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A class of tests for exponentiality based on a continuum of moment conditions

Simos G. Meintanis (2009)


The empirical moment process is utilized to construct a family of tests for the null hypothesis that a random variable is exponentially distributed. The tests are consistent against the 'new better than used in expectation' (NBUE) class of alternatives. Consistency is shown and the limit null distribution of the test statistic is derived, while efficiency results are also provided. The finite-sample properties of the proposed procedure in comparison to more standard procedures are investigated via...

A counting process model of survival of parallel load-sharing system

Petr Volf, Aleš Linka (2001)


A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit test. We also...

A generalized bivariate lifetime distribution based on parallel-series structures

Vahideh Mohtashami-Borzadaran, Mohammad Amini, Jafar Ahmadi (2019)


In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences...

A new family of compound lifetime distributions

A. Asgharzadeh, Hassan S. Bakouch, Saralees Nadarajah, L. Esmaeili (2014)


In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual...

A note on stochastic ordering of estimators of exponential reliability

Piotr Nowak (2011)

Applicationes Mathematicae

Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which the maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that the MLEs for those plans are also stochastically ordered. We also give some applications to the estimation of reliability.

A sensitivity analysis for causal parameters in structural proportional hazards models.

Els Goetghebeur, Tom Loeys (2003)


Deviations from assigned treatment occur often in clinical trials. In such a setting, the traditional intent-to-treat analysis does not measure biological efficacy but rather programmatic effectiveness. For all-or-nothing compliance situation, Loeys and Goetghebeur (2003) recently proposed a Structural Proportional Hazards method. It allows for casual estimation in the complier subpopulation provided the exclusion restriction holds: randomization per se has no effect unless exposure has changed....

A study of the number of solutions of the system of the log-likelihood equations for the 3-parameter Weibull distribution

George Tzavelas (2012)

Applications of Mathematics

The maximum likelihood estimators of the parameters for the 3-parameter Weibull distribution do not always exist. Furthermore, computationally it is difficult to find all the solutions. Thus, the case of missing some solutions and among them the maximum likelihood estimators cannot be excluded. In this paper we provide a simple rule with help of which we are able to know if the system of the log-likelihood equations has even or odd number of solutions. It is a useful tool for the detection of all...

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