A review of the <i>CTP</i> distribution: a comparison with other over- and underdispersed count data models

Olmo-Jiménez, María José; Avi, José Rodríguez; Cueva-López, Valentina

doi:10.1080/00949655.2018.1482897

Cited by 5 publications

(9 citation statements)

References 13 publications

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“…In general, we can observe that in an overdispersed scenario the most distant models from the EBW distribution are the CBP and HP distributions and the closest ones to the EBW distribution are the GP and NB distributions. On the other hand, in an underdispersed scenario the HP distribution, which is very similar to the CMP distribution, is the closest one [21]. Nevertheless, these distances in relation to the EBW distribution are really small, which implies that the performance of these distributions is very similar.…”

Section: Comparison With Other Count Data Distributionsmentioning

confidence: 86%

“…Proof. The proof is straightforward since the pmf of the CTP(α, 0, γ) with α ∈ R and γ > 0, see for instance [21], coincides with the pmf of the EBW(α, γ) given in Equation ( 3). This result is also true when α > 0.…”

Section: α >mentioning

confidence: 88%

“…In the aforementioned paper, a detailed study of the GHD when α, β and γ are positive real numbers and 0 < λ ≤ 1 (denoted by type I) is made. The case when α and β are conjugate complex numbers, γ > 0 and 0 < λ ≤ 1 (denoted by type II distributions) has been studied in [18,19,21]. Type VII distributions, a finite case which may be seen as a generalization of the beta-binomial model, have been addressed by [22].…”

Section: Definitionmentioning

confidence: 99%

“…We have also carried out the Kolmogorov-Smirnov test for discontinuous distributions [28] using the ks.test function of the dgof package in R, but in all the cases the p-values are greater than 0.1. It can be seen as a particular case of a CTP distribution [18,21], which arises when the polynomial L(x) in Equation ( 1) has conjugate complex roots α = a + ib and β = a − ib; specifically, we have the following result.…”

Section: α >mentioning

confidence: 99%

“…We focus on the overdispersed scenario since the underdispersed one, for being the EBW distribution a particular case of the CTP distribution, was already carried out by [21].…”

Section: Comparison With Other Count Data Distributionsmentioning

confidence: 99%

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An Over and Underdispersed Biparametric Extension of the Waring Distribution

Cueva-López¹,

Olmo-Jiménez²,

Avi³

2021

Mathematics

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A new discrete distribution for count data called extended biparametric Waring (EBW) distribution is developed. Its name is related to the fact that, in a specific configuration of its parameters, it can be seen as a biparametric version of the univariate generalized Waring (UGW) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the UGW distribution, the EBW can model both overdispersed and underdispersed data sets. In fact, the EBW distribution is a particular case of a UWG distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson (CTP) distribution. Hence, this new model inherits most of their properties and, moreover, it helps to solve the identification problem in the variance components of the UGW model. We compare the EBW with the UGW by a simulation study, but also with other over and underdispersed distributions through the Kullback-Leibler divergence. Additionally, we have carried out a simulation study in order to analyse the properties of the maximum likelihood parameter estimates. Finally, some application examples are included which show that the proposed model provides similar or even better results than other models, but with fewer parameters.

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Section: Comparison With Other Count Data Distributionsmentioning

confidence: 86%

Section: α >mentioning

confidence: 88%

Section: Definitionmentioning

confidence: 99%

Section: α >mentioning

confidence: 99%

“…We focus on the overdispersed scenario since the underdispersed one, for being the EBW distribution a particular case of the CTP distribution, was already carried out by [21].…”

Section: Comparison With Other Count Data Distributionsmentioning

confidence: 99%

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An Over and Underdispersed Biparametric Extension of the Waring Distribution

Cueva-López¹,

Olmo-Jiménez²,

Avi³

2021

Mathematics

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EM algorithm for an extension of the Waring distribution

Cueva-López

Olmo-Jiménez

Avi

2019

Comp and Math Methods

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The extended biparametric Waring (EBW) distribution is a useful model for overdispersed and underdispersed count data. When its first parameter α is positive, the EBW is a particular case of the univariate generalized Waring distribution, so it inherits its main properties, in particular, its expression as a Poisson mixture and hence the decomposition of the variance as a combination of three components (randomness, liability, and proneness), which make it of great interest. In this paper, we take advantage of the first property to obtain the maximum likelihood (ML) estimates of the EBW parameters by the expectation‐maximization algorithm. This algorithm, for mixed distributions, reduces the problem of ML estimation to one of ML estimations of the mixing distribution, which is usually easier.

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Socio-environmental predictors of diabetes incidence disparities in Tanzania mainland: a comparison of regression models for count data

Mbwambo,

Mbago,

Rao

2024

BMC Med Res Methodol

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Background Diabetes is one of the top four non-communicable diseases that cause death and illness to many people around the world. This study aims to use an efficient count data model to estimate socio-environmental factors associated with diabetes incidences in Tanzania mainland, addressing lack of evidence on the efficient count data model for estimating factors associated with disease incidences disparities. Methods This study analyzed diabetes counts in 184 Tanzania mainland councils collected in 2020. The study applied generalized Poisson, negative binomial, and Poisson count data models and evaluated their adequacy using information criteria and Pearson chi-square values. Results The data were over-dispersed, as evidenced by the mean and variance values and the positively skewed histograms. The results revealed uneven distribution of diabetes incidence across geographical locations, with northern and urban councils having more cases. Factors like population, GDP, and hospital numbers were associated with diabetes counts. The GP model performed better than NB and Poisson models. Conclusion The occurrence of diabetes can be attributed to geographical locations. To address this public health issue, environmental interventions can be implemented. Additionally, the generalized Poisson model is an effective tool for analyzing health information system count data across different population subgroups.

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A review of the CTP distribution: a comparison with other over- and underdispersed count data models

Cited by 5 publications

References 13 publications

An Over and Underdispersed Biparametric Extension of the Waring Distribution

An Over and Underdispersed Biparametric Extension of the Waring Distribution

EM algorithm for an extension of the Waring distribution

Socio-environmental predictors of diabetes incidence disparities in Tanzania mainland: a comparison of regression models for count data

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