scholarly journals Series evaluation of Tweedie exponential dispersion model densities

2005 ◽  
Vol 15 (4) ◽  
pp. 267-280 ◽  
Author(s):  
Peter K. Dunn ◽  
Gordon K. Smyth
Keyword(s):  
Dispersion Model ◽  
Exponential Dispersion Model ◽  
Series Evaluation

scholarly journals THE FULL TAILS GAMMA DISTRIBUTION APPLIED TO MODEL EXTREME VALUES

2017 ◽  
Vol 47 (3) ◽  
pp. 895-917 ◽  
Author(s):  
Joan del Castillo ◽  
Jalila Daoudi ◽  
Isabel Serra
Keyword(s):  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Extreme Values ◽  
Dispersion Model ◽  
Value Theory ◽  
Quantitative Modelling ◽  
Exponential Distributions ◽  
Exponential Dispersion Model ◽  
Aggregate Loss ◽  
Very High

AbstractIn this paper, we introduce the simplest exponential dispersion model containing the Pareto and exponential distributions. In this way, we obtain distributions with support (0, ∞) that in a long interval are equivalent to the Pareto distribution; however, for very high values, decrease like the exponential. This model is useful for solving relevant problems that arise in the practical use of extreme value theory. The results are applied to two real examples, the first of these on the analysis of aggregate loss distributions associated to the quantitative modelling of operational risk. The second example shows that the new model improves adjustments to the destructive power of hurricanes, which are among the major causes of insurance losses worldwide.

scholarly journals Spatial and Seasonal Variations and Inter-Relationship in Fitted Model Parameters for Rainfall Totals across Australia at Various Timescales

Climate ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 4 ◽  
Author(s):  
Md Masud Hasan ◽  
Barry F. W. Croke ◽  
Fazlul Karim
Keyword(s):  
Probabilistic Models ◽  
Dispersion Model ◽  
Synthetic Data ◽  
Daily Rainfall ◽  
Seasonal Rainfall ◽  
Model Parameters ◽  
Exponential Dispersion Model ◽  
Gamma Distributions ◽  
Using Data ◽  
Combined Data

Probabilistic models are useful tools in understanding rainfall characteristics, generating synthetic data and predicting future events. This study describes the results from an analysis on comparing the probabilistic nature of daily, monthly and seasonal rainfall totals using data from 1327 rainfall stations across Australia. The main objective of this research is to develop a relationship between parameters obtained from models fitted to daily, monthly and seasonal rainfall totals. The study also examined the possibility of estimating the parameters for daily data using fitted parameters to monthly rainfall. Three distributions within the Exponential Dispersion Model (EDM) family (Normal, Gamma and Poisson-Gamma) were found to be optimal for modelling the daily, monthly and seasonal rainfall total. Within the EDM family, Poisson-Gamma distributions were found optimal in most cases, whereas the normal distribution was rarely optimal except for the stations from the wet region. Results showed large differences between regional and seasonal ϕ-index values (dispersion parameter), indicating the necessity of fitting separate models for each season. However, strong correlations were found between the parameters of combined data and those derived from individual seasons (0.70–0.81). This indicates the possibility of estimating parameters of individual season from the parameters of combined data. Such relationship has also been noticed for the parameters obtained through monthly and daily models. Findings of this research could be useful in understanding the probabilistic features of daily, monthly and seasonal rainfall and generating daily rainfall from monthly data for rainfall stations elsewhere.

Stationary Time Series Models with Exponential Dispersion Model Margins

1998 ◽  
Vol 35 (01) ◽  
pp. 78-92 ◽  
Author(s):  
Bent Jørgensen ◽  
Peter Xue-Kun Song
Keyword(s):  
Time Series ◽  
Dispersion Model ◽  
Moving Average ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Infinitely Divisible ◽  
Finite Moment ◽  
Exponential Dispersion Model ◽  
Exponential Dispersion Models ◽  
Moving Average Processes

We consider a class of stationary infinite-order moving average processes with margins in the class of infinitely divisible exponential dispersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued time series. As a special case we obtain a class of autoregressive moving average processes that are different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distributions with finite moment generating functions, hereunder many known discrete, continuous and mixed distributions.

Stationary Time Series Models with Exponential Dispersion Model Margins

1998 ◽  
Vol 35 (1) ◽  
pp. 78-92 ◽  
Author(s):  
Bent Jørgensen ◽  
Peter Xue-Kun Song
Keyword(s):  
Time Series ◽  
Dispersion Model ◽  
Moving Average ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Infinitely Divisible ◽  
Finite Moment ◽  
Exponential Dispersion Model ◽  
Exponential Dispersion Models ◽  
Moving Average Processes

We consider a class of stationary infinite-order moving average processes with margins in the class of infinitely divisible exponential dispersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued time series. As a special case we obtain a class of autoregressive moving average processes that are different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distributions with finite moment generating functions, hereunder many known discrete, continuous and mixed distributions.

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