An approximation for simuiation of gamma distributions

1975 ◽  
Vol 3 (3) ◽  
pp. 225-232 ◽  
Author(s):  
Donald J. Wheeler
Keyword(s):  
Gamma Distributions

scholarly journals Zero-inflated-censored Weibull and gamma regression models to estimate wild boar population dispersal distance

2021 ◽  
Author(s):  
Eduardo de Freitas Costa ◽  
Silvana Schneider ◽  
Giulia Bagatini Carlotto ◽  
Tainá Cabalheiro ◽  
Mauro Ribeiro de Oliveira Júnior
Keyword(s):  
Wild Boar ◽  
Regression Models ◽  
Likelihood Function ◽  
Complex Structure ◽  
Dispersal Distance ◽  
Wild Boar Population ◽  
Gamma Distributions ◽  
Excess Of Zeros ◽  
Censored Observations ◽  
Positive Effect

AbstractThe dynamics of the wild boar population has become a pressing issue not only for ecological purposes, but also for agricultural and livestock production. The data related to the wild boar dispersal distance can have a complex structure, including excess of zeros and right-censored observations, thus being challenging for modeling. In this sense, we propose two different zero-inflated-right-censored regression models, assuming Weibull and gamma distributions. First, we present the construction of the likelihood function, and then, we apply both models to simulated datasets, demonstrating that both regression models behave well. The simulation results point to the consistency and asymptotic unbiasedness of the developed methods. Afterwards, we adjusted both models to a simulated dataset of wild boar dispersal, including excess of zeros, right-censored observations, and two covariates: age and sex. We showed that the models were useful to extract inferences about the wild boar dispersal, correctly describing the data mimicking a situation where males disperse more than females, and age has a positive effect on the dispersal of the wild boars. These results are useful to overcome some limitations regarding inferences in zero-inflated-right-censored datasets, especially concerning the wild boar’s population. Users will be provided with an R function to run the proposed models.

scholarly journals Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 908
Author(s):  
Perla Celis ◽  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Héctor W. Gómez
Keyword(s):  
Survival Data ◽  
Maximum Likelihood Estimates ◽  
New Class ◽  
New Family ◽  
Gamma Distributions ◽  
Special Cases ◽  
Log Normal ◽  
Positive Support ◽  
Positive Distributions ◽  
Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

mvClaim : an R package for multivariate general insurance claims severity modelling

2021 ◽  
pp. 1-17
Author(s):  
Sen Hu ◽  
T. Brendan Murphy ◽  
Adrian O’Hagan
Keyword(s):  
R Package ◽  
Finite Mixture ◽  
Current Version ◽  
Mixture Of Experts ◽  
Insurance Claim ◽  
General Insurance ◽  
Gamma Distributions ◽  
Approach Theory ◽  
Modelling Approach ◽  
Model Family

Abstract The mvClaim package in R provides flexible modelling frameworks for multivariate insurance claim severity modelling. The current version of the package implements a parsimonious mixture of experts (MoE) model family with bivariate gamma distributions, as introduced in Hu et al., and a finite mixture of copula regressions within the MoE framework as in Hu & O’Hagan. This paper presents the modelling approach theory briefly and the usage of the models in the package in detail. This package is hosted on GitHub at https://github.com/senhu/.

scholarly journals On Genetic Map Functions

Genetics ◽  
1996 ◽  
Vol 142 (4) ◽  
pp. 1369-1377
Author(s):  
Hongyu Zhao ◽  
Terence P Speed
Keyword(s):  
Genetic Distance ◽  
Genetic Map ◽  
Probability Model ◽  
Recombination Fraction ◽  
Renewal Processes ◽  
Gamma Distributions ◽  
Multilocus Analysis ◽  
Map Function ◽  
Better Than

Abstract Various genetic map functions have been proposed to infer the unobservable genetic distance between two loci from the observable recombination fraction between them. Some map functions were found to fit data better than others. When there are more than three markers, multilocus recombination probabilities cannot be uniquely determined by the defining property of map functions, and different methods have been proposed to permit the use of map functions to analyze multilocus data. If for a given map function, there is a probability model for recombination that can give rise to it, then joint recombination probabilities can be deduced from this model. This provides another way to use map functions in multilocus analysis. In this paper we show that stationary renewal processes give rise to most of the map functions in the literature. Furthermore, we show that the interevent distributions of these renewal processes can all be approximated quite well by gamma distributions.

scholarly journals How Biased Is Aircraft Cloud Sampling?

2016 ◽  
Vol 33 (1) ◽  
pp. 185-189 ◽  
Author(s):  
Paul R. Field ◽  
Kalli Furtado
Keyword(s):  
Order Statistics ◽  
Sampling Strategy ◽  
Model Testing ◽  
Resource Limitations ◽  
Cloud Properties ◽  
Gamma Distributions

AbstractAircraft are the dominant method for in situ sampling of cloud properties. Resource limitations mean that aircraft tend to follow a sampling strategy when there is more than one cloud from which to choose. This can result in biased cloud statistics that are used for parameterization development and model testing. In this study, order statistics are used to estimate the potential magnitude of this bias when a strategy based on choosing the larger cloud is employed. It is found for cloud properties following gamma distributions that a typical bias of a factor of 1.5 can result when the larger of two clouds is repeatedly chosen for sampling.

scholarly journals On the free Gamma distributions

2014 ◽  
Vol 63 (4) ◽  
pp. 1159-1194 ◽  
Author(s):  
Steen Thorbjornsen ◽  
Uffe Haagerup
Keyword(s):  
Gamma Distributions

NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS

2018 ◽  
Vol 49 (1) ◽  
pp. 169-187 ◽  
Author(s):  
Zhehao Zhang
Keyword(s):  
Infinite Time ◽  
Catastrophe Insurance ◽  
Compound Poisson ◽  
Gamma Distributions ◽  
Time Period ◽  
Heavy Tailed

AbstractThis paper focuses on the distribution of Poisson sums of discounted claims over a finite or infinite time period. It gives two new results when claim amounts follow Mittag-Leffler distributions and two new results when claim amounts follow gamma distributions. Further, as Mittag-Leffler distribution is of heavy-tailed nature and its moments only exist for order strictly smaller than one, this distribution can be used for modelling insurance whose claim amounts are extremely large, that is, catastrophe insurance.

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