The regenerative process with rare event appears on the second phase.
Theoretical aspects of total time on test transform of weighted variables and applications
Although the total time on test (TTT) transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the TTT transform for the weighted random variables and investigates the...
Una medida matricial para la comparación de experimentos censurados.
En este trabajo se desarrolla un método de comparación de experimentos con datos censurados. Dicho método se basa en la evaluación de la pérdida de información que se produce en estudios de supervivencia y fiabilidad cuando los tiempos de vida se censuran aleatoriamente por la derecha. Se supone que la distribución del tiempo de vida depende de un parámetro k-variante desconocido θ; y se usa la matriz de Fisher como medida de información apropiada acerca de θ. Se propone una medida matricial de...
Unbiased estimation for two-parameter exponential distribution under time censored sampling
The problem considered is that of unbiased estimation for a two-parameter exponential distribution under time censored sampling. We obtain a necessary form of an unbiasedly estimable parametric function and prove that there does not exist any unbiased estimator of the parameters and the mean of the distribution. For reliability estimation at a specified time point, we give a necessary and sufficient condition for the existence of an unbiased estimator and suggest an unbiased estimator based on a...
Unbiased estimation of reliability for two-parameter exponential distribution under time censored sampling
The problem considered is that of unbiased estimation of reliability for a two-parameter exponential distribution under time censored sampling. We give necessary and sufficient conditions for the existence of uniformly minimum variance unbiased estimator and also provide a characterization of a complete class of unbiased estimators in situations where unbiased estimators exist.
Une extension de l'approche résistance/contrainte appliquée à la modélisation des lois de défaillance des composants électroniques
Uniformly Most Accurate Equivariant Prediction Limit.
Univariate parametric survival analysis using GS-distributions.
The GS-distribution is a family of distributions that provide an accurate representation of any unimodal univariate continuous distribution. In this contribution we explore the utility of this family as a general model in survival analysis. We show that the survival function based on the GS-distribution is able to provide a model for univariate survival data and that appropriate estimates can be obtained. We develop some hypotheses tests that can be used for checking the underlying survival model...
Variance components and nonlinearity
Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the...
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).
Несмещенные оценки суммы ряда Неймана по методу Монте-Карло
Применение метода, свободного от распределений, при обработке резултатов испытаний на надежностъ
Статистическая оценка функции сохранности при экспоненциальном и неизвестном законе надежности кибернетических систем