检索结果-南通市图书馆

Estimation of Aggregate Losses of Secondary Cancer Using PH-OPPL and PH-TPPL Distributions

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Open Journal of Statistics 2021年第5期11卷 838-853页

作者： Cynthia Mwende Patrick Weke Davis Bundi joseph ottieno Department of Mathematics and Actuarial Science Kisii University Kisii Kenya School of Mathematics University of Nairobi Nairobi Kenya

Kenyan insurance firms have introduced insurance policies of chronic illnesses like cancer; however, they have faced a huge challenge in the pricing of these policies as cancer can transit into different stages, which consequently leads to variation in the cost of treatment. This has made the estimation of aggregate losses of diseases which have multiple stages of transitions such as cancer, an area of interest of many insurance firms. Mixture phase type distributions can be used to solve this setback as they can in-cooperate the transition in the estimation of claim frequency while also in-cooperating the heterogeneity aspect of claim data. In this paper, we estimate the aggregate losses of secondary cancer cases in Kenya using mixture phase type Poisson Lindley distributions. Phase type (PH) distributions for one and two parameter Poisson Lindley are developed as well their compound distributions. The matrix parameters of the PH distributions are estimated using continuous Chapman Kolmogorov equations as the disease process of cancer is continuous while severity is modeled using Pareto, Generalized Pareto and Weibull distributions. This study shows that aggregate losses for Kenyan data are best estimated using PH-OPPL-Weibull model in the case of PH-OPPL distribution models and PH-TPPL-Generalized Pareto model in the case of PH-TPPL distribution models. Comparing the two best models, PH-OPPL-Weibull model pr

关键词： PH One Parameter Poisson Lindley PH Two Parameter Poisson Lindley PH Three Parameter Poisson Linldey Discrete Fourier Transform Discretization

Gamma-Generalized Inverse Gaussian Class of Distributions

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Open Journal of Statistics 2021年第6期11卷 1026-1043页

作者： Richard L. K. Tinega Joash M. Kerongo joseph A. M. ottieno Kisii University Kisii Kenya

Gamma distribution nests exponential, chi-squared and Erlang distributions;while generalized Inverse Gaussian distribution nests quite a number of distributions. The aim of this paper is to construct a gamma mixture using Generalized inverse Gaussian mixing distribution. The rth moment of the mixture is obtained via the rth moment of the mixing distribution. Special cases and limiting cases of the mixture are deduced.

关键词： GIG Mixture Special Cases Limiting Cases Gamma Mixing Distribution

A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied Mathematics 2022年第2期13卷 163-177页

作者： Calvin B. Maina Patrick G. O. Weke Carolyne A. Ogutu joseph A. M. ottieno Department of Mathematics and Actuarial Science Kisii University Kisii Kenya School of Mathematics University of Nairobi Nairobi Kenya

High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.

关键词： Inverse Gaussian Finite Mixture Weighted Distribution Mixed Model EM-Algorithm

A Finite Mixture of Generalised Inverse Gaussian with Indexes -1/2 and -3/2 as Mixing Distribution for Normal Variance Mean Mixture with Application

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Open Journal of Statistics 2021年第6期11卷 963-976页

Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mixture model. The mixing distribution is a finite mixture of two special cases of Generalised Inverse Gaussian distribution with indexes -1/2 and -3/2. The parameters of the mixed model are obtained via the Expectation-Maximization (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.

关键词： Finite Mixture Weighted Distribution Mixed Model EM-Algorithm

A Special Weight for Inverse Gaussian Mixing Distribution in Normal Variance Mean Mixture with Application

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Open Journal of Statistics 2021年第6期11卷 977-992页

Normal Variance-Mean Mixture (NVMM) provides a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, i.e. daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-Nielsen (1977) which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, i.e., the index parameter of the GIG is . The NIG is very popular because of its analytical tractability. In the mixing mechanism, the mix

关键词： Finite Mixture Weighted Distribution Mixed Model EM-Algorithm