1,721,043 research outputs found
Cumulative measures of information and stochastic orders
No full textIn this paper we present some known results on cumulative measures of information, study their properties and relate these definitions to concepts of reliability theory. We give some relations of these measures of discrimination with some well-known stochastic orders and with the relative reversed hazard rate order. We investigate also a stochastic comparison among the empirical cumulative measures that can be related to the cumulative measures. Large part of this paper is a survey article; however, in the last section, we define a new measure of discrimination between residual lifetimes and study some of its properties
Some mathematical properties of the ROC curve and their applications
No full textIn this paper we present ROC methodology and analyze the ROC curve. We describe first the historical background and its relation with signal detection theory. Some mathematical properties of this curve are given, and in particular the relation with stochastic orders and statistical hypotheses testing are described. We present also a medical application of the Neymann–Pearson lemma
The up reversed hazard rate stochastic order
No full textA stochastic order consisting of a shifted version of the well-known re- versed hazard rate order is proposed. Namely, for two continuous random variables
X and Y we say that X is smaller than Y in the up reversed hazard rate order, denoted
as X rh" Y , if X
x rh Y for each x 0. Some properties of such order are
presented, including the preservation under (i) transformations by strictly monotone
convex functions, (ii) formation of coherent systems, (iii) Poisson shock models
Some properties of cumulative Tsallis entropy
No full textThe cumulative entropy is an information measure which is alternative to the differential entropy. Indeed, the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X. In this paper we propose a new generalized cumulative entropy based on Tsallis entropy (CTE) and its dynamic version (DCTE). We study some properties and characterization results for this measure
On weighted residual and past entropies
No full textWe consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of "weighted residual entropy" and "weighted past entropy", that are suitable to describe dynamic information of random lifetimes, in analogy with the entropies of residual and past lifetimes introduced in [9] and [6], respectively. The obtained results include their behaviors under monotonic transformations
Existence and uniqueness results for second order elliptic equations in unbounded domains
No full textOn dynamic mutual information for bivariate lifetimes
No full textWe consider dynamic versions of the mutual information of lifetime distributions, with
focus on past lifetimes, residual lifetimes and mixed lifetimes evaluated at different instants.
This allows to study multicomponent systems, by measuring the dependence in conditional
lifetimes of two components having possibly different ages. We provide some bounds,
and investigate the mutual information of residual lifetimes within the time-transformed
exponential model (under both the assumptions of unbounded and truncated lifetimes).
Moreover, with reference to the order statistics of a random sample, we evaluate explicitly
the mutual information between the minimum and the maximum, conditional on inspection
at different times, and show that it is distribution-free. Finally, we develop a copula-based
approach aiming to express the dynamic mutual information for past and residual bivariate
lifetimes in an alternative way
Properties for generalized cumulative past measures of information
No full textThe Shannon entropy based on the probability density function is a key information measure with applications in different areas. Some alternative information measures have been proposed in the literature. Two relevant ones are the cumulative residual entropy (based on the survival function) and the cumulative past entropy (based on the distribution function). Recently, some extensions of these measures have been proposed. Here, we obtain some properties for the generalized cumulative past entropy. In particular, we prove that it determines the underlying distribution. We also study this measure in coherent systems and a closely related generalized past cumulative Kerridge inaccuracy measure
Some improvements on generalized reversed aging intensity functions
No full textRecently, the generalized reversed aging intensity functions have been studied in the literature revealing to be a tool to characterize distributions, under suitable conditions. In this paper, some improvements on these functions are given and the relation between two cumulative distribution functions leading to the same generalization is studied.
In particular, a link with the two-parameters Weibull distributions is found and a new stochastic order is defined in terms of the generalized reversed aging intensity. This order is strictly related to the definition of extropy, that is the dual measure of entropy, and some connections with well-known stochastic orders are analyzed. Finally, the possibility of introducing the concept of generalized aging intensity is studied also in terms of cumulative distribution functions with non-positive support
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