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Reversible jump MCMC for two-state multivariate Poisson mixtures

Jani Lahtinen, Jouko Lampinen (2003)

Kybernetika

The problem of identifying the source from observations from a Poisson process can be encountered in fault diagnostics systems based on event counters. The identification of the inner state of the system must be made based on observations of counters which entail only information on the total sum of some events from a dual process which has made a transition from an intact to a broken state at some unknown time. Here we demonstrate the general identifiability of this problem in presence of multiple...

Robust estimation of the scale and weighted distributions

Paweł Błażej (2007)

Applicationes Mathematicae

The concept of robustness given by Zieliński (1977) is considered in cases where violations of models are generated by weight functions. Uniformly most bias-robust estimates of the scale parameter, based on order statistics, are obtained for some statistical models. Extensions of results of Zieliński (1983) and Bartoszewicz (1986) are given.

Sharp bounds for expectations of spacings from decreasing density and failure rate families

Katarzyna Danielak, Tomasz Rychlik (2004)

Applicationes Mathematicae

We apply the method of projecting functions onto convex cones in Hilbert spaces to derive sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density and with decreasing failure rate. We also characterize the distributions for which the bounds are attained.

Simulation of transient performance measures for stiff markov chains

Abdelaziz Nasroallah (2010)

RAIRO - Operations Research

We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and Conditioning...

Some properties of the proportional odds model

Magdalena Benduch-Frąszczak (2010)

Applicationes Mathematicae

Marshall and Olkin (1997) introduced a new family of distributions by adding a tilt parameter. The same family was obtained by Kirmani and Gupta (2001) as the proportional odds model, which had been proposed by Clayton (1974). In this paper, stochastic ordering of distributions from this class and preservation of classes of life distributions by adding a parameter are obtained. The proportional odds family is also considered as a family of weighted distributions.

Some results on a doubly truncated generalized discrimination measure

Suchandan Kayal, Rajesh Moharana (2016)

Applications of Mathematics

Doubly truncated data appear in some applications with survival and astrological data. Analogous to the doubly truncated discrimination measure defined by Misagh and Yari (2012), a generalized discrimination measure between two doubly truncated non-negative random variables is proposed. Several bounds are obtained. It is remarked that the proposed measure can never be equal to a nonzero constant which is independent of the left and right truncated points. The effect of monotone transformations on...

Stability of characterizations of distribution functions using failure rate functions

Maia Koicheva, Edward Omey (1990)

Aplikace matematiky

Let λ denote the failure rate function of the d , f . F and let λ 1 denote the failure rate function of the mean residual life distribution. In this paper we characterize the distribution functions F for which λ 1 = c λ and we estimate F when it is only known that λ 1 / λ or λ 1 - c λ is bounded.

Statistical inference for fault detection: a complete algorithm based on kernel estimators

Piotr Kulczycki (2002)

Kybernetika

This article presents a new concept for a statistical fault detection system, including the detection, diagnosis, and prediction of faults. Theoretical material has been collected to provide a complete algorithm making possible the design of a usable system for statistical inference on the basis of the current value of a symptom vector. The use of elements of artificial intelligence enables self-correction and adaptation to changing conditions. The mathematical apparatus is founded on the methodology...

Stochastic comparisons of moment estimators of gamma distribution parameters

Piotr Nowak (2012)

Applicationes Mathematicae

Recently the order preserving property of estimators has been intensively studied, e.g. by Gan and Balakrishnan and collaborators. In this paper we prove the stochastic monotonicity of moment estimators of gamma distribution parameters using the standard coupling method and majorization theory. We also give some properties of the moment estimator of the shape parameter and derive an approximate confidence interval for this parameter.

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