On the negative binomial-generalized exponential distribution and its applications (original) (raw)
Related papers
Zero inflated negative binomial-generalized exponential distributionand its applications
Songklanakarin Journal of Science and Technology, 2014
In this paper, we propose a new zero inflated distribution, namely, the zero inflated negative binomial-generalized exponential (ZINB-GE) distribution. The new distribution is used for count data with extra zeros and is an alternative for data analysis with over-dispersed count data. Some characteristics of the distribution are given, such as mean, variance, skewness, and kurtosis. Parameter estimation of the ZINB-GE distribution uses maximum likelihood estimation (MLE) method. Simulated and observed data are employed to examine this distribution. The results show that the MLE method seems to have highefficiency for large sample sizes. Moreover, the mean square error of parameter estimation is increased when the zero proportion is higher. For the real data sets, this new zero inflated distribution provides a better fit than the zero inflated Poisson and zero inflated negative binomial distributions.
Communications in Statistics - Theory and Methods, 2020
Count data often exhibits the property of dispersion and have large number of zeros. In order to take these properties into account, a new generalized negative binomial-Lindley distribution with four parameters is proposed, of which the two-parameter and three-parameter negative binomial-Lindley distributions are special cases. Several statistical properties of the proposed distribution are presented. The dispersion index for the proposed distribution is derived and based on the index, it is clear that the proposed distribution can adequately fit the data with properties of overdispersion or underdispersion depending on the choice of the parameters. The proposed distribution is fitted to three overdispersed datasets with large proportion of zeros. The best fitted model is selected based on the values of AIC, mean absolute error and root mean squared error. From the model fittings, it can be concluded that the proposed distribution outperforms Poisson and negative binomial distributions in fitting the count data with overdispersion and large number of zeros.
ON THE ZERO AND k-INFLATED NEGATIVE BINOMIAL DISTRIBUTION WITH APPLICATIONS
Advances and Applications in Statistics
In the literature, there are a significant number of studies on mixtures and compound probability distributions used for count data with inflated frequencies. This study extended some existing zero-inflated distributions, by considering the flexibility of peaks in the data with excessive counts other than zeros and handled an overdispersion in the data. Moreover, this study formulated a proposed zero-and k-inflated
A generalized negative binomial distribution based on an extended Poisson process
Brazilian Journal of Probability and Statistics, 2010
In this article we propose a generalized negative binomial distribution, which is constructed based on an extended Poisson process (a generalization of the homogeneous Poisson process). This distribution is intended to model discrete data with presence of zero-inflation and over-dispersion. For a dataset on animal abundance which presents over-dispersion and a high frequency of zeros, a comparison between our extended distribution and other common distributions used for modeling this kind of data is addressed, supporting the fitting of the proposed model.
The zero inflated negative binomial – Crack distribution : some properties and parameter estimation
2015
The zero inflated negative binomial-Crack (ZINB-CR) distribution is a mixture of Bernoulli distribution and negative binomial-Crack (NB-CR) distribution, which is an alternative distribution for the excessive zero counts and overdispersion. In this paper, some properties of the ZINB-CR distribution are discussed. Statistical inference of the parameters is derived by maximum likelihood estimation (MLE) and the method of moments (MM). Monte Carlo Simulations are used to evaluate the performance of parameter estimation methods in term of mean squared error (MSE). An application of the distribution is carried out on a sample of excess zero-count data. Simulation results show that the MLE method outperforms the MM method in specific parameter values. Furthermore, the ZINB-CR provides a better fit compared to the zero inflated Poisson (ZIP), the zero inflated negative binomial (ZINB) and the negative binomial-Crack (NB-CR) distributions.
Zero inflated negative binomial-Sushila distribution and its application
AIP Conference Proceedings, 2017
In statistics literature, there is significant study of mixtures and compound probability distributions used for count model especially for the data contains excess zeros. In this paper, we introduce a new probability distribution which is obtained as a compound of zero-inflated negative binomial (ZINB) distribution and Sushila distribution and it is named as zero-inflated negative binomial-Sushila (ZINB-S) distribution. It can be used as an alternative and effective way of modeling over dispersed count data. The probability mass function (PMF) and some vital characteristics of ZINB-S distribution are derived. MLE method is employed for estimating the model parameters. Further the example is given to show that ZINB-S provides better fit compare to traditional models for over dispersed count data.
Pakistan Journal of Statistics and Operation Research
In this paper, a new mixture distribution for count data, namely the negative binomial-new generalized Lindley (NB-NGL) distribution is proposed. The NB-NGL distribution has four parameters, and is a flexible alternative for analyzing count data, especially when there is over-dispersion in the data. The proposed distribution has sub-models such as the negative binomial-Lindley (NB-L), negative binomial-gamma (NB-G), and negative binomial-exponential (NB-E) distributions as the special cases. Some properties of the proposed distribution are derived, i.e., the moments and order statistics density function. The unknown parameters of the NB-NGL distribution are estimated by using the maximum likelihood estimation. The results of the simulation study show that the maximum likelihood estimators give the parameter estimates close to the parameter when the sample is large. Application of NB-NGL distribution is carry out on three samples of medical data, industry data, and insurance data. Ba...
Poisson and negative binomial regression models for zero-inflated data: an experimental study
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Count data regression has been widely used in various disciplines, particularly health area. Classical models like Poisson and negative binomial regression may not provide reasonable performance in the presence of excessive zeros and overdispersion problems. Zero-inflated and Hurdle variants of these models can be a remedy for dealing with these problems. As well as zero-inflated and Hurdle models, alternatives based on some biased estimators like ridge and Liu may improve the performance against to multicollinearity problem except excessive zeros and overdispersion. In this study, ten different regression models including classical Poisson and negative binomial regression with their variants based on zero-inflated, Hurdle, ridge and Liu approaches have been compared by using a health data. Some criteria including Akaike information criterion, log-likelihood value, mean squared error and mean absolute error have been used to investigate the performance of models. The results show th...
IOP Conference Series: Materials Science and Engineering
Poisson regression analysis shows the relationship between predictor variables and response variables that follow the Poisson distribution which has equal dispersion and average values (λ), a situation called equidispersion. However, the variance can also be greater than the average value, called overdispersion. This can be caused by excess opportunities for the emergence of zero values in the response variable or zero excess. The parameter of the overdispersed data analysis can be underestimated so that the results become biased. This bias issue can be, hopefully, overcome by the Zero Inflated Negative Binomial (ZINB) regression analysis. In the 2016 Maternal Mortality Rate data in Bojonegoro District, overdipersion was overcome by ZINB regression even though there was no significant predictor variable found affecting the response variable. ZINB regression analysis can also be applied to generated data (simulation). We had the data with average λ = (0.2, 0.4, 0.6, 0.8, 1.0, 5.0) proportion of zeros p = (0.4, 0.6, 0.8), and the number of observations n = (200,500, 800), with each setting was repeated 100 times. From the simulation study it was found that all overdispersion events were always accompanied by zero excess events but not vice versa. The greater the value of λ then the greater the dispersion coefficient. The ZINB regression is proven to be able to overcome overdispersion in various conditions of different values of λ, p, n which can be seen from the value τ (dispersion coefficient) after ZINB regression is less than 1 in all conditions.
Quasi-negative binomial distribution: Properties and applications
Computational Statistics & Data Analysis, 2011
In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting distribution of QNBD is the generalized Poisson distribution under certain conditions. A zero-inflated QNBD is also defined. Applications of QNBD and zero-inflated QNBD in various fields are presented and compared with some other existing distributions including Poisson, generalized Poisson and negative binomial distributions as well as their zero-inflated versions. In general, the QNBD or its zero-inflated version performs better than the other models based on the chi-square statistic and the Akaike Information Criterion, especially for the cases where the data are highly skewed, have heavy tails or excessive numbers of zeros.