1,720,974 research outputs found
A past inaccuracy measure based on the reversed relevation transform
No full textNumerous information indices have been developed in the information theoretic literature and extensively used in various disciplines. One of the relevant developments in this area is the Kerridge inaccuracy measure. Recently, a new measure of inaccuracy was introduced and studied by using the concept of relevation transform, which is related to the upper record values of a sequence of independent and identically distributed random variables. Along this line of research, we introduce an analogue of the inaccuracy measure based on the reversed relevation transform. We discuss some theoretical merits of the proposed measure and provide several results involving equivalent formulas, bounds, monotonicity and stochastic orderings. Our results are also based on the mean inactivity time and the new concept of reversed relevation inaccuracy ratio
Fractional generalized cumulative entropy and its dynamic version
No full textFollowing the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fractional cumulative entropy as a non-parametric estimator of the new measure. It is shown that the empirical measure converges to the proposed notion almost surely. Then, we address the stability of the empirical measure and provide an example of application to real data. Finally, a central limit theorem is established under the exponential distribution
Analysis of the past lifetime in a replacement model through stochastic comparisons and differential entropy
No full textA suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time an item is planned to be replaced by another one having the same age but a different lifetime
distribution. We investigate the past lifetime of this system, given that at a larger time the system is found to be failed.
Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly
truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement
evaluated at , which is finalized to measure the goodness of the replacement procedure.
The characterization and the properties of the differential entropy of the system lifetime are also discussed.
Finally, an example of application to the firing activity of a stochastic neuronal model is provided
Weighted fractional generalized cumulative past entropy and its properties
Full text linkIn this paper, we introduce weighted fractional generalized cumulative past
entropy of a nonnegative absolutely continuous random variable with bounded
support. Various properties of the proposed weighted fractional measure are
studied. Bounds and stochastic orderings are derived. A connection between the
proposed measure and the left-sided Riemann-Liouville fractional integral is
established. Further, the proposed measure is studied for the proportional
reversed hazard rate models. Next, a nonparametric estimator of the weighted
fractional generalized cumulative past entropy is suggested based on empirical
distribution function. Various examples with a real life data set are
considered for the illustration purposes. Finally, large sample properties of
the proposed empirical estimator are studied.Comment: 24 pages, 8 figure
Copula-based extropy measures, properties and dependence in bivariate distributions
No full textIn this work, we propose extropy measures based on density copula,
distributional copula, and survival copula, and explore their properties. We
study the effect of monotone transformations for the proposed measures and
obtain bounds. We establish connections between cumulative copula extropy and
three dependence measures: Spearman's rho, Kendall's tau, and Blest's measure
of rank correlation. Finally, we propose estimators for the cumulative copula
extropy and survival copula extropy with an illustration using real life
datasets
Stochastic comparison of the second-order statistics arising from exponentiated location-scale model
No full textIn this article, we consider stochastic comparisons between second-order statistics arising from general exponentiated location-scale models. When the random variables are independent, we establish usual stochastic and hazard rate orders between second-order statistics. Further, similar ordering results are obtained when the random observations are dependent. Some applications of the established results are presented
Some results on a doubly truncated generalized discrimination measure
Full text linksummary:Doubly truncated data appear in some applications with survival and astrological data. Analogous to the doubly truncated discrimination measure defined by Misagh and Yari (2012), a generalized discrimination measure between two doubly truncated non-negative random variables is proposed. Several bounds are obtained. It is remarked that the proposed measure can never be equal to a nonzero constant which is independent of the left and right truncated points. The effect of monotone transformations on the proposed measure is discussed. Finally, a simulation study is added to provide the estimates of the proposed discrimination measure
Extended fractional cumulative past and paired phi-entropy measures
Full text linkVery recently, extended fractional cumulative residual entropy (EFCRE) has
been proposed by Foroghi et al. (2022). In this paper, we introduce extended
fractional cumulative past entropy (EFCPE), which is a dual of the EFCRE. The
newly proposed measure depends on the logarithm of fractional order and the
cumulative distribution function (CDF). Various properties of the EFCPE have
been explored. This measure has been extended to the bivariate setup.
Furthermore, the conditional EFCPE is studied and some of its properties are
provided. The EFCPE for inactivity time has been proposed. In addition, the
extended fractional cumulative paired phi-entropy has been introduced and
studied. The proposed EFCPE has been estimated using empirical CDF.
Furthermore, the EFCPE is studied for coherent systems. A validation of the
proposed measure is provided using logistic map. Finally, an application is
reported
Some Results on a Generalized Residual Entropy based on Order Statistics
Full text linkIn the present paper, we discuss some monotone properties of the GRE of order (α, β) in order statistics under various assumptions. It is shown that monotone properties are preserved under the formation of a parallel system but not under the formation of a series system. A counter example is presented. Bounds of the GRE of order statistics are obtained. The GRE of parallel and series systems are shown to be monotone function of the number of observations of a given sample. Numerical simulation is carried out for verification of the theoretical results. Maximum likelihood estimators of GRE of X, X1:n and Xn:n are obtained when independent data are drawn from exponential distribution
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