Tail orderings and the total time on test transform
The paper presents some connections between two tail orderings of distributions and the total time on test transform. The procedure for testing the pure-tail ordering is proposed.
Dispersive functions and stochastic orders
Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented
Estimation of the parameters for the exponential reliability
W praktycznych zastosowaniach teorii niezawodności konieczna jest znajomość liczbowych wartości charakterystyk, takich jak średni czas życia elementu lub systemu, intensywność awarii elementu, niezawodność elementu lub systemu. Jedynym rozsądnym sposobem określenia tych wielkości jest ich ocena oparta o badanie statystyczne, to znaczy estymacja na podstawie próby. W niniejszym artykule dokonamy przeglądu metod estymacji wspomnianych wyżej charakterystyk niezawodności. Ograniczymy się przy tym do...
Review: J. R. Barra; Fundamentals of Statistics
The article contains no abstract
Weighting, likelihood ratio order and life distributions
We use weighted distributions with a weight function being a ratio of two densities to obtain some results of interest concerning life and residual life distributions. Our theorems are corollaries from results of Jain et al. (1989) and Bartoszewicz and Skolimowska (2006).
Robust estimation based on spacings in weighted exponential models
Using Zieliński's (1977, 1983) formalization of robustness Błażej (2007) obtained uniformly most bias-robust estimates (UMBREs) of the scale parameter for some statistical models (including the exponential model), in a class of linear functions of order statistics, when violations of the models are generated by weight functions. In this paper the UMBRE of the scale parameter, based on spacings, in two weighted exponential models is derived. Extensions of results of Bartoszewicz (1986, 1987) are...
Invariance of relative inverse function orderings under compositions of distributions
Bartoszewicz and Benduch (2009) applied an idea of Lehmann and Rojo (1992) to a new setting and used the GTTT transform to define invariance properties and distances of some stochastic orders. In this paper Lehmann and Rojo's idea is applied to the class of models which is based on distributions which are compositions of distribution functions on [0,1] with underlying distributions. Some stochastic orders are invariant with respect to these models.
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