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In reliability and survival analysis, to model lifetime data, size-biased distributions are useful. In this paper, a mixture model of size-biased distributions is introduced and studied. Several reliability properties of this model are investigated. In addition, some implications of well-known stochastic orders and aging classes concerning the model are established. To underline the usefulness of...
The receiver operating characteristic (ROC) curve is a popular graphical tool for describing the accuracy of a diagnostic test. Based on the idea of estimating the ROC curve as a distribution function, we propose a new kernel smoothing estimator of the ROC curve which is invariant under nondecreasing data transformations. We prove that the estimator has better asymptotic mean squared error properties...
In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some $$k\in \{1,\ldots ,n\}$$ k ∈ { 1 , … , n } such that the common failure rate of the first k failure times is different from the common failure rate of the last $$n-k$$ n - k failure times, based on an exponential lifetime distribution...
In a sequence of n binary ( $$0{-}1$$ 0 - 1 ) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k, $$1\le k\le n$$ 1 ≤ k ≤ n . Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this...
In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore,...
This paper studies order statistics from random variables following the scale model. In the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes and the second smallest order statistic, the dispersive order and the star order of the sample extremes.
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