The nonlinear optical Galton board (NLOGB), a quantum walk like (but nonlinear) discrete time quantum automaton, is shown to admit a complex evolution leading to long time thermalized states. The continuous limit of the Galton board is derived and shown to be a nonlinear Dirac equation (NLDE). The (Galerkin-truncated) NLDE evolution is shown to thermalize toward states qualitatively similar to ...

Abstract Statistical inferences of the parameters included in a competing risks model are presented. It is assumed here that the causes of failures may occur at times that follow modified Weibull distributions. The case of Weibull distributions can be derived as special case of the problem studied in this paper. The maximum likelihood procedure is used to get the point estimations and asymptoti...

We show analytically that the answer to the question, " The longer it has been since the last earthquake, the longer the expected time till the next? " depends crucially on the statistics of the fluctuations in the interval times between earthquakes. The periodic, uniform, semigaussian, Rayleigh and truncated statistical distributions of interval times, as well as the Weibull distributions with...

Knowledge of a truncated Fourier series expansion for a discontinuous 2^-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval [-1, 1], is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree M for the M locations of discontinuities in e...

The authors study a validity timescale of the discrete truncated Wigner approximation for several quantum-spin systems with long-range interactions step-function form by using Bogoliubov-Born-Green-Kirkwood-Yvon equation.

In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modified Weibull-p...

In this paper, we propose a new parametric distribution which called as the Beta Modified Weibull Power Series (BMWPS) distribution. This distribution is obtained by compounding Beta Modified Weibull (BMW) and power series distributions. BMWPS distribution contains, as special sub-models, such as Beta Modified Weibull Poisson (BMWP) distribution, Beta Modified Weibull Geometric (BMWG) distribut...

growth analysis is a valuable method in the quantitative analysis of crop growth, development and crop production. there are many regression models to describe the sigmoid growth patterns. by considering that, the parameters of non-linear regression models have physiological meanings, they are preferable relation to linear regression models. the aim of this study was to collect and evaluate the...

Usually, the parameters of a Weibull distribution are estimated by maximum likelihood estimation. To reduce the biases of the maximum likelihood estimators (MLEs) of two-parameter Weibull distributions, we propose analytic bias-corrected MLEs. Two other common estimators of Weibull distributions, least-squares estimators and percentiles estimators, are also introduced. Based on a comparison of ...