Consider k success counts from a binomial distribution with unknown N and success probability p. We consider the problem of estimating N. By integrating the likelihood for Nand p over a beta density for p, we obtain the beta-binomial distribution which results in stable and reasonably efficient estimators of N, which compare favorably with and are often better than the estimates introduced by O...

In this paper, we are concerned with the situations, where sometimes value two is reported erroneously as one in relation to size biased generalized negative binomial distribution (SBGNBD) with probability αα. We have obtained the Maximum likelihood estimator and Bayes estimator under general entropy loss function. A simulated study is carried out to access the performance of the maximum likeli...

The number of new gadolinium-enhancing lesions discovered via magnetic resonance imaging is a well-established outcome for multiple sclerosis studies, especially Phase II Studies. Due to the high cost of magnetic resonance imaging scans, many investigators select participants for the presence of lesions. While this selection procedure is thought to improve the power of inferences, the effect of...

The paper [Howard E. Brandt, ”Conclusive eavesdropping in quantum key distribution,” J. Opt. B: Quantum Semiclass. Opt. 7 (2005)] is generalized to include the full range of error rates for the projectively measured quantum cryptographic entangling probe, and also the full range of inconclusive rates for the entangling probe measured with the POVM receiver.

A b s t r a c t . In this paper, we investigate the exact distribution of the waiting time for the r-th t-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of order k and an extended Poisson distr...

SEIR epidemiological models with the inclusion of quarantine and isolation are used to study the control and intervention of infectious diseases. A simple ordinary differential equation (ODE) model that assumes exponential distribution for the latent and infectious stages is shown to be inadequate for assessing disease control strategies. By assuming arbitrarily distributed disease stages, a ge...

Algorithms where offsprings (new search points) are generated according to the estimated probability model of the good parents are called the Probabilistic Model-Building Genetic Algorithms (PMBGAs). In this paper, a new model of PMBGA, Distributed PMBGA (DPMBGA), is proposed. In the DPMBGA, the correlation between the design variables is considered by PCA when the offsprings are generated. The...

The on-axis image irradiance obtained from a radially symmetric optical system under broadband illumination is analysed in the phase-space domain of the Wigner distribution function associated with a modified one-dimensional pupil aperture. To this end, a coordinate transformation is employed in such a way that the varying on-axis irradiance can be derived from different slices of a two-dimensi...