相关论文: Modeling frequency distribution above a priority i…

We revisit Schnieper's model, which decomposes incurred but not reported (IBNR) reserves into two components: reserves for newly reported claims (true IBNR) and reserves for changes over time in the estimated cost of already reported claims…

The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as…

The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information.…

The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…

The Chain-Ladder (CL) method remains the dominant macro-level technique for claims reserving in non-life insurance, yet its classical formulation lacks a coherent probabilistic foundation. Existing stochastic extensions-including the Mack…

The paper proposes an original methodology for constructing quantitative statistical models based on multidimensional distribution functions constructed on the basis of the insurance companies' data on inshurance policies (including…

The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…

Accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, the classification and regression trees…

The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…

The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within…

The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver…

Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…

Prediction of outstanding claims has been done via nonparametric models (chain ladder), semiparametric models (overdispersed poisson) or fully parametric models. In this paper, we propose models based on negative binomial distributions for…

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…

Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…

Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…

Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large…

The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application.…

This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable…