On Some Properties of Quasi-Negative-Binomial Distribution and Its Applications

Hassan, Anwar; Bilal, Sheikh

doi:10.22237/jmasm/1225513500

Cited by 5 publications

(7 citation statements)

References 6 publications

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“…Formally, negative binomial is the count of the number of trials in a series of independent and identically distributed binary trials until a specified number of successes (or failures) occurs, and the Poisson is the count of times an event occurs in a period of time. Both distributions assume each event is independent; however, because people change their behaviour based on recent experiences, this may not always be true (Hassan & Bilal, 2008 ). For example, a person’s preference for choosing to exercise might change based on recent experience.…”

Section: Count Distributionsmentioning

confidence: 99%

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Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Green

2021

Health Psychology and Behavioral Medicine

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Background: Dependent variables in health psychology are often counts, for example, of a behaviour or number of engagements with an intervention. These counts can be very strongly skewed, and/or contain large numbers of zeros as well as extreme outliers. For example, ‘How many cigarettes do you smoke on an average day?’ The modal answer may be zero but may range from 0 to 40+. The same can be true for minutes of moderate-to-vigorous physical activity. For some people, this may be near zero, but take on extreme values for someone training for a marathon. Typical analytical strategies for this data involve explicit (or implied) transformations (smoker v. non-smoker, log transformations). However, these data types are ‘counts’ (i.e. non-negative whole numbers) or quasi-counts (time is ratio but discrete minutes of activity could be analysed as a count), and can be modelled using count distributions – including the Poisson and negative binomial distribution (and their zero-inflated and hurdle extensions, which alloweven more zeros). Methods: In this tutorial paper I demonstrate (in R, Jamovi, and SPSS) the easy application of these models to health psychology data, and their advantages over alternative ways of analysing this type of data using two datasets – one highly dispersed dependent variable (number of views on YouTube, and another with a large number of zeros (number of days on which symptoms were reported over a month). Results: The negative binomial distribution had the best fit for the overdispersed number of views on YouTube. Negative binomial, and zero-inflated negative binomial were both good fits for the symptom data with over-abundant zeros. Conclusions: In both cases, count distributions provided not just a better fit but would lead to different conclusions compared to the poorly fitting traditional regression/linear models.

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Section: Count Distributionsmentioning

confidence: 99%

“…This is a pity, as the distribution has the type of properties we would be interested in. Specifically, where there are not an oversupply of zeros it can often produce a good fit for more highly skewed data as it has a ‘fat tail’ – more extreme high values 3 (Hassan & Bilal, 2008 ; Li, Yang, Famoye, Lee, & Black, 2011 ).…”

Section: Count Distributionsmentioning

confidence: 99%

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Green

2021

Health Psychology and Behavioral Medicine

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“…The quasi-negative binomial distribution Janardan (1975); Sen & Jain (1996) and very recently by Li et al (2011) has the probability mass function Hassan & Bilal (2008) of the form:…”

Section: The Quasi-negative Binomial-qnbdmentioning

confidence: 99%

“…That is, we have observations designated in k+ categories. We give example below, which is adapted from Hassan & Bilal (2008) and relates to the number of absenteeism among shift workers in steel industry as reported in Arbous & Sichel (1954). The category 25+ actually stands for counts in categories (25-48) and are combined in that category with a frequency count of 16.…”

Section: The Extended Com-poisson (Ecomp) Distributionmentioning

confidence: 99%

Correcting for Non-Sum to 1 Estimated Probabilities in Applications of Discrete Probability Models to Count Data

Lawal¹

2017

IJSP

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In this paper, we examine some often ignored or assumed problems relating with fitting probability models to count data either exhibiting over, equi, or under dispersion. Of particular concern are last category truncated data, where most often, expected values in this last category are collapsed together so that the sum of the expected values sum to the sample size in the data. That is, so that k ∑ i=0m i = n, the sample size. We shall for illustrative purposes in this paper, consider the following distributions: the negative binomial (NB), the Inverse trinomial (IT), the hyper-Poisson (HP), the Quasinegative binomial (QNBD), the extended com-Poisson distribution (ECOMP) as well as the negative binomial-exponential distribution (NBGE).Though, we have restricted our discussion to these six distributions, other distributions may also be employed but the patterns are always the same, that is, the sum of the estimated probabilities does not equal 1.00 and consequently, the sum of the expected values is always less or equal (Poisson case only) the sample size in the observed data. We propose a common procedure to rectify this problem for both right truncated or non-truncated frequency count data exhibiting either excess zeros or regular frequency data.

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“…He also explored its properties with an application to the fluctuations of sample function of stochastic process. Nandi and Das (1994) also obtained a class of Abel series distributions Hassan and Bilal (2008). showed that the QNBD model belongs to a family of Abel series distributions by taking the Abel series expansion of…”

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confidence: 99%

On Some Negative Integer Moments of Quasi-Negative-Binomial Distribution

Hassan

Bilal²

2012

J. Mod. App. Stat. Meth.

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Negative integer moments of the quasi-negative-binomial distribution (QNBD) are investigated. This distribution includes recurrence relations which are helpful in the solution of many applied statistical problems, particularly in life testing and survey sampling, where ratio estimators are useful. Results study show the negative-binomial distribution when the parameter 2 θ is zero and also indicate the mean of the QNBD model when its parameters are changed.

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On Some Properties of Quasi-Negative-Binomial Distribution and Its Applications

Cited by 5 publications

References 6 publications

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Correcting for Non-Sum to 1 Estimated Probabilities in Applications of Discrete Probability Models to Count Data

On Some Negative Integer Moments of Quasi-Negative-Binomial Distribution

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