Univariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applications

Gómez–Déniz, Emilio; Sarabia, José Marı́a; Calderín–Ojeda, Enrique

doi:10.1016/j.insmatheco.2006.12.001

Cited by 33 publications

(25 citation statements)

References 13 publications

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“…The first two moments about zero and the factorial moment of order k of a negative binomial distribution are given respectively by Gómez et al (2008):…”

Section: Methodsmentioning

confidence: 99%

“…Gómez et al (2008) showed that the factorial moment of order k of a mixed negative binomial distribution where p = exp(-λ) can be obtained by using:…”

Section: Methodsmentioning

confidence: 99%

“…The mixing of negative binomial with inverse Gaussian which considers the reparameterization of p = exp(-λ) was introduced by Gómez et al (2008) who considered the distribution in univariate and multivariate versions and estimated the parameters using the method of moment and the maximum likelihood estimation. The distribution of PoissonLindley for modeling count data was introduced by Sankaran (1970).…”

Section: Introductionmentioning

confidence: 99%

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Negative Binomial-Lindley Distribution and Its Application

Zamani

Ismail²

2010

Journal of Mathematics and Statistics

105

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Problem statement: The modeling of claims count is one of the most important topics in actuarial theory and practice. Many attempts were implemented in expanding the classes of mixed and compound distributions, especially in the distribution of exponential family, resulting in a better fit on count data. In some cases, it is proven that mixed distributions, in particular mixed Poisson and mixed negative binomial, provided better fit compared to other distributions. Approach: In this study, we introduce a new mixed negative binomial distribution by mixing the distributions of negative binomial (r,p) and Lindley (θ), where the reparameterization of p = exp(-λ) is considered. Results: The closed form and the factorial moment of the new distribution, i.e., the negative binomial-Lindley distribution, are derived. In addition, the parameters estimation for negative binomial-Lindley via the method of moments (MME) and the Maximum Likelihood Estimation (MLE) are provided. Conclusion: The application of negative binomial-Lindley distribution is carried out on two samples of insurance data. Based on the results, it is shown that the negative binomial-Lindley provides a better fit compared to the Poisson and the negative binomial for count data where the probability at zero has a large value.

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“…The first two moments about zero and the factorial moment of order k of a negative binomial distribution are given respectively by Gómez et al (2008):…”

Section: Methodsmentioning

confidence: 99%

“…Gómez et al (2008) showed that the factorial moment of order k of a mixed negative binomial distribution where p = exp(-λ) can be obtained by using:…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Negative Binomial-Lindley Distribution and Its Application

Zamani

Ismail²

2010

Journal of Mathematics and Statistics

105

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“…The first two data sets, shown in Tables 2 and 3, are taken from Willmot (1987) and they concern the number of automobile insurance claims per policy in two portfolios from Great Britain and Zaire, respectively. These data present overdispersion, i.e., the Table 4 Distribution of a number of claims of automobile liability policies (Gómez-Déniz et al, 2008;Klugman et al, 1998 variance is greater than the mean, and they are heavily skewed. Furthermore, in these sets there is a high proportion of zero values (the observed value has a zero vertex).…”

Section: Applications With Real Datamentioning

confidence: 99%

A new discrete distribution with actuarial applications

Gómez–Déniz

Sarabia

Calderín–Ojeda

2011

Insurance: Mathematics and Economics

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“…Examples of mixed Poisson and mixed negative binomial distributions are Negative Binomial (NB) obtained as a mixture of Poisson and gamma, Poisson-Lindley (PL) (Sankaran, 1970;Ghitany et al, 2008), Poisson-Inverse Gaussian (PIG) (Trembley, 1992;Willmot, 1987), Negative BinomialPareto (NBP) (Meng et al, 1999), Negative BinomialInverse Gaussian (NBIG) (Gomez-Deniz et al, 2008), negative binomial-Lindley (NBL) (Zamani and Ismail, 2010;Lord and Geedipally, 2011) and Poisson-Weighted Exponential (PWE) (Zamani et al, 2014a) distributions.…”

Section: Introductionmentioning

confidence: 99%

Bivariate Poisson-Lindley Distribution with Application

Zamani¹,

Faroughi

Ismail³

2015

Journal of Mathematics and Statistics

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This study applies a Bivariate Poisson-Lindley (BPL) distribution for modeling dependent and over-dispersed count data. The advantage of using this form of BPL distribution is that the correlation coefficient can be positive, zero or negative, depending on the multiplicative factor parameter. Several properties such as mean, variance and correlation coefficient of the BPL distribution are discussed. A numerical example is given and the BPL distribution is compared to Bivariate Poisson (BP) and Bivariate Negative Binomial (BNB) distributions which also allow the correlation coefficient to be positive, zero or negative. The results show that BPL distribution provides the smallest Akaike Information Criterion (AIC), indicating that the distribution can be used as an alternative for fitting dependent and over-dispersed count data, with either negative or positive correlation.

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Univariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applications

Cited by 33 publications

References 13 publications

Negative Binomial-Lindley Distribution and Its Application

Negative Binomial-Lindley Distribution and Its Application

A new discrete distribution with actuarial applications

Bivariate Poisson-Lindley Distribution with Application

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