## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (191.996 recursos)

Afrika Statistika

1. #### An Extended Power Lindley Distribution and its Application

ELBATAL, Ibrahim; EL GEBALY, Yehia Mousa; AMIN, Essam Ali
This paper introduces a new five-parameter lifetime model called the exponentiated Kumaraswamy power Lindley distribution, that extends the power Lindley distribution and some well-known distributions. Various structural properties of the new model including expansions for the density function, explicit expressions for the ordinary and conditional moments, residual and reversed residual life functions and mean deviations are derived. The maximum likelihood method is used to estimate the model parameters. The usefulness and flexibility of the proposed model are illustrated empirically by means of two real data sets.

2. #### Robust Bayesian Inference of Generalized Pareto Distribution

MOKRANI, Fatiha; FELLAG, Hocine; NECIR, Abdelhakim
In this work, robust Bayesian estimation of the generalized Pareto distribution is proposed. The methodology is presented in terms of oscillation of posterior risks of the Bayesian estimators. By using a Monte Carlo simulation study, we show that, under a suitable generalized loss function, we can obtain a robust Bayesian estimator of the model.

3. #### Sparse Gaussian graphical mixture model

ANANI, Lotsi; WIT, Ernst
This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables coupled with the degenerate nature of the likelihood. We propose as a solution a penalized maximum likelihood technique by imposing an l1 penalty on the precision matrix. Our approach shrinks the parameters thereby resulting in better identifiability and variable selection.

4. #### Nonparametric confidence intervals for tail dependence based on copulas

SECK, Cheikh Tidiane; DIAM, Ba; LO, Gane Samb
We propose nonparametric asymptotic confidence intervals for the upper and lower tail dependence coefficients. These latter are obtained from confidence bands established for the copula function itself and based upon three kernel-type estimators. We show the performance of these confidence intervals through a simulation study. We also apply these results to financial data stemming from the CAC 40 stock index which reveals the existence of extreme dependence between larger values of the opening and closing prices for this index during the considered period.

5. #### Moderate deviations principle for the kernel estimator of nonrandom regression functions

The aim of this paper is to provide pointwise and uniform moderate deviations principles for the kernel estimator of a nonrandom regression function. Moreover, we give an application of these moderate deviations principles to the construction of confidence regions for the regression function.

6. #### Impact of the stability bound choice on the approximation of ruin probabilities

BERECHE, Aicha; CHERFAOUI, Mouloud; AÏSSANI, Djamil
This paper aims to establish the effect of the choice of a stability bound for the ruin probability on the quality of the approximation of the characteristics (ruin probabilities) of two classical risk models to approach (ideal an perturbed models) regarding to different large claims. In particular, we use two versions of the strong stability method: strong stability of a Markov chain and strong stability of a Lindley process. A comparative study, based on numerical results obtained by simulation, is performed between the two versions.

7. #### Asymptotic Normality of Non-parametric Estimator for the FGT Poverty Index with when the parameter is strictly between 0 and 1

CISS, Youssou; DIAKHABY, Aboubakary
In this paper, we study the kernel estimator of Foster, Greer and Thorbecke class of measures when the poverty aversion parameter is strictly between zero and one, as a genreralization of the work of Dia(2016). We solved an open problem arising in mentioned paper. The asymptotic normality of the estimator is established. As an illustration, we determine the confidence intervals for different regions of Senegal. The study of this application demonstrated that our methodology is not only more efficient than the empirical estimator, but it also provides better confidence intervals for the poverty index.

8. #### Robust bayesian analysis of an autoregressive model with exponential innovations

LARBI, Lydia; FELLAG, Hocine
In this work, robust Bayesian analysis of the Bayesian estimation of an autoregressive model with exponential innovations is performed. Using a Bayesian robustness methodology, we show that, using a suitable generalized quadratic loss, we obtain optimal Bayesian estimators of the parameters corresponding to the smallest oscillation of the posterior risks.

9. #### On Misclassification Probabilities of Linear and Quadratic Classifiers

MAKINDE, Olusola Samuel
We study the theoretical misclassification probability of linear and quadratic classifiers and examine the performance of these classifiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift.

10. #### Association measures and estimation of copula parameters

Benelmir, Imane; Meraghni, Djamel
We apply the inversion method of estimation, with several combinations of two among the four most popular association measures, to estimate the parameters of copulas in the case of bivariate distributions. We carry out a simulation study with two examples, namely Farlie-Gumbel-Morgenstern and Marshall-Olkin two-parameter copulas to make comparisons between the obtained estimators, with respect to bias and root of the mean squared error.

11. #### A pseudo Lindley distribution and its application

ZEGHDOUDI, Halim; NEDJAR, Sihem
In this paper, we introduce a new distribution named as the Pseudo Lindley Distribution (PsLD) as a generalization of the Lindley distribution (LD). A full and detailed description are provided in terms of moments, cumulates, characteristic function, failure, rate function, stochastic ordering, distributions of sums, and parameters estimation. Simulations studies and data driven applications are also reported.

12. #### Statistical properties of the Seasonal Fractionally Integrated Separable Spatial Autoregressive Model

CISSE, Papa Ousmane; DIONGUE, Abdou Kâ; GUEGAN, Dominique
In this paper we introduce a new model called Fractionally Integrated Separable Spatial Autoregressive processes with Seasonality and denoted Seasonal FISSAR. We focus on the class of separable spatial models whose correlation structure can be expressed as a product of correlations. This new modelling allows taking into account the seasonality patterns observed in spatial data. We investigate the properties of this new model providing stationary conditions, some explicit form of the autocovariance function and the spectral density. We also establish the asymptotic behaviour of the spectral density function near the seasonal frequencies.

13. #### Statistical estimate of the proportional hazard premium of loss under random censoring

LOUIZA, Soltane; DJAMEL, Meraghni; NECIR, Abdelhakim
Many insurance premium principles are defined and various estimation procedures introduced in the literature. In this paper, we focus on the estimation of the excess-of-loss reinsurance premium when losses are randomly censored. The asymptotic normality of the proposed estimator is established under suitable conditions and its performance evaluated through sets of simulated data.

14. #### Robust estimator of distortion risk premiums for heavy-tailed losses

BRAHIMI, Brahim; ZOUBIR, Kenioua
We use the so-called t-Hill tail index estimator proposed by Fabián (2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of losses. Under the second-order condition of regular variation, we establish its asymptotic normality. By simulation study, we show that this new estimator is more robust than of Necir and Meraghni (2009) both for small and large samples.

15. #### A review on asymptotic normality of sums of associated random variables

GANE SAMB, LO; HAROUNA, Sangare; NDIAYE, Cheikhna Hamallah
Association between random variables is a generalization of independence of these random variables. This concept is more and more commonly used in current trends in any research fields in Statistics. In this paper, we proceed to a simple, clear and rigorous introduction to it. We will present the fundamental asymptotic normality theorem on stationary and associated sequences of random variables. A coherent and modern frame is used. This review will be profitable to new researchers in the topic.

16. #### Improved Randomized Response Technique for Two Sensitive Attributes

EWEMOOJE, Olusegun S.; AMAHIA, Godwin N.
We proposed new and more efficient estimators for estimating population proportion of respondents belonging to two related sensitive attributes in survey sampling by extending the work of Mangat(1994). Our proposed estimators are more efficient than Lee et al. (2013) simple and crossed model estimators as the population proportion of possessing the sensitive attribute increases.

17. #### Bilinear regression model with Kronecker and linear structures for the covariance matrix

NZABANIT, Joseph; VON ROSEN, Dietrich; SINGULL, Martin
In this paper, the bilinear regression model based on normally distributed random matrix is studied. For these models, the dispersion matrix has the so called Kronecker product structure and they can be used for example to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations in a flip-flop relation are established and the consistency of estimators is studied.

18. #### Some Inferences on Truncated Generalized Cauchy Distribution

Rider(1957) introduced the generalized Cauchy distribution. In this paper we will consider a truncated version of the generalized Cauchy distribution. One possible use of the model is in life testing problem when the domain of application is non negative. Here we will consider several distributional properties of the truncated generalized Cauchy distribution. Someome characterizations of this distribution based on truncated moments, order statistics and record values, will be given.

20. #### Reliability of linear and circular consecutive-$k$-out-of-$n$ systems with shock model
A consecutive k-out-of-n system consists of an ordered sequence of $n$ components, such that the system functions if and only if at least $k$ $(k\leq n)$ consecutive components function. The system is called linear ($L$) or circular ($C$) depending on whether the components are arranged on a straight line or form a circle. In the first part, we use a shock model to obtain the reliability function of consecutve-k-out-of-n systems with dependent and nonidentical components. In the second part, we treat some numerical examples to show the derive results and deduce the failure rate of each component and the system.