2,327 research outputs found
Inverted Exponential Distribution Under a Bayesian Viewpoint
The objective of this study was to examine the properties of Bayes estimators of the parameter, reliability function and hazard rate under the symmetric and asymmetric loss functions for the inverted exponential model. The Bayes predictive interval and the Bayes estimate of shift point are also determined. A simulation study was carried out to study the properties of the Bayes estimators
Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring
The hybrid censoring is a mixture of Type I and Type II censoring schemes.
This paper presents the statistical inferences of the Inverse Weibull
distribution when the data are Type-I hybrid censored. First we consider the
maximum likelihood estimators of the unknown parameters. It is observed that
the maximum likelihood estimators can not be obtained in closed form. We
further obtain the Bayes estimators and the corresponding highest posterior
density credible intervals of the unknown parameters under the assumption of
independent gamma priors using the importance sampling procedure. We also
compute the approximate Bayes estimators using Lindley's approximation
technique. We have performed a simulation study and a real data analysis in
order to compare the proposed Bayes estimators with the maximum likelihood
estimators.Comment: This paper is under review in the Austrian Journal of Statistics and
will likely be published ther
Revisiting Relations between Stochastic Ageing and Dependence for Exchangeable Lifetimes with an Extension for the IFRA/DFRA Property
We first review an approach that had been developed in the past years to
introduce concepts of "bivariate ageing" for exchangeable lifetimes and to
analyze mutual relations among stochastic dependence, univariate ageing, and
bivariate ageing. A specific feature of such an approach dwells on the concept
of semi-copula and in the extension, from copulas to semi-copulas, of
properties of stochastic dependence. In this perspective, we aim to discuss
some intricate aspects of conceptual character and to provide the readers with
pertinent remarks from a Bayesian Statistics standpoint. In particular we will
discuss the role of extensions of dependence properties. "Archimedean" models
have an important role in the present framework. In the second part of the
paper, the definitions of Kendall distribution and of Kendall equivalence
classes will be extended to semi-copulas and related properties will be
analyzed. On such a basis, we will consider the notion of "Pseudo-Archimedean"
models and extend to them the analysis of the relations between the ageing
notions of IFRA/DFRA-type and the dependence concepts of PKD/NKD
Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference
Information geometric techniques and inductive inference methods hold great
promise for solving computational problems of interest in classical and quantum
physics, especially with regard to complexity characterization of dynamical
systems in terms of their probabilistic description on curved statistical
manifolds. In this article, we investigate the possibility of describing the
macroscopic behavior of complex systems in terms of the underlying statistical
structure of their microscopic degrees of freedom by use of statistical
inductive inference and information geometry. We review the Maximum Relative
Entropy (MrE) formalism and the theoretical structure of the information
geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special
focus is devoted to the description of the roles played by the sectional
curvature, the Jacobi field intensity and the information geometrodynamical
entropy (IGE). These quantities serve as powerful information geometric
complexity measures of information-constrained dynamics associated with
arbitrary chaotic and regular systems defined on the statistical manifold.
Finally, the application of such information geometric techniques to several
theoretical models are presented.Comment: 29 page
The Weibull-Inverted Exponential Distribution: A Generalization of the Inverse Exponential Distribution
In this paper, the Inverse Exponential
distribution was extended using the weibull generalized family
of distributions. The probability density function (pdf) and
cumulative density function (cdf) of the resulting model were
defined and some of its statistical properties were studied. The
method of maximum likelihood estimation was proposed in
estimating the model parameters. The model was applied to a
real life data set in order to assess its flexibility over its parent
distribution
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