. If all lines are occupied at the time of arrival of a call, then the call is lost. The distribution $F(x)$ of the service time, with finite first moment \[ s = - \int_0^\infty {xd} F(x) \] is assumed to be azbitrary.In the investigation it is proved that the probability that k lines will be occupied at time t converges, as $t \to \infty $, to the value \[ [ k ] = \frac{{( {\lambda s} )^k }}{{k!}} \left\{ {\sum\limits_{j = 0}^n {\frac{{( {\lambda s} )^j }}{{j!}}} } \right\}^{ - 1} ,\quad 1 \leqq k \leqq n. \] The method used represents a further development of an idea which was employed earlier by Lundquist [3].

Direct and Reverberant Field Amplitude Distributions in Nearly Hard Rooms

The probability distribution of pressure amplitudes in a room is studied theoretically and experimentally. A point source is assumed to emit a Poisson sequence of pulses. The method of cumulant generating functions is used to obtain the distribution of response in the direct field, the reverberant field, and the transition region. In the direct field, the source statistics are reproduced. For sufficiently reverberant spaces, the reverberant field tends to normality independently of the source distribution. For sufficiently short pulses (or short autocorrelation time of the source) the direct and reverberant fields are statistically independent. When these simplifying conditions are not met, we indicate how the results may be generalized. Implications for calculations of random fatigue and component malfunction are discussed briefly.

Direct and Reverberant Field Statistics in Nearly Hard Rooms

Calculations of the first-order density of pressure amplitudes in a reverberant room are reported. The random source is presumed to emit a Poisson sequence of pulses which have random amplitudes but identical shapes. It is shown that sufficiently near the source the distribution of pressure amplitudes reproduces that of the source, and that in the reverberant field there is a tendency to normality due to the great image overlap. The conditions for normality are presented, as well as those for statistical independence of the direct and reverberant fields. An experimental illustration of the theoretical ideas is included. Implications for calculations of random fatigue and malfunction are discussed. (Supported in part by Wright Air Development Division and by B+K Instruments, Inc.)

Spatial multiresolution cluster detection method

A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to select the optimal test threshold. The MCD method is compared with single scale testing methods controlling for false discovery rate and the spatial scan statistics using simulation and f-MRI data. The MCD method is shown to be more effective for discovering irregularly shaped clusters, and the implementation of this method does not require heavy computation, making it suitable for cluster detection for large spatial data.