The negative binomial-generalized exponential (NB-GE) distribution

Aryuyuen, Sirinapa; Bodhisuwan, Winai

doi:10.12988/ams.2013.13099

Cited by 21 publications

(21 citation statements)

References 13 publications

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“…The first data set is the number of automobile liability policies in Switzerland for private cars taken originally from [9] and recently analyzed in [2]. The data is presented in Table I with Y representing the number of accidents and n i the corresponding observed frequencies.…”

Section: Data Set Imentioning

confidence: 99%

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On the negative binomial-generalized exponential distribution and its applications

Lawal¹

2017

ams

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In this paper, we fit the negative binomial-generalized exponential (NB-GE) distribution to data exhibiting excess zeros. Thus we employed the NB-GE and its zero-inflated derivative to three sets of frequency data that have been employed in standard literature on the subject. Our results are compared with both the Poisson, negative binomial and corresponding zero-inflated distributions (ZIP and ZINB). All analyses were carried out using PROC NLMIXED in SAS. Parameter estimates, as well as the expected frequencies under each model and the corresponding goodness-of-fit statistics are computed. Our results extend previous results on the analyzes of the chosen data in this example. Further, results obtained here indicate that some results in earlier studies on some of the example data sets employed in this study may be inaccurate. In others however, our results are consistent with previous analyses on the data sets chosen for this article. While we do not pretend that the results obtained are entirely new, however, the analyses give opportunities to researchers in the field the much needed means of implementing these models in SAS without having to resort to R or Stata. We must also recognize that because the probability mass function of the NB-GE has an infinite value range, estimated probabilities may therefore not necessarily add up to 1.00 over the finite range of values of our discrete random variable and consequently, the sum of estimated expected values may not add up to the observed sample size n.

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Section: Data Set Imentioning

confidence: 99%

“…In such cases, mixed NB or Poisson models have been suggested- [7]; [21] and [18]. Recently, however, the negative binomial-generalized exponential (NB-GE) model has been suggested for heavily tailed count data (see [2] and [20] amongst several others). We present in the next section, a brief introduction to these models.…”

Section: Introductionmentioning

confidence: 99%

On the negative binomial-generalized exponential distribution and its applications

Lawal¹

2017

ams

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“…In the Zero-Inflated Poisson (ZIP) distribution which usually handles the problem of overdispersion with excess zeros, the number of zeros that can be overcome with the ZIP distribution is only about 50-80% zeros in the data [4]. Therefore, another alternative distribution is needed to overcome the problem of overdispersion with extreme excess zeros, because rare cases sometimes have zeros of more than 80% in the data.In 2013, Sirinapa Aryuyuen and Winai Bodhisuwan introduced a new distribution, namely the Negative Binomial-Generalized Exponential (NB-GE) distribution which a mixture distribution from Negative Binomial (NB) distribution and Generalized Exponential (GE) distribution, aims to deal with the problem of overdispersion caused by extreme excess zeros (more than 80% zeros) [5].…”

Section: Introductionmentioning

confidence: 99%

A New Mixture Distribution for Extreme Excess Zeros: Negative Binomial-Generalized Exponential (NB-GE) Distribution

Prameswari¹,

Fithriani²,

Nurrohmah³

2020

Proceedings of the Proceedings of the 1st International Conference on Statistics and Analytics, ICSA 2019, 2-3 August 2019, Bog

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Negative Binomial-Generalized Exponential (NB-GE) distribution is a distribution that capable for modeling overdispersion data with extreme excess zeros, which is more than 80% zeros in a data. The distribution is a mixture distribution that obtained by mixing the Negative Binomial (NB) distribution with the Generalized Exponential (GE) distribution. The formation of the Negative Binomial-Generalized Exponential (NB-GE) distribution and the characteristics of the Negative Binomial-Generalized Exponential (NB-GE) distribution such as the probability density function, kth moment, mean, variance, skewness and kurtosis are discussed in this paper. Estimation of the parameters from the Negative Binomial-Generalized Exponential (NB-GE) distribution using the maximum likelihood method. As an illustration, Negative Binomial-Generalized Exponential (NB-GE) distribution used to model the data of fatal crash that has more than 80% zeros.

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“…The negative binomial distribution is obtained as a mixture of Poisson and gamma distribution (Pudprommarat et al, 2012), this paper also introduced a new mixture distribution by mixing negative binomial whose probability of success parameter p = e −λ and Λ follows exponential distribution. Mixture distribution in various research has been developed by several researchers in term of univariate and multivariate analysis of mixture distribution negative binomial-invers Gaussian (Gomez-Deniz et al, 2008), application of negative binomialbeta distribution (Pudprommarat et al, 2012), mixture negative binomial-general exponential (Aryuyuen and Bodhisuwan, 2013), negative binomial-Crack distribution (Saengthong and Bodhisuwan, 2013), the negative binomial-Erlang distribution with applications (Kongrod et al, 2014), exponential-beta distributions (Nadarajah and Kotz, 2006), negative binomial-Lindley distribution (Zamani and Ismail, 2010) and application negative binomial-Lindley distribution (Shirazi et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

The Characteristic Function Property of Mixture Negative Binomial-Exponential Distribution

Devianto

Sarah²,

Kumala³

et al. 2018

sci. technol. indones.

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This paper introduces a new distribution by mixing the negative binomial distribution and exponential distribution namely negative binomial-exponential (NB-E) distribution. In is given the probability distribution function of NB-E distribution and its characteristic function by using Fourier-Stieltjes transform. In addition we present the some properties of characteristic function from NB-E distribution.

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The negative binomial-generalized exponential (NB-GE) distribution

Cited by 21 publications

References 13 publications

On the negative binomial-generalized exponential distribution and its applications

On the negative binomial-generalized exponential distribution and its applications

A New Mixture Distribution for Extreme Excess Zeros: Negative Binomial-Generalized Exponential (NB-GE) Distribution

The Characteristic Function Property of Mixture Negative Binomial-Exponential Distribution

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