## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (202.106 recursos)

Afrika Statistika

1. #### Comparison between two bivariate Poisson distributions through the phi-divergence

Nganga, Prévot C. Batsindila; Bidounga, Rufin; Mizère, Dominique; Kokonendji, Célestin C.
In the literature, there are two probabilistic models of bivariate Poisson : the model according to Holgate and the model according to Berkhout and Plug. These two models express themselves by their probability mass function. The model of Holgate puts in evidence a strictly positive correlation, which is not always realistic. To remedy this problem, Berkhout and Plug proposed a bivariate Poisson distribution accepting the correlation as well negative, equal to zero, that positive. In this paper, we show that these models are nearly everywhere asymptotically equal. From this survey that the $\phi$-divergence converges toward zero, both models are therefore...

2. #### Bayesian Inference of C-AR(1) Time Series Model with Structural Break

Kumar, Jitendra; Kumar, Ashok; Agiwal, Varun; Shangodoyin, Dahud Kehinde
A variable may be affected by some associated variables which may influence the estimation and testing procedures and also not much important to model separately, such types of variables are called covariates. The present paper dealt the covariate autoregressive (C-AR(1)) time series model with structural break in mean and variance under Bayesian framework. Parameters of the model have been estimated considering appropriate prior assumptions and compared with maximum likelihood estimator. A simulation study has been carried out to validate the theoretical results, and then the same implemented on the monthly REER time series of SAARC countries. Both studies, empirical and...

3. #### Generalized Stacy-Lindley Mixture Distribution

In this paper, we introduce a five parameter extension of mixture of two Stacy gamma distributions called generalized Stacy-Lindley mixture distribution. Several statistical properties are derived. Two types of estimation techniques are used for estimating the parameters. Asymptotic confidence interval is also calculated for these parameters. Finally, a real data application illustrates the performance of our proposed distribution.

4. #### The mode-dispersion approach for constructing continuous associated kernels

Libengue Dobele-Kpoka, Francial Giscard Baudin; Kokonendji, Célestin C.
We introduce the mode-dispersion approach for constructing the (asymmetric) continuous associated kernels fromsuitable parametric probability density functions (p.d.f.) that we shall call the type of kernel. This leads us to value the choice of the associated kernel, since it takes into account the support of the unknown density $f$, to be estimated. All associated kernel density estimators must be without edge effect. For illustrating this, we introduce the extended beta kernel, which is a typical model of kernels with bounded supports. However, in the presence of a large bias of the density estimator, we propose a general but light modification...

5. #### On the strong convergence of the hazard rate and its maximum risk point estimators in presence of censorship and functional explanatory covariate

Agbokou, Komi; Gneyou, Kossi Essona
In the literature much work has been devoted to the non-parametric estimation of survival analysis functions. In this work, we focus on the nonparametric estimation of the conditional hazard rate and the point of its maximum, in the model of right censored data with presence of functional covariate. We establish the almost uniform complete convergence of these estimators at appropriate rates. This generalizes the almost sure convergence obtained in the literature.

6. #### The Kumaraswamy G Exponentiated Gumbel Type-2 Distribution

Okorie, Idika Eke; Akpanta, Anthony Chukwudi; Ohakwe, Johnson; Chikezie, David Chidi; Obi, Eunice Oluchi
The distribution due to Okorie et al. (2016) is further extended to a wider family of distribution called the Kumaraswamy Generalized Exponentiated Gumbel type-2 distribution. Twenty two distributions are identified as sub-models of the new distribution. Some of its important statistical properties are explicitly derived and the parameters of the new distribution are estimated through the method of maximum likelihood estimation.

7. #### A Modified Procedure for Estimating the Population Mean in Two-occasion Successive Samplings

Singh, Housila Prasad; Pal, Surya Kant
This paper addresses the problem of estimating the current population mean in two occasion successive sampling. Utilizing the readily available information on two auxiliary variables on both occasions and the information on study variable from the previous occasion, some new estimation procedures have been developed. Properties of the proposed estimators have been studied and their respective optimum replacement policies are discussed. Relative comparison of efficiencies of the suggested estimators with the sample mean estimator when there is no matching from previous occasion and the optimum successive sampling estimator when no auxiliary information is used have been incorporated. Empirical study is...

8. #### On change-point detection in volatile series using GARCH models

Katchekpele, Edoh; Gneyou, Kossi Essona; Diongue, Abdou Kâ
We study a Cumulative Sum (CUSUM)-type test to detect a change in the unconditional variance of GARCH models. We show that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using Monte Carlo simulation, we demonstrate that the asymptotic power of the test is almost the unity and compare the test result with existing results in the literature. Finally, the test procedure is applied to real-world situation namely the Standard and Poor (S&P) 500 stock market returns (09/16/1980 to 01/31/2008) where we are able to detect a change in the unconditional variance at a very early stage of...

9. #### On change-point detection in volatile series using GARCH models

Katchekpele, Edoh; Gneyou, Kossi Essona; Diongue, Abdou Kâ
We study a Cumulative Sum (CUSUM)-type test to detect a change in the unconditional variance of GARCH models. We show that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using Monte Carlo simulation, we demonstrate that the asymptotic power of the test is almost the unity and compare the test result with existing results in the literature. Finally, the test procedure is applied to real-world situation namely the Standard and Poor (S&P) 500 stock market returns (09/16/1980 to 01/31/2008) where we are able to detect a change in the unconditional variance at a very early stage of...

10. #### An application of optimal control to the effective utilization of a renewable resource

Ibrahim, Mahmud; Benyah, Francis
The study explores the optimal harvesting of renewable resources like fisheries. The fish biomass dynamics is described by a nonlinear growth model that maximizes the total net revenue whilst taking into consideration the sustainable and effective utilization of the resource. In addition, stability dynamics of the model is assessed through bifurcation analysis. Pontryagin's maximum principle is used to derive the optimality system and characterize the optimal control. A numeric iterative method employing the fourth order Runge-Kutta scheme facilitates the solution of the optimality system. The simulation results obtained are then discussed. The results show that the sum of the maximum allowable harvest and the final biomass level must not...

11. #### An application of optimal control to the effective utilization of a renewable resource

Ibrahim, Mahmud; Benyah, Francis
The study explores the optimal harvesting of renewable resources like fisheries. The fish biomass dynamics is described by a nonlinear growth model that maximizes the total net revenue whilst taking into consideration the sustainable and effective utilization of the resource. In addition, stability dynamics of the model is assessed through bifurcation analysis. Pontryagin's maximum principle is used to derive the optimality system and characterize the optimal control. A numeric iterative method employing the fourth order Runge-Kutta scheme facilitates the solution of the optimality system. The simulation results obtained are then discussed. The results show that the sum of the maximum allowable harvest and the final biomass level must not...

12. #### The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

Ben Gherbal, Hanane; Mezerdi, Brahim
This paper is concerned with optimal control of systems driven by stochastic differential equations (SDEs), with jump processes, where the control variable appears in the drift and in the jump term. We study the relaxed problem, in which admissible controls are measure-valued processes and the state variable is governed by an SDE\ driven by a counting measure valued process called relaxed Poisson measure such that the compensator is a product measure. Under some conditions on the coefficients, we prove that every diffusion process associated to a relaxed control is a limit of a sequence of diffusion processes associated to strict controls. As a consequence, we show that the...

13. #### The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

Ben Gherbal, Hanane; Mezerdi, Brahim
This paper is concerned with optimal control of systems driven by stochastic differential equations (SDEs), with jump processes, where the control variable appears in the drift and in the jump term. We study the relaxed problem, in which admissible controls are measure-valued processes and the state variable is governed by an SDE\ driven by a counting measure valued process called relaxed Poisson measure such that the compensator is a product measure. Under some conditions on the coefficients, we prove that every diffusion process associated to a relaxed control is a limit of a sequence of diffusion processes associated to strict controls. As a consequence, we show that the...

14. #### Progressive Censored Burr Type-XII Distribution Under Random Removal Scheme: Some Inferences

Prakash, Gyan
When some sample values at either or both the extremes might have been assorted, a censoring scheme is much useful. Nevertheless, in some reliability experiments, the number of items fell out the experiment cannot be prefixed random in some situations. For such situations, a random removal scheme with censoring scheme may offer a good result. Here, a random removal scheme with the Progressive censoring plan is assumed for statistical inference, when fill out items of the experiments cannot be prefixed. The analysis of the present discussion has carried out with the help of a real data set for the Burr Type-XII distribution.

15. #### Progressive Censored Burr Type-XII Distribution Under Random Removal Scheme: Some Inferences

Prakash, Gyan
When some sample values at either or both the extremes might have been assorted, a censoring scheme is much useful. Nevertheless, in some reliability experiments, the number of items fell out the experiment cannot be prefixed random in some situations. For such situations, a random removal scheme with censoring scheme may offer a good result. Here, a random removal scheme with the Progressive censoring plan is assumed for statistical inference, when fill out items of the experiments cannot be prefixed. The analysis of the present discussion has carried out with the help of a real data set for the Burr Type-XII distribution.

16. #### Network estimation in State Space Models with L1-regularization constraint

Anani, Lotsi; Wit, Ernst
Microarray technologies and related methods coupled with appropriate mathematical and statistical models have made it possible to identify dynamic regulatory networks by measuring time course expression levels of many genes simultaneously. However one of the challenges is the high-dimensional nature of such data coupled with the fact that these gene expression data are known not to include various biological process. As genomic interactions are highly structured, the aim was to derive a method for inferring a sparse dynamic network in a high dimensional data setting. The paper assumes that the observations are noisy measurements of gene expression in the form of mRNAs, whose dynamics can be described by some...

17. #### Network estimation in State Space Models with L1-regularization constraint

Anani, Lotsi; Wit, Ernst
Microarray technologies and related methods coupled with appropriate mathematical and statistical models have made it possible to identify dynamic regulatory networks by measuring time course expression levels of many genes simultaneously. However one of the challenges is the high-dimensional nature of such data coupled with the fact that these gene expression data are known not to include various biological process. As genomic interactions are highly structured, the aim was to derive a method for inferring a sparse dynamic network in a high dimensional data setting. The paper assumes that the observations are noisy measurements of gene expression in the form of mRNAs, whose dynamics can be described by some...

18. #### Influence of the density pole on the performances of its gamma-kernel estimator

Cherfaoui, Mouloud; Boualem, Mohamed; Aïssani, Djamil; Adjabi, Smaïl
In this paper, we aim at highlighting the influence of the density pole on the performances of its gamma-kernel estimator. To do this, we performed a comparative study for the performances of the gamma-kernel estimators with those provided by other bias effect correction techniques at the bounds, using the simulation technique. In conclusion, the results obtained confirm those provided in the literature and show that in some cases the normalization of the gamma estimators can considerably improve local and global performances of the gamma-kernel estimators.

19. #### Influence of the density pole on the performances of its gamma-kernel estimator

Cherfaoui, Mouloud; Boualem, Mohamed; Aïssani, Djamil; Adjabi, Smaïl
In this paper, we aim at highlighting the influence of the density pole on the performances of its gamma-kernel estimator. To do this, we performed a comparative study for the performances of the gamma-kernel estimators with those provided by other bias effect correction techniques at the bounds, using the simulation technique. In conclusion, the results obtained confirm those provided in the literature and show that in some cases the normalization of the gamma estimators can considerably improve local and global performances of the gamma-kernel estimators.

20. #### A modified Champernowne transformation to improve boundary effect in kernel distribution estimation

Tour, Madiha; Sayah, Abdallah; Yahia, Djebrane
Kernel distribution estimators are not consistent near the boundary of its support. Several solutions to this problem have already been proposed. In this paper, we propose a new kernel estimation of the cumulative distribution function for heavy tailed distributions based on the method of the transformation of the data set with a modification of the Champernowne distribution and the generalized reflection method of boundary correction for kernel distribution estimation. The asymptotic bias, variance and mean squared error of the proposed estimator are given. Simulations are drawn to show that the proposed method perform quite well when compared with other existing methods.

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