Variations on the arbelos

We recall the ancient notion of arbelos and introduce a number of concepts generalizing it. We follow the ideas presented by J. Sondow in his article on parbelos, the parabolic analogue of the classic arbelos. Our concepts concern the curves constructed of arcs which resemble each other and surfaces obtained in a similar way. We pay special attention to ellarbelos, the curves built of semi-ellipses, because of their possible application in engineering, e.g. in determining the static moments of arc rod constructions or in problems of structural stability and durability of constructions

On some methods of calculating the integrals of trigonometric rational functions

The paper presents original methods of calculating integrals of selected trigonometric rational functions

On a strongly consistent estimator of the squared L_2-norm of a function

A kernel estimator of the squared $L_2$-norm of the intensity function of a Poisson random field is defined. It is proved that the estimator is asymptotically unbiased and strongly consistent. The problem of estimating the squared $L_2$-norm of a function disturbed by a Wiener random field is also considered

G_{1,−1}-minimax estimation of the parameters of a distribution of exponential type

.The abstract is available at MR0518661

Properties of efficient sequential plans for a birth and death process

W pracy udowodniono własności efektywnych planów sekwencyjnych dla procesu urodzin i śmierci o przeliczalnej ilości stanów. Podano przykłady takich planów.A birth and death process with parameters θ=(λ,μ), λ>0, μ>0, is considered. The absolute continuity of measures generated by this process is proved. The Rao-Cramér inequality for the variance of the unbiased estimator of a function h(θ) is derived. Some properties of the estimator attaining the Rao-Cramér lower bound are asserted

On the consistency of sieve bootstrap prediction intervals for stationary time series

In the article, we consider construction of prediction intervals for stationary time series using Bühlmann's [8], [9] sieve bootstrapapproach. Basic theoretical properties concerning consistency are proved. We extend the results obtained earlier by Stine [21], Masarotto and Grigoletto [13] for an autoregressive time series of finite order to the rich class of linear and invertible stationary models. Finite sample performance of the constructed intervals is investigated by computer simulations

Estimation of the hazard rate function with a reduction of bias and variance at the boundary

In the article, we propose a new estimator of the hazard rate function in the framework of the multiplicative point process intensity model. The technique combines the reflection method and the method of transformation. The new method eliminates the boundary effect for suitably selected transformations reducing the bias at the boundary and keeping the asymptotics of the variance. The transformation depends on a pre-estimate of the logarithmic derivative of the hazard function at the boundary

Esther Muñiz Espada, Derecho Agroalimentario y Ciberseguridad, Editorial Reus, S.A., Madrid 2019

Recenzj