Afrika Statistika最新文献

{"title":"On Nonparametric Estimation of a Nonparametric Autoregressive Conditionally Heteroscedastic Process","authors":"Ben Célestin Kouassi, O. Hili, Edoh Katchekpele","doi":"10.16929/as/2022.3318.307","DOIUrl":"https://doi.org/10.16929/as/2022.3318.307","url":null,"abstract":"Since the studies of Engel (1982) and Bollerslev (1986), the ARCH and GARCH processes have been used extensively to model volatile series. However, Pagan and Schwert (1990) have shown the limits of these choices. This deficiency is overcome by the NonParametric AutoRegressive Conditionally Heteroscedastic (NPARCH) processes. In this work, we use the Nadaraya-Watson method to estimate the autoregression and volatility functions of a NPARCH process. We show the strong consistency and the asymptotic normality of these estimators. Through brief simulations, we illustrate these two properties.","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117063405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Nonparametric Conditional Quantile Estimation for Non-stationary Random","authors":"Ben Célestin Kouassi, Ouagnina Hili, Edoh Katchekpele","doi":"10.16929/as/2022.3293.307","DOIUrl":"https://doi.org/10.16929/as/2022.3293.307","url":null,"abstract":"Since the studies of Engel (1982) and Bollerslev (1986), the ARCH and GARCH processes have been used extensively to model volatile series. However, Pagan and Schwert (1990) have shown the limits of these choices. This deficiency is overcome by the NonParametric AutoRegressive Conditionally Heteroscedastic (NPARCH) processes. In this work, we use the Nadaraya-Watson method to estimate the autoregression and volatility functions of a NPARCH process. We show the strong consistency and the asymptotic normality of these estimators. Through brief simulations, we illustrate these two properties.","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"226 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130798028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Kumaraswamy Pseudo-Lindley distribution : statistical properties, extremal characterization and record values","authors":"Moumouni Diallo, Modou Ngom, A. M. Fall, G. Lo","doi":"10.16929/as/2022.3259.306","DOIUrl":"https://doi.org/10.16929/as/2022.3259.306","url":null,"abstract":"The Pseudo-Lindley distribution is generalized in this paper by using the Kumaraswamy-G distribution developed by Cordeiro et al. (2010a). By fusing the Pseudo-Lindley distribution in the Kumaraswamy generator of distribution, we present a new unique four parameters of continuous model of distribution titled the Kumaraswamy Pseudo-Lindley distribution (Kum-PL). The moments and related measures, moment generating function , order statistic, uniform quantile and extremal quantile function are all carefully examined as basic statistical aspects of the new distribution. Moreover, the extremal characterizations and record values of the new model are investigated. The proposed distribution parameters were evaluated using the maximum likelihood procedures. The stability of the parameter estimations is explored using a Monte Carlo simulation study","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129055952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic normality for kernel weighted averages estimation","authors":"Brahima Soro, O. Hili","doi":"10.16929/as/2022.3237.305","DOIUrl":"https://doi.org/10.16929/as/2022.3237.305","url":null,"abstract":"This paper presents a set of general normality results for kernel weighted averages. We extend existing results in literature for independent data a s in Yao (2017) to stationary dependent longitudinal data. The asymptotic properties of the proposed weighted averages are investigated under (alpha)-mixing conditions. These results are useful for covariance function estimation based on nonparametric kernel method.","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122141242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Choice of the spectral window width by cross-validation: Case of the almost periodically correlated process with continuous time","authors":"Sylvestre Placide Ekra, V. Monsan","doi":"10.16929/as/2022.3217.303","DOIUrl":"https://doi.org/10.16929/as/2022.3217.303","url":null,"abstract":"This work presents a procedure to choose the width of the spectral window used in the smoothing of a periodogram when estimating the spectral density of an almost periodically correlated process. The cross-validation procedure we propose is based on the estimation of the integrated square error using the \"Leave-out-I\" principle.","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131522654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on a modification of the adaptive kernel density estimation of income distribution and poverty index via the range}","authors":"Baradine Zakaria, Youssou Ciss","doi":"10.16929/as/2022.3189.301","DOIUrl":"https://doi.org/10.16929/as/2022.3189.301","url":null,"abstract":"In this paper we propose an estimator of Foster, Greer and Thorbecke class of poverty measures. The new estimator is constructed with adaptive kernel and the bandwidth of the new improvement is obtained depending on the range of the observations. Simulated example is presented, including comparisons with four others estimators. The performance of the proposed new estimator is evaluated via the variance and the mean square error criterion. The results of the simulation study are very promising; they show that our modified estimator performs well in all cases.","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"111 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124412384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compound Joint-life Annuity Frailty Modeling","authors":"W. Onchere, P. Weke, J. Ottieno, C. Ogutu","doi":"10.16929/2022.3199.302","DOIUrl":"https://doi.org/10.16929/2022.3199.302","url":null,"abstract":"Grouping insureds in clusters such as joint-life annuities imposes statistical dependence. In this paper, we propose the shared compound frailty approach in collective valuation of joint-life annuity products where most applications have been in bio-statistics. The positive stable compound process used entails the frailty mixing distribution with the weighted exponential, generalized exponential and weighted Weibull as the base force of mortality distributions calibrated on a large Kenyan insurer joint-life last-survivor dataset. The findings shows that the positive stable generalized exponential model addresses time-varying heterogeneity effects positively and negatively associated with dependence","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"366 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134426079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modelling Skewed and Heavy-tailed Data Using a Normal Weighted Inverse Gaussian Distribution","authors":"Calvin B. Maina, P. Weke, C. Ogutu, J. Ottieno","doi":"10.16929/as/20212.3165.300","DOIUrl":"https://doi.org/10.16929/as/20212.3165.300","url":null,"abstract":"The normal distribution is inadequate in capturing skewed and heavy-tailed behaviour of data taken over short time intervals. In addition the data can be leptokurtic. For this reason a normal weighted inverse Gaussian distribution is proposed as an alternative to the normal inverse Gaussian distribution to handle such data. The mixing distribution used in the normal variance mean mixture is a finite mixture of two special cases of Generalized Inverse Gaussian ((textit{GIG})) distribution. The two special cases and the finite mixture are weighted inverse Gaussian distribution. The motivation for this work is that a finite mixture is more flexible than a single/standard distribution. The (textit{EM})-algorithm has been used for parameter estimation.","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129462628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modification of the adaptive kernel density estimation of income distribution and poverty index using the arithmetic mean","authors":"Youssou Ciss, Baradine Zakaria","doi":"10.16929/as/2022.3115.197","DOIUrl":"https://doi.org/10.16929/as/2022.3115.197","url":null,"abstract":"The new estimator is constructed with adaptive kernel and the bandwidth of the new improvement is obtained depending on the arithmetic mean of the observations. A simulated example is presented, including comparisons with three others estimators. The performance of the proposed new estimator is evaluated via the variance and the mean square error criterion. The results of the simulation study were very promising; they show that our modified estimator performs well in all cases.","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122100831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase Type Zero Truncated Poisson Lindley Distributions and their application in modeling Secondary Cancer Cases","authors":"Cynthia Mwende Mwau, P. Weke, Bundi Davis Ntwiga, J. Ottieno","doi":"10.16929/as/20212.3145.199","DOIUrl":"https://doi.org/10.16929/as/20212.3145.199","url":null,"abstract":"Insurance of chronic illness is slowly gaining ground in Kenya which has lead to insurance firms introducing insurance products of chronic illness among them being cancer insurance policies. However, unlike other chronic illnesses, cancer can move from the organ of origin to another which will consequently lead to increased cost of treatment. This can not be modeled using ordinary distributions hence it has become an area of interest for many researchers. Zero-truncated phase type distributions are used to solve this drawback of ordinary distributions as it can in-cooperate these transitions while modeling claim count data. They further improve modeling of claim count data as they only consider positive values of claim count excluding zeros. This is the nature of real claim count data as zero claim frequency can not attract any claim severity amount. In this paper aggregate claim losses of secondary cancers in Kenya are estimated using Zero-truncated Poisson Lindley distributions. Zero-truncated one parameter as well as Zero-truncated two parameter Poisson Lindley distributions are derived. Their compound probability generating functions are also constructed. The transitions states of secondary cancer states are estimated using continuous Chapman Kolmogorov equation and used as the matrix parameters for the claim count distributions. Pareto, Generalized Pareto, Weibull, OPPL and TPPL distributions are the distributions considered in this research in modeling claim numbers. This study concludes that aggregate losses of secondary cancer cases using Kenyan data are best modeled by PH-ZTOPPL Generalized Pareto model for PH-ZTOPPL distribution models while for PH-ZTTPPL distribution models the best model was PH-ZTTPPL-Generalized Pareto model. The two best models were compared and PH-ZTTPPL-Generalized Pareto model was proven to be the best model. Comparing this model with PH-TPPL Generalized Pareto model from earlier research PH-TPPL Generalized Pareto model proved to be a better model implying that zero claim count data should be considered in estimation of aggregate losses","PeriodicalId":430341,"journal":{"name":"Afrika Statistika","volume":"52 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116836918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}