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The \(\alpha\)-Mixture of Cumulative Distribution Functions: Properties, Applications to Parallel System and Stochastic Comparisons
Heterogeneity in populations or components is one of the most important issues in the reliability theory, and should be considered in the relevant...
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Recursive Kernel Density Estimation and Optimal Bandwidth Selection Under α: Mixing Data
In this paper, we extend the work of Slaoui (J Probab Stat, https://doi.org/10.1155/2014/739640 ,
2014 ) to the case of strong mixing data. Then, we... -
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A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model
In this manuscript, we present exponential inequalities for spatial lattice processes which take values in a separable Hilbert space and satisfy...
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Introduction to Mixture Models
In Chap. 1, we introduce the fundamental concept of a statistical model and provide a detailed definition of both mixture models and finite mixture...
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Rate of Convergence
The fundamental requirement in data analysis is the consistent estimation of a parameter. As the sample size increases, the precision of the...
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Modified Likelihood Ratio Test
While achieving a profound understanding of the limiting distribution of the likelihood ratio test under mixture models is indeed a grand success,...
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Modified Likelihood Ratio Test for Higher Order
Chapter 12 centers around the modified likelihood test for high-order null hypotheses within the finite mixture model. While the fundamental concept...
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New copula families and mixing properties
We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new...
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Test of Homogeneity
The quest for effective tests of homogeneity within mixture models has a long history. An illustrative example provided by Hartigan shows that the...
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em-Test for Univariate Finite Gaussian Mixture Models
While the success of the EM-test in the previous two chapters was confined to finite mixture models with subpopulation distributions belonging to a...
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Parameter Estimation for Some Discretely Observed Class of Stable Driven Stochastic Differential Equations
In this paper, we consider the problem of parameter estimation for a real stochastic model observed at some discrete times, that is a solution of a...
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Some practical and theoretical issues related to the quantile estimators
The paper contains the comparative analysis of the efficiency of different qunatile estimators for various distributions. Additionally, we show...
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On Mathai–Haubold Past Entropy Measure
In this paper, Mathai–Haubold past entropy measure is proposed and its properties are studied. Also some generalized inequalities related to...
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A Simple Isotropic Correlation Family in \({\mathbb R}^3\) with Long-Range Dependence and Flexible Smoothness
Most geostatistical applications use covariance functions that display short-range dependence, in part due to the wide variety and availability of...
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Clustering Circular Data via Finite Mixtures of von Mises Distributions and an Application to Data on Wind Directions
The von Mises distribution, which is also known as the Circular Normal distribution is a well-studied and commonly used distribution for analyzing...
